1 #LyX 2.0 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
20 % set fonts for nicer pdf view
21 \IfFileExists{lmodern.sty}
22 {\usepackage{lmodern}}{}
24 \fi % end if pdflatex is used
26 % Folgendes Problem lösen:
27 % Besteht die Kapitelnummer aus zu vielen Ziffern, wird die
28 % Kapitelüberschrift im Inhaltsverzeichnis direkt an oder über
29 % die Kapitelnummer geschrieben.
30 % Als Lösung wird mehr Platz zwischen Nummer und
31 % Überschrift eingefügt.
32 \renewcommand{\l@subsection}{\@dottedtocline{2}{1.5em}{2.8em}}
33 \renewcommand{\l@subsubsection}{\@dottedtocline{3}{4.3em}{3.6em}}
35 % To be able to enter the character ° and · directly in LyX,
37 \DeclareInputText{176}{\ifmmode^\circ\else\textdegree\fi}
38 \DeclareInputText{183}{\ifmmode\cdot\else\textperiodcentered\fi}
40 % increase link area for cross-references and autoname them,
41 \AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}}
42 \addto\extrasenglish{%
43 \renewcommand*{\equationautorefname}[1]{}
44 \renewcommand{\sectionautorefname}{sec.\negthinspace}
45 \renewcommand{\subsectionautorefname}{sec.\negthinspace}
46 \renewcommand{\subsubsectionautorefname}{sec.\negthinspace}
49 % don't load packages twice
50 % see first footnote in sec. 9.3
51 \@ifundefined{textcolor}{\usepackage{color}}{}
53 % the pages of the TOC are numbered roman
54 % and a PDF-bookmark for the TOC is added
56 \let\myTOC\tableofcontents
57 \renewcommand{\tableofcontents}{%
59 \pdfbookmark[1]{\contentsname}{}
62 \pagenumbering{arabic}}
64 % insert additional vertical space of 1.5 mm between footnotes,
66 \renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
68 % provides caption formatting
69 \setkomafont{captionlabel}{\bfseries}
72 \usepackage[samesize]{cancel}
74 % enables calculation of values
77 % for multiple columns used in sec. 24.7
83 % for the Fourier transformation symbol
86 % define a color, used in sec.9.3
87 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
89 % declare operators (see sec. 10.4 and sec. 15.2)
90 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
91 \DeclareMathOperator{\sgn}{sgn}
93 \newcommand{\spce}{\textvisiblespace}
95 % example definitions for sec. 20.1
96 \newcommand{\gr}{\Longrightarrow}
97 \newcommand{\us}[1]{\underline{#1}}
98 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
99 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
100 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
102 % example macro from sec. 19.4
103 %\def\tagform@#1{\maketag@@@{|#1|}}
105 % macro from sec. 10.2
106 \def\clap#1{\hbox to 0pt{\hss #1\hss}}
107 \def\mathclap {\mathpalette \mathclapinternal}
108 \def\mathclapinternal #1#2{\clap{$\mathsurround =0pt #1{#2}$}}
111 % ------------------------------------
112 % used to check for needed LaTeX packages
115 % check for package eurosym
116 % used for the Euro symbol
118 \IfFileExists{eurosym.sty}
119 {\usepackage[gennarrow]{eurosym}
120 \setboolean{eurosym}{true}}
121 {\setboolean{eurosym}{false}}
123 % check for package braket
124 % used for physical vectors
126 \IfFileExists{braket.sty}
128 \setboolean{braket}{true}}
129 {\setboolean{braket}{false}}
131 % check for package cancel
133 \IfFileExists{cancel.sty}
135 \setboolean{cancel}{true}}
136 {\setboolean{cancel}{false}}
138 % check for package upgreek
140 \IfFileExists{upgreek.sty}
141 {\usepackage{upgreek}
142 \setboolean{upgreek}{true}}
143 {\setboolean{upgreek}{false}}
145 \options bibliography=totoc,index=totoc,BCOR7.5mm,titlepage,captions=tableheading
146 \use_default_options false
147 \maintain_unincluded_children false
149 \language_package default
154 \font_typewriter default
155 \font_default_family default
156 \use_non_tex_fonts false
163 \default_output_format default
165 \bibtex_command default
166 \index_command default
170 \pdf_title "LyX's Math Manual"
171 \pdf_author "LyX Team, Uwe Stöhr"
172 \pdf_subject "LyX-documentation about math"
173 \pdf_keywords "LyX, Mathed"
175 \pdf_bookmarksnumbered true
176 \pdf_bookmarksopen true
177 \pdf_bookmarksopenlevel 1
178 \pdf_breaklinks false
182 \pdf_pdfusetitle false
183 \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false"
193 \paperorientation portrait
196 \notefontcolor #0000ff
203 \paragraph_separation skip
205 \quotes_language english
208 \paperpagestyle plain
212 \tracking_changes true
213 \output_changes false
216 \html_be_strict false
217 \author -1853239151 "scott"
223 LyX's detailed Math manual
231 \begin_layout Plain Layout
233 If you have comments or error corrections, please send them to the LyX Documenta
237 \begin_inset CommandInset href
239 name "lyx-docs@lists.lyx.org"
240 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
251 \begin_inset Note Note
254 \begin_layout Plain Layout
261 \begin_inset Newline newline
265 \begin_inset Newline newline
273 \begin_layout Standard
274 \begin_inset CommandInset toc
275 LatexCommand tableofcontents
282 \begin_layout Standard
283 \begin_inset Note Note
286 \begin_layout Plain Layout
287 To export this document to PDF, PS or DVI the LaTeX-packages
289 braket, cancel, eurosym, mathdots, mhchem
296 If they are not installed the document can be exported anyway but the sections
297 where the packages are required will not appear in the output.
302 ; if it is not installed, this file cannot be exported.
305 \begin_layout Plain Layout
306 The latest PDF-version of this document can be found here:
307 \begin_inset Newline newline
312 http://wiki.lyx.org/LyX/DocumentationDevelopment#Math
320 \begin_layout Standard
321 \begin_inset Newpage newpage
327 \begin_layout Section
331 \begin_layout Standard
332 This document explains LyX's math features and is furthermore a collection
333 of LaTeX-commands used for mathematical characters and constructs.
334 The explanations are designed for the usage of commands.
335 It is therefore required that you have read the section
346 \begin_layout Standard
347 Most of the characters and many constructs explained in this manual are
348 also accessible via the menu
352 \SpecialChar \menuseparator
368 But everybody who has to write lots of formulas will notice that it is
369 much faster to use commands instead of the math toolbar.
370 Therefore this manual is focused on commands but also mentions the correspondin
371 g toolbar buttons when available.
374 \begin_layout Standard
375 If not specially mentioned the commands are only available within formulas.
376 To be able to use all commands explained in this document, the option
380 must be checked in the document settings (menu
382 Document\SpecialChar \menuseparator
383 Settings\SpecialChar \menuseparator
394 \begin_layout Plain Layout
397 Use AMS math package automatically
403 \begin_layout Plain Layout
412 -math when math constructs are found that are supported by LyX.
420 \begin_layout Standard
421 This document doesn't list all
425 \begin_layout Plain Layout
438 \begin_layout Plain Layout
443 \begin_layout Plain Layout
452 -math commands is in the file
455 \begin_inset CommandInset href
458 target "ftp://ctan.tug.org/tex-archive/macros/amstex/doc/amsguide.ps"
464 , which is part of every LaTeX standard installation.
469 for lucidity reasons.
472 \begin_layout Section
476 \begin_layout Standard
477 To create an inline formula
478 \begin_inset Index idx
481 \begin_layout Plain Layout
487 that is embedded into a text line, use one of the shortcuts
493 or the toolbar button
494 \begin_inset Graphics
495 filename ../images/math-mode.png
501 \begin_inset Newline newline
504 To create a display style formula
505 \begin_inset Index idx
508 \begin_layout Plain Layout
509 Formula ! display style
514 which will appear bigger, has a different format, and will be in a separate
515 paragraph, use one of these shortcuts:
524 \begin_layout Standard
525 To change a display style formula to an inline formula, set the cursor into
526 the formula and use one of the shortcuts
534 Edit\SpecialChar \menuseparator
535 Math\SpecialChar \menuseparator
539 The same way is used to change an inline formula to a display style formula.
542 \begin_layout Standard
543 To display parts of an inline formula in the size of a display style formula,
551 \begin_inset Index idx
554 \begin_layout Plain Layout
563 Then a new blue box appears in which the desired formula part is inserted.
566 \begin_layout Standard
567 Only inline formulas are allowed inside tables.
570 \begin_layout Standard
575 can be turned on in the menu
577 View\SpecialChar \menuseparator
581 When you click there on
582 \begin_inset Quotes eld
586 \begin_inset Quotes erd
589 the toolbar will be shown permanently at the bottom; this state is visualized
594 menu with a checkmark.
595 When you click in this state again on
596 \begin_inset Quotes eld
600 \begin_inset Quotes erd
611 is only shown when the cursor is within a formula; this state is visualized
612 by the renaming of the menu entry from
613 \begin_inset Quotes eld
617 \begin_inset Quotes erd
621 \begin_inset Quotes eld
629 \begin_inset Quotes erd
635 \begin_layout Standard
637 \begin_inset Index idx
640 \begin_layout Plain Layout
646 is invoked by pressing the toolbar button
647 \begin_inset Graphics
648 filename ../images/ert-insert.png
655 Insert\SpecialChar \menuseparator
660 \begin_layout Plain Layout
676 \begin_inset Note Note
679 \begin_layout Plain Layout
680 In LyX there are three
681 \begin_inset Quotes eld
685 \begin_inset Quotes erd
688 that appear in the output with sub- and superscript letters: TeX, LaTeX
692 \begin_layout Plain Layout
693 To avoid that these names are recognized as proper names, a TeX-brace pair
702 \begin_layout Standard
703 To change the LaTeX-preamble
704 \begin_inset Index idx
707 \begin_layout Plain Layout
715 Document\SpecialChar \menuseparator
716 Settings\SpecialChar \menuseparator
721 \begin_layout Plain Layout
737 \begin_layout Standard
738 To edit matrices, case differentiations and multiline formulas subsequently,
741 Edit\SpecialChar \menuseparator
746 Edit\SpecialChar \menuseparator
748 \begin_inset space \thinspace{}
752 \begin_inset space \thinspace{}
762 When lines and columns are swapped via the menu, the column or line where
763 the cursor is in is exchanged with the column to the right or the line
765 Is the cursor in the last column or row, the exchange is done with the
766 column to the left or the line above.
769 \begin_layout Standard
770 To write text in formulas
774 \begin_layout Plain Layout
775 For multiline formulas the command
782 \begin_inset CommandInset ref
784 reference "sub:Text-in-multiline"
798 \begin_inset Index idx
801 \begin_layout Plain Layout
808 \begin_inset Index idx
811 \begin_layout Plain Layout
818 This mode is invoked with the shortcut
824 or by the insertion of the command
831 \begin_inset Index idx
834 \begin_layout Plain Layout
843 The text appears black in LyX and can therefore be distinguished from the
844 other formula parts which appear blue.
845 In the output mathematical text is set upright, in contrary to other formula
849 \begin_layout Subsection*
853 \begin_layout Standard
854 Most of the LaTeX-commands for math constructs have the following scheme:
857 \begin_layout Standard
873 \begin_layout Standard
874 A command always starts with a backslash
875 \begin_inset Quotes gld
885 \begin_inset Quotes grd
889 To omit optional arguments, also omit the associated brackets.
890 The braces around the required arguments are named in this document as
892 \begin_inset Index idx
895 \begin_layout Plain Layout
902 If you add in a formula a left brace to a command name, LyX automatically
904 In all other cases TeX-braces are created in formulas with the command
912 TeX-braces appear red in LyX, in contrary to normal braces which appear
914 In TeX-mode no command is needed to get TeX-braces.
915 TeX-braces don't appear in the output.
918 \begin_layout Standard
919 When commands without arguments, like commands for symbols are entered in
920 TeX-mode, a space character must
924 be behind the command to end it.
925 This space doesn't appear in the output.
926 When the space should appear in the output, the space must be followed
927 by a protected space in normal text.
930 \begin_layout Standard
931 A protected space is inserted with
934 arg "command-alternatives space-insert protected ; math-space"
940 \begin_layout Subsection*
941 \begin_inset Newpage newpage
947 \begin_layout Itemize
952 \begin_layout Plain Layout
953 This visible space character can be created with the command
960 \begin_inset Index idx
963 \begin_layout Plain Layout
971 , inserted in TeX-mode.
980 \begin_layout Plain Layout
993 denotes a space character to be input.
996 \begin_layout Itemize
998 \begin_inset Formula $\to$
1001 denotes the usage of the corresponding arrow key on the keyboard.
1003 \change_inserted -1853239151 1332304617
1008 can often be used to replace
1009 \begin_inset Formula $\to$
1013 \begin_inset Formula $\downarrow$
1021 \begin_inset Formula $\leftarrow$
1025 \begin_inset Formula $\uparrow$
1033 \begin_layout Subsection*
1037 \begin_layout Standard
1039 \begin_inset Float table
1045 \begin_layout Plain Layout
1047 \begin_inset Caption
1049 \begin_layout Plain Layout
1050 \begin_inset CommandInset label
1052 name "tab:Available-units"
1064 \begin_layout Plain Layout
1066 \begin_inset Tabular
1067 <lyxtabular version="3" rows="13" columns="2">
1068 <features tabularvalignment="middle">
1069 <column alignment="center" valignment="top" width="0">
1070 <column alignment="center" valignment="top" width="0">
1072 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1075 \begin_layout Plain Layout
1081 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1084 \begin_layout Plain Layout
1092 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1095 \begin_layout Plain Layout
1101 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1104 \begin_layout Plain Layout
1112 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1115 \begin_layout Plain Layout
1121 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1124 \begin_layout Plain Layout
1132 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1135 \begin_layout Plain Layout
1141 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1144 \begin_layout Plain Layout
1146 \begin_inset space \thinspace{}
1150 \begin_inset space \thinspace{}
1160 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1163 \begin_layout Plain Layout
1169 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1172 \begin_layout Plain Layout
1174 \begin_inset space \thinspace{}
1178 \begin_inset space \thinspace{}
1188 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1191 \begin_layout Plain Layout
1197 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1200 \begin_layout Plain Layout
1202 \begin_inset space \thinspace{}
1206 \begin_inset space \thinspace{}
1216 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1219 \begin_layout Plain Layout
1225 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1228 \begin_layout Plain Layout
1230 \begin_inset space \thinspace{}
1234 \begin_inset space \thinspace{}
1244 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1247 \begin_layout Plain Layout
1253 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1256 \begin_layout Plain Layout
1258 \begin_inset space \thinspace{}
1262 \begin_inset space \thinspace{}
1272 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1275 \begin_layout Plain Layout
1281 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1284 \begin_layout Plain Layout
1286 \begin_inset space \thinspace{}
1290 \begin_inset Formula $\approx$
1294 \begin_inset space \thinspace{}
1304 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1307 \begin_layout Plain Layout
1313 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1316 \begin_layout Plain Layout
1318 \begin_inset space \thinspace{}
1322 \begin_inset space \thinspace{}
1332 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1335 \begin_layout Plain Layout
1341 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1344 \begin_layout Plain Layout
1348 \begin_inset Quotes eld
1354 \begin_inset Quotes erd
1364 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1367 \begin_layout Plain Layout
1373 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1376 \begin_layout Plain Layout
1378 \begin_inset Quotes eld
1386 \begin_inset Quotes erd
1396 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1399 \begin_layout Plain Layout
1405 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1408 \begin_layout Plain Layout
1410 \begin_inset space \thinspace{}
1414 \begin_inset Formula $\nicefrac{1}{18}$
1418 \begin_inset space \thinspace{}
1439 \begin_layout Standard
1440 \begin_inset Newpage newpage
1446 \begin_layout Section
1450 \begin_layout Subsection
1452 \begin_inset Index idx
1455 \begin_layout Plain Layout
1462 \begin_inset Index idx
1465 \begin_layout Plain Layout
1472 \begin_inset Index idx
1475 \begin_layout Plain Layout
1480 \begin_layout Plain Layout
1491 \begin_layout Plain Layout
1504 \begin_inset Index idx
1507 \begin_layout Plain Layout
1512 \begin_layout Plain Layout
1523 \begin_layout Plain Layout
1538 \begin_layout Standard
1539 Indices are created with an underscore
1540 \begin_inset Quotes eld
1544 \begin_inset Quotes erd
1547 or via the math toolbar button
1548 \begin_inset Graphics
1549 filename ../images/math-subscript.png
1554 , exponents with a caret
1555 \begin_inset Quotes eld
1559 \begin_inset Quotes erd
1562 or via the math toolbar button
1563 \begin_inset Graphics
1564 filename ../images/math-superscript.png
1572 \begin_layout Standard
1574 \begin_inset Tabular
1575 <lyxtabular version="3" rows="4" columns="2">
1576 <features tabularvalignment="middle">
1577 <column alignment="center" valignment="top" width="0pt">
1578 <column alignment="center" valignment="top" width="0pt">
1580 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1583 \begin_layout Plain Layout
1589 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1592 \begin_layout Plain Layout
1594 \begin_inset Note Note
1597 \begin_layout Plain Layout
1604 is only used as spacer.
1616 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1619 \begin_layout Plain Layout
1625 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1628 \begin_layout Plain Layout
1629 \begin_inset Formula $B_{V}$
1639 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1642 \begin_layout Plain Layout
1648 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1651 \begin_layout Plain Layout
1652 \begin_inset Formula $\raisebox{5mm}{}B^{V}$
1662 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1665 \begin_layout Plain Layout
1670 \begin_layout Plain Layout
1684 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1687 \begin_layout Plain Layout
1688 \begin_inset Formula $\raisebox{5mm}{}B^{A}$
1704 \begin_layout Standard
1705 As the caret is in some languages an accent, vowels will be accentuated
1706 in this case and not set as exponents
1710 \begin_layout Plain Layout
1711 Depending on the used keyboard settings this can also happen for characters
1718 To get exponents in this case, press
1722 after the caret as in the last example.
1725 \begin_layout Subsection
1727 \begin_inset CommandInset label
1729 name "sub:Fractions"
1734 \begin_inset Index idx
1737 \begin_layout Plain Layout
1746 \begin_layout Standard
1747 Fractions are generated with the command
1754 \begin_inset Index idx
1757 \begin_layout Plain Layout
1765 or via the math toolbar button
1766 \begin_inset Graphics
1767 filename ../images/math/frac.png
1773 The font size is adjusted automatically, depending on whether the fraction
1774 is in an inline or display style formula.
1775 With the math toolbar button
1776 \begin_inset Graphics
1777 filename ../images/math/frac-square.png
1782 you can select different fraction types.
1785 \begin_layout Standard
1793 \begin_inset Index idx
1796 \begin_layout Plain Layout
1804 a fraction can be created that always has the size of a display style formula.
1812 \begin_inset Index idx
1815 \begin_layout Plain Layout
1823 the fraction appears always with the size of an inline formula.
1827 \begin_layout Standard
1828 A line with the fraction
1829 \begin_inset Formula $\frac{1}{2}$
1832 that was created with the command
1841 \begin_layout Standard
1842 A line with the fraction
1843 \begin_inset Formula $\dfrac{1}{2}$
1846 that was created with the command
1855 \begin_layout Standard
1857 \begin_inset Tabular
1858 <lyxtabular version="3" rows="4" columns="2">
1859 <features tabularvalignment="middle">
1860 <column alignment="center" valignment="top" width="0pt">
1861 <column alignment="center" valignment="top" width="0pt">
1863 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1866 \begin_layout Plain Layout
1872 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1875 \begin_layout Plain Layout
1877 \begin_inset Note Note
1880 \begin_layout Plain Layout
1887 is only used as spacer.
1899 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1902 \begin_layout Plain Layout
1909 \begin_layout Plain Layout
1919 \begin_inset Formula $\downarrow$
1927 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1930 \begin_layout Plain Layout
1931 \begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$
1941 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1944 \begin_layout Plain Layout
1951 \begin_layout Plain Layout
1961 \begin_inset Formula $\downarrow$
1969 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1972 \begin_layout Plain Layout
1973 \begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$
1983 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1986 \begin_layout Plain Layout
1993 \begin_layout Plain Layout
2006 \begin_layout Plain Layout
2021 \begin_layout Plain Layout
2031 \begin_inset Formula $\downarrow$
2035 \begin_inset Formula $\downarrow\downarrow$
2043 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2046 \begin_layout Plain Layout
2047 \begin_inset Formula $\raisebox{8mm}{}\dfrac{e^{\frac{1}{2}}}{3}\raisebox{-4mm}{}$
2063 \begin_layout Standard
2064 \begin_inset VSpace bigskip
2068 \begin_inset Newpage newpage
2071 For nested fractions the command
2078 \begin_inset Index idx
2081 \begin_layout Plain Layout
2091 \begin_inset VSpace -3mm
2097 \begin_layout Standard
2098 \begin_inset Formula
2100 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
2101 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}
2109 \begin_layout Standard
2110 The command for the example above is:
2113 \begin_layout Standard
2122 \begin_layout Plain Layout
2132 \begin_inset Formula $\downarrow$
2141 \begin_layout Plain Layout
2156 \begin_layout Plain Layout
2166 \begin_inset Formula $\downarrow$
2170 \begin_inset Formula $\downarrow$
2176 \begin_layout Standard
2177 \begin_inset VSpace medskip
2183 \begin_layout Standard
2190 sets the fraction always in the size of a displayed formula, also when
2191 it is part of another fraction.
2194 \begin_layout Standard
2195 It is possible to specify the alignment of the numerator.
2202 is used to left align it, the command
2215 centers the numerator.
2216 These fractions demonstrate the different alignments:
2219 \begin_layout Standard
2222 \begin_inset Formula
2224 \cfrac[l]{A}{B+C}\,,\,\cfrac{A}{B+C}\,,\,\cfrac[r]{A}{B+C}
2232 \begin_layout Standard
2233 \begin_inset Note Greyedout
2236 \begin_layout Plain Layout
2253 are no real LaTeX commands but represent the command
2257 cfrac[alignment]{numerator}{denominator}
2260 Therefore you cannot use them in TeX code.
2268 \begin_layout Standard
2269 \begin_inset VSpace medskip
2272 It is often advantageous to combine
2285 \begin_inset Formula
2287 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}
2295 \begin_layout Standard
2296 For inline fractions with a sloped fraction stroke you can use the command
2304 \begin_inset Index idx
2307 \begin_layout Plain Layout
2316 \begin_inset Formula $\nicefrac{5}{31}$
2326 \begin_inset Index idx
2329 \begin_layout Plain Layout
2338 \begin_inset Formula $\unitfrac{5}{31}$
2341 There is furthermore the command
2347 that offers to write a fraction in combination with a number:
2348 \begin_inset Formula $\unitfrac[2]{1}{3}$
2354 \begin_layout Standard
2355 \begin_inset Note Greyedout
2358 \begin_layout Plain Layout
2369 is not a real LaTeX command but the command
2370 \begin_inset Newline newline
2377 unitfrac[number]{numerator}{denominator}
2380 Therefore you cannot use it in TeX code.
2388 \begin_layout Standard
2389 How to define own fractions where the fraction stroke can be changed, is
2391 \begin_inset CommandInset ref
2393 reference "sub:Self-defined-Fractions"
2400 \begin_layout Standard
2401 \begin_inset Newpage newpage
2407 \begin_layout Subsection
2409 \begin_inset Index idx
2412 \begin_layout Plain Layout
2421 \begin_layout Standard
2422 Square roots are created with
2429 \begin_inset Index idx
2432 \begin_layout Plain Layout
2440 or the math toolbar button
2441 \begin_inset Graphics
2442 filename ../images/math/sqrt.png
2447 , all other roots with the command
2454 \begin_inset Index idx
2457 \begin_layout Plain Layout
2465 or with the math toolbar button
2466 \begin_inset Graphics
2467 filename ../images/math/root.png
2475 \begin_layout Standard
2477 \begin_inset Tabular
2478 <lyxtabular version="3" rows="3" columns="2">
2479 <features tabularvalignment="middle">
2480 <column alignment="center" valignment="top" width="0pt">
2481 <column alignment="center" valignment="top" width="0pt">
2483 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2486 \begin_layout Plain Layout
2492 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2495 \begin_layout Plain Layout
2497 \begin_inset Note Note
2500 \begin_layout Plain Layout
2507 is only used as spacer.
2519 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2522 \begin_layout Plain Layout
2529 \begin_layout Plain Layout
2543 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2546 \begin_layout Plain Layout
2547 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$
2557 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
2560 \begin_layout Plain Layout
2567 \begin_layout Plain Layout
2577 \begin_inset Formula $\downarrow$
2585 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
2588 \begin_layout Plain Layout
2589 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$
2605 \begin_layout Standard
2606 A square root can also be created with
2612 when the root index field is left empty.
2615 \begin_layout Standard
2616 With certain indices the distance to the root is too small, like in this
2618 \begin_inset Formula $\sqrt[\beta]{B}$
2622 \begin_inset Newline newline
2626 \begin_inset Formula $\beta$
2630 To avoid this, the commands
2637 \begin_inset Index idx
2640 \begin_layout Plain Layout
2655 \begin_inset Index idx
2658 \begin_layout Plain Layout
2666 are used with the following scheme:
2669 \begin_layout Standard
2683 \begin_layout Standard
2684 Distance is the number of Big Points (unit bp;
2685 \begin_inset Formula $\mathrm{72\, bp=1\, inch}$
2688 ), that the index should be moved to the left or top, resp..
2689 The commands are written to the index.
2690 This way the command
2691 \begin_inset Newline newline
2701 \begin_inset Formula $\to$
2707 \begin_inset Formula $\to$
2716 \begin_layout Plain Layout
2726 \begin_inset Formula $\to$
2730 \begin_inset Newline newline
2735 produces a correct typeset formula:
2736 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2742 \begin_layout Subsection
2743 Binomial Coefficients
2744 \begin_inset Index idx
2747 \begin_layout Plain Layout
2748 Binomial coefficients
2756 \begin_layout Standard
2757 Binomial coefficients are inserted with the command
2764 \begin_inset Index idx
2767 \begin_layout Plain Layout
2775 or with the submenu of the math toolbar button
2776 \begin_inset Graphics
2777 filename ../images/math/frac-square.png
2795 there are the commands
2802 \begin_inset Index idx
2805 \begin_layout Plain Layout
2820 \begin_inset Index idx
2823 \begin_layout Plain Layout
2832 For other brackets around binomial coeficients there are the commands
2839 \begin_inset Index idx
2842 \begin_layout Plain Layout
2857 \begin_inset Index idx
2860 \begin_layout Plain Layout
2871 \begin_layout Standard
2873 \begin_inset Tabular
2874 <lyxtabular version="3" rows="6" columns="2">
2875 <features tabularvalignment="middle">
2876 <column alignment="center" valignment="top" width="0pt">
2877 <column alignment="center" valignment="top" width="0pt">
2879 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2882 \begin_layout Plain Layout
2888 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2891 \begin_layout Plain Layout
2893 \begin_inset Note Note
2896 \begin_layout Plain Layout
2903 is only used as spacer.
2915 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2918 \begin_layout Plain Layout
2925 \begin_layout Plain Layout
2935 \begin_inset Formula $\downarrow$
2943 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2946 \begin_layout Plain Layout
2947 \begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$
2957 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2960 \begin_layout Plain Layout
2967 \begin_layout Plain Layout
2977 \begin_inset Formula $\downarrow$
2985 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2988 \begin_layout Plain Layout
2989 \begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$
2999 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3002 \begin_layout Plain Layout
3009 \begin_layout Plain Layout
3019 \begin_inset Formula $\downarrow$
3027 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3030 \begin_layout Plain Layout
3031 \begin_inset Formula $\raisebox{5mm}{}\tbinom{A}{B}\raisebox{-2.5mm}{}$
3041 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3044 \begin_layout Plain Layout
3051 \begin_layout Plain Layout
3061 \begin_inset Formula $\downarrow$
3069 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3072 \begin_layout Plain Layout
3073 \begin_inset Formula $\raisebox{5mm}{}{A \brack B}\raisebox{-2.5mm}{}$
3083 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3086 \begin_layout Plain Layout
3093 \begin_layout Plain Layout
3103 \begin_inset Formula $\downarrow$
3111 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3114 \begin_layout Plain Layout
3115 \begin_inset Formula $\raisebox{5mm}{}{A \brace B}\raisebox{-2.5mm}{}$
3131 \begin_layout Subsection
3132 Case Differentiations
3133 \begin_inset Index idx
3136 \begin_layout Plain Layout
3137 Case differentiations
3145 \begin_layout Standard
3147 \begin_inset Tabular
3148 <lyxtabular version="3" rows="3" columns="2">
3149 <features tabularvalignment="middle">
3150 <column alignment="center" valignment="top" width="0pt">
3151 <column alignment="center" valignment="top" width="0pt">
3153 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3156 \begin_layout Plain Layout
3162 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3165 \begin_layout Plain Layout
3173 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3176 \begin_layout Plain Layout
3183 \begin_layout Plain Layout
3193 \begin_inset Formula $\to$
3197 \begin_inset Index idx
3200 \begin_layout Plain Layout
3213 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3216 \begin_layout Plain Layout
3217 \begin_inset Formula $\begin{cases}
3228 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3231 \begin_layout Plain Layout
3238 \begin_layout Plain Layout
3250 arg "newline-insert newline"
3258 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3261 \begin_layout Plain Layout
3262 \begin_inset Formula $\begin{cases}
3263 A & \textrm{for }x>0\\
3264 B & \textrm{for }x=0
3281 \begin_layout Standard
3288 or pressing the math toolbar button
3289 \begin_inset Graphics
3290 filename ../images/math/cases.png
3295 you can create new lines with the shortcut
3298 arg "newline-insert newline"
3301 or the table toolbar button
3302 \begin_inset Graphics
3303 filename ../images/tabular-feature_append-row.png
3311 \begin_layout Standard
3318 is also available via the menu
3320 Insert\SpecialChar \menuseparator
3321 Math\SpecialChar \menuseparator
3327 \begin_layout Subsection
3329 \begin_inset Index idx
3332 \begin_layout Plain Layout
3341 \begin_layout Standard
3349 \begin_inset Index idx
3352 \begin_layout Plain Layout
3360 every character can be displayed canceled.
3361 The characters are quasi accentuated by a slash.
3364 \begin_layout Standard
3366 \begin_inset Tabular
3367 <lyxtabular version="3" rows="4" columns="2">
3368 <features tabularvalignment="middle">
3369 <column alignment="center" valignment="top" width="0pt">
3370 <column alignment="center" valignment="top" width="0pt">
3372 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3375 \begin_layout Plain Layout
3381 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3384 \begin_layout Plain Layout
3392 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3395 \begin_layout Plain Layout
3403 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3406 \begin_layout Plain Layout
3407 \begin_inset Formula $\not=$
3417 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3420 \begin_layout Plain Layout
3430 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3433 \begin_layout Plain Layout
3434 \begin_inset Formula $\not\le$
3444 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3447 \begin_layout Plain Layout
3457 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3460 \begin_layout Plain Layout
3461 \begin_inset Formula $\not\parallel$
3477 \begin_layout Standard
3478 The last example shows that not all negations look good.
3479 Therefore there are special commands for some negations (see
3480 \begin_inset CommandInset ref
3482 reference "sub:Mathematical-Symbols"
3487 \begin_inset CommandInset ref
3489 reference "sec:Relations"
3496 \begin_layout Subsection
3498 \begin_inset CommandInset label
3500 name "sub:Placeholders"
3505 \begin_inset Index idx
3508 \begin_layout Plain Layout
3515 \begin_inset Index idx
3518 \begin_layout Plain Layout
3519 Chemical characters ! Isotopes
3525 \begin_inset Index idx
3528 \begin_layout Plain Layout
3533 \begin_layout Plain Layout
3544 \begin_layout Plain Layout
3559 \begin_layout Standard
3561 \begin_inset space \thinspace{}
3565 \begin_inset space \space{}
3572 \begin_layout Plain Layout
3573 Typesetting isotopes and chemical symbols is described in
3574 \begin_inset CommandInset ref
3576 reference "sub:Chemical-Symbols-and"
3585 the following problem occurs:
3588 \begin_layout Standard
3590 \begin_inset Tabular
3591 <lyxtabular version="3" rows="2" columns="2">
3592 <features tabularvalignment="middle">
3593 <column alignment="center" valignment="top" width="0pt">
3594 <column alignment="center" valignment="top" width="0pt">
3596 <cell alignment="center" valignment="top" usebox="none">
3599 \begin_layout Plain Layout
3600 Indices created with sub- and superscripts:
3605 <cell alignment="center" valignment="top" usebox="none">
3608 \begin_layout Plain Layout
3609 \begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
3619 <cell alignment="center" valignment="top" usebox="none">
3622 \begin_layout Plain Layout
3628 <cell alignment="center" valignment="top" usebox="none">
3631 \begin_layout Plain Layout
3632 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3646 \begin_inset Note Note
3649 \begin_layout Plain Layout
3656 is only used as spacer.
3664 \begin_layout Standard
3665 The shorter index is by default placed below or above the first character
3666 of the longer index.
3667 To avoid this there is the command
3674 \begin_inset Index idx
3677 \begin_layout Plain Layout
3685 or the math toolbar button
3686 \begin_inset space \thinspace{}
3693 \begin_layout Plain Layout
3694 can be found in the submenu of the toolbar button
3695 \begin_inset Graphics
3696 filename ../images/math/space.png
3707 \begin_inset Graphics
3708 filename ../images/math/phantom.png
3713 that creates one or more phantom characters.
3720 a small blue box appears that is superposed with two red arrows.
3721 The arrows indicate that the complete width and height of the box content
3722 will be created as placeholder.
3723 Phantom characters are accordingly placeholders with the size of the characters.
3726 \begin_layout Standard
3728 \begin_inset Tabular
3729 <lyxtabular version="3" rows="4" columns="2">
3730 <features tabularvalignment="middle">
3731 <column alignment="center" valignment="top" width="0">
3732 <column alignment="center" valignment="top" width="0">
3734 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3737 \begin_layout Plain Layout
3743 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3746 \begin_layout Plain Layout
3748 \begin_inset Note Note
3751 \begin_layout Plain Layout
3758 is only used as spacer.
3770 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3773 \begin_layout Plain Layout
3778 \begin_layout Plain Layout
3793 \begin_layout Plain Layout
3803 \begin_inset Formula $\to$
3810 \begin_layout Plain Layout
3824 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3827 \begin_layout Plain Layout
3828 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
3838 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3841 \begin_layout Plain Layout
3846 \begin_layout Plain Layout
3861 \begin_layout Plain Layout
3871 \begin_inset Formula $\to$
3878 \begin_layout Plain Layout
3892 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3895 \begin_layout Plain Layout
3896 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
3906 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3909 \begin_layout Plain Layout
3916 \begin_layout Plain Layout
3931 \begin_layout Plain Layout
3941 \begin_inset Formula $\to$
3948 \begin_layout Plain Layout
3962 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3965 \begin_layout Plain Layout
3966 \begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
3982 \begin_layout Standard
3983 Furthermore there are the commands
3990 \begin_inset Index idx
3993 \begin_layout Plain Layout
4002 \begin_inset space ~
4006 \begin_inset Graphics
4007 filename ../images/math/vphantom.png
4019 \begin_inset Index idx
4022 \begin_layout Plain Layout
4031 \begin_inset space ~
4035 \begin_inset Graphics
4036 filename ../images/math/hphantom.png
4048 creates only space for the maximal height of the characters in the box
4049 but not for its width.
4056 creates only space for the width of the box content.
4057 Therefore the boxes of both commands have only one red arrow.
4060 \begin_layout Standard
4061 For example the command
4071 \begin_layout Plain Layout
4086 creates space for the height of the integral sign,
4090 \begin_layout Plain Layout
4097 creates an integral sign, see
4098 \begin_inset CommandInset ref
4100 reference "sub:Big-Operators"
4109 because this is the larger character.
4110 An example application is in
4111 \begin_inset CommandInset ref
4113 reference "sub:Multiline-Brackets"
4120 \begin_layout Standard
4121 Placeholders can also be used for text when they are inserted via the menu
4124 Insert\SpecialChar \menuseparator
4125 Formatting\SpecialChar \menuseparator
4131 \begin_layout Standard
4133 \begin_inset Newline newline
4137 \begin_inset Phantom Phantom
4140 \begin_layout Plain Layout
4149 \begin_layout Subsection
4151 \begin_inset Index idx
4154 \begin_layout Plain Layout
4161 \begin_inset Index idx
4164 \begin_layout Plain Layout
4165 Formula ! underlined
4173 \begin_layout Standard
4175 \begin_inset Tabular
4176 <lyxtabular version="3" rows="4" columns="2">
4177 <features tabularvalignment="middle">
4178 <column alignment="center" valignment="top" width="0pt">
4179 <column alignment="center" valignment="top" width="0pt">
4181 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4184 \begin_layout Plain Layout
4190 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4193 \begin_layout Plain Layout
4195 \begin_inset Note Note
4198 \begin_layout Plain Layout
4205 is only used as spacer.
4217 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4220 \begin_layout Plain Layout
4227 \begin_layout Plain Layout
4237 \begin_inset Index idx
4240 \begin_layout Plain Layout
4253 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4256 \begin_layout Plain Layout
4257 \begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
4267 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
4270 \begin_layout Plain Layout
4277 \begin_layout Plain Layout
4287 \begin_inset Index idx
4290 \begin_layout Plain Layout
4303 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
4306 \begin_layout Plain Layout
4307 \begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
4317 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4320 \begin_layout Plain Layout
4327 \begin_layout Plain Layout
4342 \begin_layout Plain Layout
4356 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4359 \begin_layout Plain Layout
4360 \begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
4376 \begin_layout Standard
4377 In the last example it doesn't matter if first
4392 \begin_layout Standard
4393 To double underline use
4402 \begin_layout Standard
4403 It is possible to place up to 6 lines above or below characters.
4406 \begin_layout Standard
4407 \begin_inset VSpace bigskip
4410 Custom lines can be created using the command
4417 \begin_inset Index idx
4420 \begin_layout Plain Layout
4428 which has the following scheme:
4431 \begin_layout Standard
4436 rule[vertical offset]{length}{thickness}
4439 \begin_layout Standard
4440 The optional vertical offset shifts the line upwards (or downwards, when
4441 the value is negative).
4443 \begin_inset CommandInset ref
4445 reference "tab:Available-units"
4449 can be used for the values.
4450 Here are two example lines created with the commands
4451 \begin_inset Newline newline
4458 rule[-2ex]{3cm}{2pt}
4469 \begin_layout Standard
4471 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4477 \begin_layout Standard
4484 can also be used for text when a line is inserted via the menu
4486 Insert\SpecialChar \menuseparator
4487 Formatting\SpecialChar \menuseparator
4489 \begin_inset space ~
4497 \begin_layout Standard
4499 \begin_inset CommandInset line
4510 \begin_layout Subsection
4512 \begin_inset CommandInset label
4519 \begin_inset Index idx
4522 \begin_layout Plain Layout
4531 \begin_layout Standard
4532 There are different types of ellipses available.
4536 \begin_layout Plain Layout
4537 In the math toolbar in the submenu of the button
4538 \begin_inset Graphics
4539 filename ../images/math/ldots.png
4549 For listings dots at the baseline are used (
4556 \begin_inset Index idx
4559 \begin_layout Plain Layout
4567 ), while for operations dots are needed that are on the same height as the
4575 \begin_inset Index idx
4578 \begin_layout Plain Layout
4587 When using the command
4594 \begin_inset Index idx
4597 \begin_layout Plain Layout
4605 , LaTeX decides on the basis of the next character what type is used.
4608 \begin_layout Standard
4610 \begin_inset Tabular
4611 <lyxtabular version="3" rows="9" columns="2">
4612 <features tabularvalignment="middle">
4613 <column alignment="center" valignment="top" width="0pt">
4614 <column alignment="center" valignment="top" width="0pt">
4616 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4619 \begin_layout Plain Layout
4625 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4628 \begin_layout Plain Layout
4636 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4639 \begin_layout Plain Layout
4644 \begin_layout Plain Layout
4659 \begin_layout Plain Layout
4673 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4676 \begin_layout Plain Layout
4677 \begin_inset Formula $A_{1},\dots,A_{n}$
4687 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4690 \begin_layout Plain Layout
4695 \begin_layout Plain Layout
4710 \begin_layout Plain Layout
4724 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4727 \begin_layout Plain Layout
4728 \begin_inset Formula $A_{1}+\dots+A_{n}$
4738 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4741 \begin_layout Plain Layout
4746 \begin_layout Plain Layout
4761 \begin_layout Plain Layout
4775 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4778 \begin_layout Plain Layout
4779 \begin_inset Formula $A_{1},\ldots,A_{n}$
4789 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4792 \begin_layout Plain Layout
4797 \begin_layout Plain Layout
4812 \begin_layout Plain Layout
4826 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4829 \begin_layout Plain Layout
4830 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4840 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4843 \begin_layout Plain Layout
4851 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4854 \begin_layout Plain Layout
4855 \begin_inset Formula $\vdots$
4865 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4868 \begin_layout Plain Layout
4876 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4879 \begin_layout Plain Layout
4880 \begin_inset Formula $\ddots$
4890 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4893 \begin_layout Plain Layout
4901 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4904 \begin_layout Plain Layout
4905 \begin_inset Formula $\iddots$
4915 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4918 \begin_layout Plain Layout
4920 \begin_inset space \thinspace{}
4923 matrix with the different dots
4928 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4931 \begin_layout Plain Layout
4932 \begin_inset Formula $\begin{array}{ccc}
4933 A_{11} & \cdots & A_{1m}\\
4934 \vdots & \ddots & \vdots\\
4935 A_{n1} & \cdots & A_{nm}
4952 \begin_layout Standard
4953 The ellipses available in menu
4955 Insert\SpecialChar \menuseparator
4957 \begin_inset space ~
4971 \begin_layout Standard
4972 \begin_inset VSpace medskip
4981 , one of the options
4983 Use mathdots package (automatically)
4985 must be set in the document settings under
4988 \begin_inset space ~
4994 \begin_inset Newline newline
4999 Use mathdots package
5001 will improve the appearance of all dots in the documents if their font
5002 style or size is not the default.
5005 \begin_layout Standard
5006 \begin_inset VSpace medskip
5009 Specially for matrices there are ellipses that span over several columns.
5010 They are created with the command
5017 \begin_inset Index idx
5020 \begin_layout Plain Layout
5028 , that has the following scheme:
5031 \begin_layout Standard
5036 hdotsfor[distance]{number of columns}
5039 \begin_layout Standard
5040 The number of columns specifies how many columns should be spanned.
5041 Distance is a factor for the distance between the dots.
5044 \begin_layout Standard
5045 In the following matrix the command
5051 was inserted in the first box of the second line, to get an ellipsis with
5052 a dot distance twice as long as with the command
5059 \begin_inset Formula
5061 \left(\begin{array}{cccc}
5070 Note that the matrix fields that should be spanned must be empty, otherwise
5071 you get LaTeX-errors.
5074 \begin_layout Standard
5075 \begin_inset VSpace bigskip
5078 Furthermore you can fill with the command
5085 \begin_inset Index idx
5088 \begin_layout Plain Layout
5096 the rest of a line with dots.
5097 The effect of these commands is the same as with
5104 \begin_inset CommandInset ref
5106 reference "sub:Variable-Space"
5113 \begin_layout Standard
5114 For example the command
5122 \begin_layout Plain Layout
5136 \begin_layout Standard
5137 \begin_inset Formula $A\dotfill B$
5143 \begin_layout Standard
5150 there is for a line the command
5157 \begin_inset Index idx
5160 \begin_layout Plain Layout
5171 \begin_layout Standard
5172 \begin_inset Formula $A\hrulefill B$
5178 \begin_layout Standard
5179 To use the commands for text, they have to be inserted in TeX-mode.
5182 \begin_layout Section
5184 \begin_inset CommandInset label
5191 \begin_inset Index idx
5194 \begin_layout Plain Layout
5203 \begin_layout Standard
5204 Matrices can be inserted via the math toolbar button
5205 \begin_inset Graphics
5206 filename ../images/dialog-show_mathmatrix.png
5213 Insert\SpecialChar \menuseparator
5214 Math\SpecialChar \menuseparator
5218 In the matrix dialog you can specify the number of columns and rows, the
5219 alignment and the decoration.
5220 The vertical alignment is only of importance for matrices in inline formulas:
5223 \begin_layout Standard
5224 The first matrix is top
5225 \begin_inset Formula $\begin{array}[t]{cccc}
5233 \begin_inset Formula $\begin{array}{cccc}
5240 and the third bottom
5241 \begin_inset Formula $\begin{array}[b]{cccc}
5251 \begin_layout Standard
5252 The horizontal alignment specifies how the column entries should be aligned.
5253 It is set by entering a letter for every column.
5258 denotes left aligned,
5267 To create for example a 4
5272 \begin_inset space ~
5275 matrix where the first column is left aligned, the second and third are
5276 centered and the last one is right aligned, one enters for the horizontal
5282 Normally in a matrix all columns are centered, therefore the default for
5290 \begin_layout Standard
5291 Horizontal alignment:
5294 \begin_layout Standard
5300 \begin_inset Formula $\begin{array}{lll}
5312 \begin_inset Formula $\begin{array}{ccc}
5324 \begin_inset Formula $\begin{array}{rrr}
5334 \begin_layout Standard
5335 To add or delete rows and columns subsequently, the math toolbar buttons
5337 \begin_inset Graphics
5338 filename ../images/tabular-feature_append-row.png
5344 \begin_inset Graphics
5345 filename ../images/tabular-feature_delete-row.png
5351 \begin_inset space \thinspace{}
5356 Edit\SpecialChar \menuseparator
5360 New rows can also be created with
5363 arg "newline-insert newline"
5369 \begin_layout Standard
5370 \begin_inset VSpace bigskip
5377 adds parentheses in the selected style around the matrix.
5378 Alternatively, parentheses can can either be created with the commands
5386 \begin_inset Index idx
5389 \begin_layout Plain Layout
5404 \begin_inset Index idx
5407 \begin_layout Plain Layout
5418 \begin_inset space ~
5424 \begin_inset CommandInset ref
5426 reference "sub:Automatic-Bracket-Size"
5430 , or by using the following commands:
5431 \begin_inset VSpace medskip
5437 \begin_layout Standard
5438 \begin_inset space \hfill{}
5442 \begin_inset Tabular
5443 <lyxtabular version="3" rows="4" columns="2">
5444 <features tabularvalignment="middle">
5445 <column alignment="center" valignment="top" width="0">
5446 <column alignment="center" valignment="top" width="0">
5448 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5451 \begin_layout Plain Layout
5457 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5460 \begin_layout Plain Layout
5462 \begin_inset Note Note
5465 \begin_layout Plain Layout
5472 is only used as spacer.
5484 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5487 \begin_layout Plain Layout
5494 \begin_layout Plain Layout
5508 \begin_inset space \thinspace{}
5516 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5519 \begin_layout Plain Layout
5520 \begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
5521 0 & \textrm{-}\mathrm{i}\\
5523 \end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
5533 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5536 \begin_layout Plain Layout
5543 \begin_layout Plain Layout
5557 \begin_inset space \thinspace{}
5565 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5568 \begin_layout Plain Layout
5569 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
5570 0 & \textrm{-}\mathrm{i}\\
5572 \end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
5582 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5585 \begin_layout Plain Layout
5592 \begin_layout Plain Layout
5606 \begin_inset space \thinspace{}
5614 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5617 \begin_layout Plain Layout
5618 \begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
5619 0 & \textrm{-}\mathrm{i}\\
5621 \end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
5635 \begin_inset space \hfill{}
5639 \begin_inset Tabular
5640 <lyxtabular version="3" rows="4" columns="2">
5641 <features tabularvalignment="middle">
5642 <column alignment="center" valignment="top" width="0">
5643 <column alignment="center" valignment="top" width="0">
5645 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5648 \begin_layout Plain Layout
5654 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5657 \begin_layout Plain Layout
5665 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5668 \begin_layout Plain Layout
5675 \begin_layout Plain Layout
5689 \begin_inset space \thinspace{}
5697 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5700 \begin_layout Plain Layout
5701 \begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
5702 0 & \textrm{-}\mathrm{i}\\
5704 \end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
5714 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5717 \begin_layout Plain Layout
5724 \begin_layout Plain Layout
5738 \begin_inset space \thinspace{}
5746 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5749 \begin_layout Plain Layout
5750 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
5751 0 & \textrm{-}\mathrm{i}\\
5753 \end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
5763 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5766 \begin_layout Plain Layout
5773 \begin_layout Plain Layout
5787 \begin_inset space \thinspace{}
5795 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5798 \begin_layout Plain Layout
5799 \begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
5800 0 & \textrm{-}\mathrm{i}\\
5802 \end{array}\end{matrix}\raisebox{-5.3mm}{}$
5816 \begin_inset space \hfill{}
5822 \begin_layout Standard
5823 \begin_inset VSpace medskip
5827 \begin_inset space \thinspace{}
5831 \begin_inset space \space{}
5840 is inserted, a blue box appears between two vertical lines where the matrix
5842 \begin_inset Newline newline
5845 Note that decorated matrices ignore the vertical alignment.
5848 \begin_layout Standard
5849 \begin_inset Note Greyedout
5852 \begin_layout Plain Layout
5857 LaTeX limits the number of matrix columns with decorations to 10.
5858 If you need more than 10
5859 \begin_inset space ~
5862 columns, you have to add this line to the document preamble:
5865 \begin_layout Plain Layout
5870 setcounter{MaxMatrixCols}{number}
5873 \begin_layout Plain Layout
5878 is the number of columns between 11 and 99.
5886 \begin_layout Standard
5887 \begin_inset VSpace bigskip
5890 As all multiline formulas are matrices, the length
5897 \begin_inset Index idx
5900 \begin_layout Plain Layout
5908 that is described in
5909 \begin_inset CommandInset ref
5911 reference "sub:Column-Separation"
5915 can also be used to change the column separation of matrices.
5918 \begin_layout Standard
5919 To change the row separation, the command
5926 \begin_inset Index idx
5929 \begin_layout Plain Layout
5938 It is used as follows:
5941 \begin_layout Standard
5948 arraystretch}{stretch factor}
5949 \begin_inset Index idx
5952 \begin_layout Plain Layout
5963 \begin_layout Standard
5970 assigns the stretch factor to the predefined command
5978 \begin_inset space \thinspace{}
5982 \begin_inset space \space{}
5985 the row separation, use the factor 2.
5986 This is then used for all following matrices.
5987 To go back to the original separation, assign the factor 1 to
5996 \begin_layout Standard
5997 To set matrices into a text line, the command
6004 \begin_inset Index idx
6007 \begin_layout Plain Layout
6016 When it is inserted a blue box with two dashed lines appears.
6017 In this box the matrix is inserted.
6020 \begin_layout Standard
6022 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
6024 \end{smallmatrix}\right)$
6030 \begin_layout Section
6031 Brackets and Delimiters
6032 \begin_inset Index idx
6035 \begin_layout Plain Layout
6042 \begin_inset Index idx
6045 \begin_layout Plain Layout
6054 \begin_layout Subsection
6055 Vertical Brackets and Delimiters
6056 \begin_inset Index idx
6059 \begin_layout Plain Layout
6068 \begin_layout Standard
6069 \begin_inset space \hfill{}
6073 \begin_inset Tabular
6074 <lyxtabular version="3" rows="9" columns="2">
6075 <features tabularvalignment="middle">
6076 <column alignment="center" valignment="top" width="0pt">
6077 <column alignment="center" valignment="top" width="0pt">
6079 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6082 \begin_layout Plain Layout
6088 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6091 \begin_layout Plain Layout
6099 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6102 \begin_layout Plain Layout
6108 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6111 \begin_layout Plain Layout
6112 \begin_inset Formula $($
6122 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6125 \begin_layout Plain Layout
6131 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6134 \begin_layout Plain Layout
6135 \begin_inset Formula $\{$
6145 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6148 \begin_layout Plain Layout
6154 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6157 \begin_layout Plain Layout
6158 \begin_inset Formula $[$
6168 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6171 \begin_layout Plain Layout
6179 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6182 \begin_layout Plain Layout
6183 \begin_inset Formula $\langle$
6193 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6196 \begin_layout Plain Layout
6204 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6207 \begin_layout Plain Layout
6208 \begin_inset Formula $\lceil$
6218 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6221 \begin_layout Plain Layout
6229 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6232 \begin_layout Plain Layout
6233 \begin_inset Formula $\lfloor$
6243 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6246 \begin_layout Plain Layout
6252 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6255 \begin_layout Plain Layout
6256 \begin_inset Formula $/$
6266 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6269 \begin_layout Plain Layout
6275 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6278 \begin_layout Plain Layout
6279 \begin_inset Formula $|$
6293 \begin_inset space \hfill{}
6297 \begin_inset Tabular
6298 <lyxtabular version="3" rows="9" columns="2">
6299 <features tabularvalignment="middle">
6300 <column alignment="center" valignment="top" width="0pt">
6301 <column alignment="center" valignment="top" width="0pt">
6303 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6306 \begin_layout Plain Layout
6312 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6315 \begin_layout Plain Layout
6323 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6326 \begin_layout Plain Layout
6332 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6335 \begin_layout Plain Layout
6336 \begin_inset Formula $)$
6346 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6349 \begin_layout Plain Layout
6355 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6358 \begin_layout Plain Layout
6359 \begin_inset Formula $\}$
6369 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6372 \begin_layout Plain Layout
6378 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6381 \begin_layout Plain Layout
6382 \begin_inset Formula $]$
6392 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6395 \begin_layout Plain Layout
6403 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6406 \begin_layout Plain Layout
6407 \begin_inset Formula $\rangle$
6417 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6420 \begin_layout Plain Layout
6428 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6431 \begin_layout Plain Layout
6432 \begin_inset Formula $\rceil$
6442 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6445 \begin_layout Plain Layout
6453 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6456 \begin_layout Plain Layout
6457 \begin_inset Formula $\rfloor$
6467 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6470 \begin_layout Plain Layout
6480 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6483 \begin_layout Plain Layout
6484 \begin_inset Formula $\backslash$
6494 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6497 \begin_layout Plain Layout
6505 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6508 \begin_layout Plain Layout
6509 \begin_inset Formula $\|$
6523 \begin_inset space \hfill{}
6529 \begin_layout Standard
6532 \begin_inset Note Greyedout
6535 \begin_layout Plain Layout
6540 In TeX-mode the command
6547 \begin_inset Index idx
6550 \begin_layout Plain Layout
6558 must be used for the backslash, because the command
6566 produces a line break there.
6574 \begin_layout Standard
6575 For all characters listed above the size can be adjusted with the commands
6576 described in the following two subsections.
6577 When using these commands, the characters < and > can directly be used
6578 instead of the commands
6593 \begin_layout Subsubsection
6595 \begin_inset CommandInset label
6597 name "sub:Manual-Bracket-Size"
6602 \begin_inset Index idx
6605 \begin_layout Plain Layout
6606 Bracket size ! manual
6614 \begin_layout Standard
6615 The bracket size can be specified manually by the LaTeX-commands
6622 \begin_inset Index idx
6625 \begin_layout Plain Layout
6658 denotes the smallest and
6664 the largest bracket size.
6667 \begin_layout Standard
6668 These commands are used to emphasize levels of brackets:
6671 \begin_layout Standard
6673 \begin_inset Tabular
6674 <lyxtabular version="3" rows="2" columns="2">
6675 <features tabularvalignment="middle">
6676 <column alignment="center" valignment="top" width="0pt">
6677 <column alignment="center" valignment="top" width="0pt">
6679 <cell alignment="center" valignment="top" usebox="none">
6682 \begin_layout Plain Layout
6683 all brackets in the same size:
6688 <cell alignment="center" valignment="top" usebox="none">
6691 \begin_layout Plain Layout
6692 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
6702 <cell alignment="center" valignment="top" usebox="none">
6705 \begin_layout Plain Layout
6711 <cell alignment="center" valignment="top" usebox="none">
6714 \begin_layout Plain Layout
6715 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6729 \begin_inset Note Note
6732 \begin_layout Plain Layout
6739 is only used as spacer.
6747 \begin_layout Standard
6748 For the second formula the command
6758 \begin_layout Plain Layout
6772 \begin_layout Standard
6773 Here is an overview about all bracket sizes:
6776 \begin_layout Standard
6796 \begin_layout Plain Layout
6813 \begin_layout Plain Layout
6826 \begin_layout Plain Layout
6842 \begin_layout Standard
6844 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6850 \begin_layout Standard
6857 -commands there is the variant
6864 \begin_inset Index idx
6867 \begin_layout Plain Layout
6875 that adds a bit more space between the bracket and its content, and the
6889 \begin_inset Index idx
6892 \begin_layout Plain Layout
6902 , that don't add additional space.
6907 at the end of the command
6913 is for a left bracket; for a right bracket this will be replaced by an
6919 A left or right bracket can each be an opening or closing bracket.
6922 \begin_layout Standard
6923 In the following table is a comparison of the variants:
6926 \begin_layout Standard
6928 \begin_inset Tabular
6929 <lyxtabular version="3" rows="5" columns="2">
6930 <features tabularvalignment="middle">
6931 <column alignment="center" valignment="middle" width="0">
6932 <column alignment="center" valignment="middle" width="0">
6934 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6937 \begin_layout Plain Layout
6943 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6946 \begin_layout Plain Layout
6948 \begin_inset Note Note
6951 \begin_layout Plain Layout
6958 is only used as spacer.
6970 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6973 \begin_layout Plain Layout
6988 \begin_layout Plain Layout
7006 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7009 \begin_layout Plain Layout
7010 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
7020 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7023 \begin_layout Plain Layout
7038 \begin_layout Plain Layout
7056 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7059 \begin_layout Plain Layout
7060 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
7070 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7073 \begin_layout Plain Layout
7088 \begin_layout Plain Layout
7106 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7109 \begin_layout Plain Layout
7110 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
7120 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7123 \begin_layout Plain Layout
7135 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7138 \begin_layout Plain Layout
7139 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
7155 \begin_layout Subsubsection
7156 Automatic Bracket Size
7157 \begin_inset CommandInset label
7159 name "sub:Automatic-Bracket-Size"
7164 \begin_inset Index idx
7167 \begin_layout Plain Layout
7168 Bracket size ! automatic
7176 \begin_layout Standard
7177 Brackets with variable size can be inserted with the commands
7184 \begin_inset Index idx
7187 \begin_layout Plain Layout
7202 \begin_inset Index idx
7205 \begin_layout Plain Layout
7213 or via the math toolbar button
7214 \begin_inset Graphics
7215 filename ../images/dialog-show_mathdelimiter.png
7233 the wanted bracket must be inserted.
7234 The bracket size will then automatically be calculated for the output.
7237 \begin_layout Standard
7239 normal bracket: The command
7249 \begin_layout Plain Layout
7259 \begin_inset Formula $\downarrow$
7266 \begin_layout Plain Layout
7278 \begin_inset Formula
7288 \begin_layout Standard
7290 multiline bracket: The command
7302 \begin_layout Plain Layout
7312 \begin_inset Formula $\downarrow$
7319 \begin_layout Plain Layout
7333 \begin_inset Formula
7335 \ln\left(\frac{A}{C}\right)
7343 \begin_layout Standard
7359 \begin_inset space ~
7365 This has the advantage that you can see in LyX immediately the real bracket
7366 size and that the matching right bracket will be created too.
7367 \begin_inset Newline newline
7370 The command for the last example would then be:
7384 \begin_layout Plain Layout
7394 \begin_inset Formula $\downarrow$
7400 \begin_layout Standard
7401 To omit a left or right bracket, a dot is inserted for the omitted bracket.
7402 For example the command
7412 \begin_layout Plain Layout
7422 \begin_inset Formula $\downarrow$
7429 \begin_layout Plain Layout
7445 \begin_inset Formula
7447 \left.\frac{A}{B}\right\}
7466 will be converted by LyX to brackets in the right size when the document
7467 is reloaded and an omitted bracket will appear as dashed line.
7470 \begin_layout Standard
7471 \begin_inset VSpace bigskip
7474 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
7482 \begin_inset Index idx
7485 \begin_layout Plain Layout
7493 is additionally available for all brackets and limits.
7494 With this command the height of the following character is adapted to the
7495 one of the surrounding brackets, what is e.
7496 \begin_inset space \thinspace{}
7500 \begin_inset space \space{}
7503 needed for physical vectors:
7504 \begin_inset Formula
7506 \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle
7511 For physical vectors there is a special LaTeX-package, described in
7512 \begin_inset CommandInset ref
7514 reference "sub:Physical-Vectors"
7521 \begin_layout Subsection
7523 \begin_inset Index idx
7526 \begin_layout Plain Layout
7527 Brackets ! horizontal
7535 \begin_layout Standard
7537 \begin_inset Tabular
7538 <lyxtabular version="3" rows="4" columns="2">
7539 <features tabularvalignment="middle">
7540 <column alignment="center" valignment="top" width="0pt">
7541 <column alignment="center" valignment="top" width="0pt">
7543 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7546 \begin_layout Plain Layout
7548 \begin_inset Note Note
7551 \begin_layout Plain Layout
7558 is only used as spacer.
7568 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7571 \begin_layout Plain Layout
7579 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7582 \begin_layout Plain Layout
7586 \begin_layout Plain Layout
7601 \begin_layout Plain Layout
7614 \begin_layout Plain Layout
7627 \begin_layout Plain Layout
7640 \begin_layout Plain Layout
7648 \begin_inset Index idx
7651 \begin_layout Plain Layout
7664 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7667 \begin_layout Plain Layout
7668 \begin_inset Formula $\overbrace{A+B}^{3}$
7678 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7681 \begin_layout Plain Layout
7685 \begin_layout Plain Layout
7700 \begin_layout Plain Layout
7713 \begin_layout Plain Layout
7726 \begin_layout Plain Layout
7734 \begin_inset Index idx
7737 \begin_layout Plain Layout
7750 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7753 \begin_layout Plain Layout
7754 \begin_inset Formula $\underbrace{A+B}_{5}$
7764 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7767 \begin_layout Plain Layout
7774 \begin_layout Plain Layout
7789 \begin_layout Plain Layout
7802 \begin_layout Plain Layout
7815 \begin_layout Plain Layout
7828 \begin_layout Plain Layout
7841 \begin_layout Plain Layout
7854 \begin_layout Plain Layout
7868 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7871 \begin_layout Plain Layout
7872 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
7888 \begin_layout Standard
7889 In the last example it doesn't matter if
7901 is inserted at first.
7904 \begin_layout Standard
7905 \begin_inset VSpace bigskip
7908 When brackets are needed that overlap each other, multiline formulas, as
7910 \begin_inset CommandInset ref
7912 reference "sec:Multiline-Formulas"
7917 \begin_inset Formula
7919 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
7920 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
7925 In the first row the formula is inserted together with the first brace.
7926 It is hereby important that the space command
7930 \begin_layout Plain Layout
7931 Space commands are explained in
7932 \begin_inset CommandInset ref
7934 reference "sub:Predefined-Space"
7949 is inserted before the first
7950 \begin_inset Formula $d$
7953 , because the brace that ends behind the
7954 \begin_inset Formula $q$
7957 prevents that the following
7958 \begin_inset Quotes eld
7962 \begin_inset Quotes erd
7965 is surrounded by space.
7969 \begin_layout Plain Layout
7970 because a bracket is not handled as a character, see
7971 \begin_inset CommandInset ref
7973 reference "sub:Binary-Operators"
7982 In the second row the second brace is inserted.
7983 As it should begin before the
7984 \begin_inset Formula $b$
7999 \begin_layout Plain Layout
8007 \begin_inset CommandInset ref
8009 reference "sub:Placeholders"
8018 This space is needed because the
8019 \begin_inset Quotes eld
8023 \begin_inset Quotes erd
8026 is also surrounded by space in the formula.
8027 The brace is placed under the command
8036 \begin_layout Standard
8037 It gets more complicated when brackets overlap each other, like in the following
8042 \begin_layout Plain Layout
8054 \begin_inset Formula
8056 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
8057 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd
8066 \begin_layout Plain Layout
8077 The first formula row is the same as the second row of the previous example,
8078 with the difference that the brace is above.
8079 The second row contains the formula together with the second brace.
8080 To avoid that there is space between the upper brace in the first row and
8081 the formula, the row spacing needs to be reduced.
8082 This is not easily possible due to a bug in LyX
8086 \begin_layout Plain Layout
8087 \begin_inset CommandInset href
8089 name "LyX-bug #1505"
8090 target "http://www.lyx.org/trac/ticket/1505"
8100 As a solution for the problem, the global formula row separation
8107 \begin_inset Index idx
8110 \begin_layout Plain Layout
8118 must be changed to -6
8119 \begin_inset space \thinspace{}
8122 pt before the formula with the command
8137 is set back after the formula to the standard value of 3
8138 \begin_inset space \thinspace{}
8141 pt using the same command.
8142 More about the row separation in formulas is explained in
8143 \begin_inset CommandInset ref
8145 reference "sub:Line-Separation"
8152 \begin_layout Section
8154 \begin_inset Index idx
8157 \begin_layout Plain Layout
8166 \begin_layout Standard
8167 Arrows can be inserted via the math toolbar button
8168 \begin_inset Graphics
8169 filename ../images/math/leftarrow.png
8174 or the commands listed in the following subsections.
8177 \begin_layout Subsection
8179 \begin_inset Index idx
8182 \begin_layout Plain Layout
8191 \begin_layout Standard
8192 \begin_inset space \hfill{}
8196 \begin_inset Tabular
8197 <lyxtabular version="3" rows="8" columns="2">
8198 <features tabularvalignment="middle">
8199 <column alignment="center" valignment="top" width="0pt">
8200 <column alignment="center" valignment="top" width="0pt">
8202 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8205 \begin_layout Plain Layout
8211 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8214 \begin_layout Plain Layout
8222 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8225 \begin_layout Plain Layout
8233 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8236 \begin_layout Plain Layout
8237 \begin_inset Formula $\gets$
8247 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8250 \begin_layout Plain Layout
8258 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8261 \begin_layout Plain Layout
8262 \begin_inset Formula $\Leftarrow$
8272 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8275 \begin_layout Plain Layout
8283 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8286 \begin_layout Plain Layout
8287 \begin_inset Formula $\longleftarrow$
8297 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8300 \begin_layout Plain Layout
8308 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8311 \begin_layout Plain Layout
8312 \begin_inset Formula $\Longleftarrow$
8322 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8325 \begin_layout Plain Layout
8333 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8336 \begin_layout Plain Layout
8337 \begin_inset Formula $\leftharpoonup$
8347 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8350 \begin_layout Plain Layout
8358 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8361 \begin_layout Plain Layout
8362 \begin_inset Formula $\leftharpoondown$
8372 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8375 \begin_layout Plain Layout
8383 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8386 \begin_layout Plain Layout
8387 \begin_inset Formula $\hookleftarrow$
8401 \begin_inset space \hfill{}
8405 \begin_inset Tabular
8406 <lyxtabular version="3" rows="8" columns="2">
8407 <features tabularvalignment="middle">
8408 <column alignment="center" valignment="top" width="0pt">
8409 <column alignment="center" valignment="top" width="0pt">
8411 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8414 \begin_layout Plain Layout
8420 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8423 \begin_layout Plain Layout
8431 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8434 \begin_layout Plain Layout
8442 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8445 \begin_layout Plain Layout
8446 \begin_inset Formula $\to$
8456 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8459 \begin_layout Plain Layout
8467 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8470 \begin_layout Plain Layout
8471 \begin_inset Formula $\Rightarrow$
8481 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8484 \begin_layout Plain Layout
8492 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8495 \begin_layout Plain Layout
8496 \begin_inset Formula $\longrightarrow$
8506 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8509 \begin_layout Plain Layout
8517 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8520 \begin_layout Plain Layout
8521 \begin_inset Formula $\Longrightarrow$
8531 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8534 \begin_layout Plain Layout
8542 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8545 \begin_layout Plain Layout
8546 \begin_inset Formula $\rightharpoonup$
8556 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8559 \begin_layout Plain Layout
8567 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8570 \begin_layout Plain Layout
8571 \begin_inset Formula $\rightharpoondown$
8581 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8584 \begin_layout Plain Layout
8592 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8595 \begin_layout Plain Layout
8596 \begin_inset Formula $\hookrightarrow$
8610 \begin_inset space \hfill{}
8616 \begin_layout Standard
8617 \begin_inset space \hfill{}
8621 \begin_inset Tabular
8622 <lyxtabular version="3" rows="6" columns="2">
8623 <features tabularvalignment="middle">
8624 <column alignment="center" valignment="top" width="0pt">
8625 <column alignment="center" valignment="top" width="0pt">
8627 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8630 \begin_layout Plain Layout
8636 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8639 \begin_layout Plain Layout
8647 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8650 \begin_layout Plain Layout
8658 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8661 \begin_layout Plain Layout
8662 \begin_inset Formula $\leftrightarrow$
8672 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8675 \begin_layout Plain Layout
8683 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8686 \begin_layout Plain Layout
8687 \begin_inset Formula $\Leftrightarrow$
8697 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8700 \begin_layout Plain Layout
8708 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8711 \begin_layout Plain Layout
8712 \begin_inset Formula $\longleftrightarrow$
8722 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8725 \begin_layout Plain Layout
8733 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8736 \begin_layout Plain Layout
8737 \begin_inset Formula $\Longleftrightarrow$
8747 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8750 \begin_layout Plain Layout
8758 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8761 \begin_layout Plain Layout
8762 \begin_inset Formula $\rightleftharpoons$
8776 \begin_inset space \hspace{}
8781 \begin_inset space \hfill{}
8785 \begin_inset Tabular
8786 <lyxtabular version="3" rows="5" columns="2">
8787 <features tabularvalignment="middle">
8788 <column alignment="center" valignment="top" width="0pt">
8789 <column alignment="center" valignment="top" width="0pt">
8791 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8794 \begin_layout Plain Layout
8800 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8803 \begin_layout Plain Layout
8811 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8814 \begin_layout Plain Layout
8822 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8825 \begin_layout Plain Layout
8826 \begin_inset Formula $\mapsto$
8836 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8839 \begin_layout Plain Layout
8847 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8850 \begin_layout Plain Layout
8851 \begin_inset Formula $\longmapsto$
8861 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8864 \begin_layout Plain Layout
8872 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8875 \begin_layout Plain Layout
8876 \begin_inset Formula $\leadsto$
8886 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8889 \begin_layout Plain Layout
8897 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8900 \begin_layout Plain Layout
8901 \begin_inset Formula $\dasharrow$
8915 \begin_inset space \hfill{}
8921 \begin_layout Standard
8922 \begin_inset VSpace medskip
8925 Arrows used as accents like e.
8926 \begin_inset space \thinspace{}
8930 \begin_inset space \space{}
8933 vector arrows are listed in
8934 \begin_inset CommandInset ref
8936 reference "sec:Accents"
8943 \begin_layout Standard
8944 \begin_inset VSpace bigskip
8947 Furthermore there are the labeled arrows
8948 \begin_inset Index idx
8951 \begin_layout Plain Layout
8964 \begin_inset Index idx
8967 \begin_layout Plain Layout
8982 \begin_inset Index idx
8985 \begin_layout Plain Layout
8992 \begin_layout Plain Layout
9007 When inserting one of these commands in a formula, an arrow with two blue
9008 boxes appear where the label can be inserted.
9009 The length of the arrow adapts to the label width.
9012 \begin_layout Standard
9014 \begin_inset Tabular
9015 <lyxtabular version="3" rows="3" columns="2">
9016 <features tabularvalignment="middle">
9017 <column alignment="center" valignment="top" width="0pt">
9018 <column alignment="center" valignment="top" width="0pt">
9020 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9023 \begin_layout Plain Layout
9029 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9032 \begin_layout Plain Layout
9034 \begin_inset Note Note
9037 \begin_layout Plain Layout
9044 is only used as spacer.
9056 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9059 \begin_layout Plain Layout
9066 \begin_layout Plain Layout
9076 \begin_inset Formula $\downarrow$
9080 \begin_inset Formula $\to$
9088 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9091 \begin_layout Plain Layout
9092 \begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
9102 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9105 \begin_layout Plain Layout
9112 \begin_layout Plain Layout
9122 \begin_inset Formula $\downarrow$
9126 \begin_inset Formula $\to$
9134 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9137 \begin_layout Plain Layout
9138 \begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
9154 \begin_layout Subsection
9155 Vertical and diagonal Arrows
9156 \begin_inset Index idx
9159 \begin_layout Plain Layout
9166 \begin_inset Index idx
9169 \begin_layout Plain Layout
9178 \begin_layout Standard
9179 \begin_inset space \hfill{}
9183 \begin_inset Tabular
9184 <lyxtabular version="3" rows="7" columns="2">
9185 <features tabularvalignment="middle">
9186 <column alignment="center" valignment="top" width="0pt">
9187 <column alignment="center" valignment="top" width="0pt">
9189 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9192 \begin_layout Plain Layout
9198 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9201 \begin_layout Plain Layout
9209 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9212 \begin_layout Plain Layout
9220 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9223 \begin_layout Plain Layout
9224 \begin_inset Formula $\uparrow$
9234 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9237 \begin_layout Plain Layout
9245 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9248 \begin_layout Plain Layout
9249 \begin_inset Formula $\Uparrow$
9259 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9262 \begin_layout Plain Layout
9270 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9273 \begin_layout Plain Layout
9274 \begin_inset Formula $\updownarrow$
9284 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9287 \begin_layout Plain Layout
9295 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9298 \begin_layout Plain Layout
9299 \begin_inset Formula $\Updownarrow$
9309 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9312 \begin_layout Plain Layout
9320 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9323 \begin_layout Plain Layout
9324 \begin_inset Formula $\Downarrow$
9334 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9337 \begin_layout Plain Layout
9345 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9348 \begin_layout Plain Layout
9349 \begin_inset Formula $\downarrow$
9363 \begin_inset space \hfill{}
9367 \begin_inset Tabular
9368 <lyxtabular version="3" rows="5" columns="2">
9369 <features tabularvalignment="middle">
9370 <column alignment="center" valignment="top" width="0pt">
9371 <column alignment="center" valignment="top" width="0pt">
9373 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9376 \begin_layout Plain Layout
9382 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9385 \begin_layout Plain Layout
9393 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9396 \begin_layout Plain Layout
9404 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9407 \begin_layout Plain Layout
9408 \begin_inset Formula $\nearrow$
9418 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9421 \begin_layout Plain Layout
9429 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9432 \begin_layout Plain Layout
9433 \begin_inset Formula $\searrow$
9443 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9446 \begin_layout Plain Layout
9454 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9457 \begin_layout Plain Layout
9458 \begin_inset Formula $\swarrow$
9468 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9471 \begin_layout Plain Layout
9479 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9482 \begin_layout Plain Layout
9483 \begin_inset Formula $\nwarrow$
9497 \begin_inset space \hfill{}
9503 \begin_layout Standard
9504 \begin_inset VSpace medskip
9507 Vertical arrows can be used also as delimiters together with the commands
9509 \begin_inset CommandInset ref
9511 reference "sub:Manual-Bracket-Size"
9516 \begin_inset CommandInset ref
9518 reference "sub:Automatic-Bracket-Size"
9525 \begin_layout Section
9527 \begin_inset CommandInset label
9534 \begin_inset Index idx
9537 \begin_layout Plain Layout
9546 \begin_layout Standard
9547 Accents can be inserted via the math toolbar button
9548 \begin_inset Graphics
9549 filename ../images/math/hat.png
9554 or the commands listed in the following subsections.
9557 \begin_layout Subsection
9558 Accents for one Character
9562 \begin_layout Plain Layout
9575 \begin_layout Plain Layout
9577 \begin_inset CommandInset ref
9579 reference "sub:Accents-in-Text"
9592 \begin_layout Plain Layout
9600 \begin_inset Note Note
9603 \begin_layout Plain Layout
9610 is used to avoid that the footnote appears in the PDF-bookmark.
9613 \begin_layout Plain Layout
9621 \begin_inset CommandInset ref
9623 reference "sub:Formulas-in-Section"
9633 \begin_inset CommandInset label
9635 name "sub:Accents-for-one"
9640 \begin_inset Index idx
9643 \begin_layout Plain Layout
9644 Accents ! for one character
9652 \begin_layout Standard
9653 \begin_inset space \hfill{}
9657 \begin_inset Tabular
9658 <lyxtabular version="3" rows="8" columns="2">
9659 <features tabularvalignment="middle">
9660 <column alignment="center" valignment="top" width="0pt">
9661 <column alignment="center" valignment="top" width="0pt">
9663 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9666 \begin_layout Plain Layout
9672 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9675 \begin_layout Plain Layout
9677 \begin_inset Note Note
9680 \begin_layout Plain Layout
9687 is only used as spacer.
9699 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9702 \begin_layout Plain Layout
9709 \begin_layout Plain Layout
9723 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9726 \begin_layout Plain Layout
9727 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
9737 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9740 \begin_layout Plain Layout
9747 \begin_layout Plain Layout
9761 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9764 \begin_layout Plain Layout
9765 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
9775 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9778 \begin_layout Plain Layout
9785 \begin_layout Plain Layout
9799 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9802 \begin_layout Plain Layout
9803 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
9813 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9816 \begin_layout Plain Layout
9823 \begin_layout Plain Layout
9837 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9840 \begin_layout Plain Layout
9841 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
9851 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9854 \begin_layout Plain Layout
9861 \begin_layout Plain Layout
9871 \begin_inset Index idx
9874 \begin_layout Plain Layout
9885 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9888 \begin_layout Plain Layout
9889 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
9899 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9902 \begin_layout Plain Layout
9909 \begin_layout Plain Layout
9923 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9926 \begin_layout Plain Layout
9927 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
9937 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9940 \begin_layout Plain Layout
9947 \begin_layout Plain Layout
9961 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9964 \begin_layout Plain Layout
9965 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
9979 \begin_inset space \hfill{}
9983 \begin_inset Tabular
9984 <lyxtabular version="3" rows="7" columns="2">
9985 <features tabularvalignment="middle">
9986 <column alignment="center" valignment="top" width="0pt">
9987 <column alignment="center" valignment="top" width="0pt">
9989 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9992 \begin_layout Plain Layout
9998 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10001 \begin_layout Plain Layout
10009 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10012 \begin_layout Plain Layout
10019 \begin_layout Plain Layout
10033 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10036 \begin_layout Plain Layout
10037 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
10047 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10050 \begin_layout Plain Layout
10057 \begin_layout Plain Layout
10071 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10074 \begin_layout Plain Layout
10075 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
10085 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10088 \begin_layout Plain Layout
10095 \begin_layout Plain Layout
10109 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10112 \begin_layout Plain Layout
10113 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
10123 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10126 \begin_layout Plain Layout
10133 \begin_layout Plain Layout
10147 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10150 \begin_layout Plain Layout
10151 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
10161 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10164 \begin_layout Plain Layout
10171 \begin_layout Plain Layout
10185 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10188 \begin_layout Plain Layout
10189 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
10199 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10202 \begin_layout Plain Layout
10209 \begin_layout Plain Layout
10223 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10226 \begin_layout Plain Layout
10227 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
10241 \begin_inset space \hfill{}
10247 \begin_layout Standard
10248 \begin_inset VSpace bigskip
10254 \begin_layout Standard
10255 You can directly insert accents like é to formulas.
10256 LyX will transform them to the corresponding accent command.
10258 \begin_inset Index idx
10261 \begin_layout Plain Layout
10267 it is better to insert a quotation mark before the vowel.
10268 These two characters are then treated by LaTeX as
10272 character when the formula part with the umlaut is marked as German.
10280 \begin_inset Quotes eld
10284 \begin_inset Quotes erd
10287 umlauts are created as demonstrated in the following example:
10290 \begin_layout Standard
10291 \begin_inset VSpace -2mm
10297 \begin_layout Standard
10299 \begin_inset Tabular
10300 <lyxtabular version="3" rows="3" columns="2">
10301 <features tabularvalignment="middle">
10302 <column alignment="center" valignment="top" width="0">
10303 <column alignment="center" valignment="top" width="0">
10305 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10308 \begin_layout Plain Layout
10314 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10317 \begin_layout Plain Layout
10319 \begin_inset Note Note
10322 \begin_layout Plain Layout
10330 \begin_inset space \thinspace{}
10333 pt space are only used as spacer.
10345 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10348 \begin_layout Plain Layout
10351 \begin_inset Quotes grd
10359 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10362 \begin_layout Plain Layout
10363 \begin_inset space \hspace{}
10370 \begin_inset Formula $"i$
10380 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10383 \begin_layout Plain Layout
10390 \begin_layout Plain Layout
10404 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10407 \begin_layout Plain Layout
10408 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
10424 \begin_layout Standard
10425 Another advantage to
10431 is that umlauts can directly be converted to mathematical text because
10432 the accent commands above are
10438 in mathematical text
10441 To convert an accented character to mathematical text, only the character
10442 under the accent may be converted.
10443 This applies also for all other conversions, e.
10444 \begin_inset space \thinspace{}
10448 \begin_inset space \space{}
10454 \begin_layout Standard
10455 In mathematical text, umlauts and other accented characters can directly
10459 \begin_layout Subsection
10460 Accents for Operators
10461 \begin_inset Index idx
10464 \begin_layout Plain Layout
10465 Accents ! for operators
10473 \begin_layout Standard
10481 \begin_inset Index idx
10484 \begin_layout Plain Layout
10499 \begin_inset Index idx
10502 \begin_layout Plain Layout
10510 characters can be placed above or below an operator, respectively, to accent
10519 \begin_inset Index idx
10522 \begin_layout Plain Layout
10530 characters can be set before and behind an operator.
10531 The command scheme is:
10534 \begin_layout Standard
10550 \begin_layout Standard
10557 must always be before the operator that should be accented.
10558 You can accent with several characters and even with other operators and
10566 for example only characters behind an operator, write nothing between the
10567 first braces but don't omit the braces.
10570 \begin_layout Standard
10571 For example the command
10576 \begin_inset Formula $\to$
10586 \begin_inset Formula $\to$
10595 \begin_layout Plain Layout
10611 \begin_inset Formula
10613 \sideset{}{'}\sum_{k=1}^{n}
10621 \begin_layout Standard
10630 \begin_layout Plain Layout
10645 \begin_layout Plain Layout
10657 \begin_inset Formula $\uparrow$
10665 \begin_inset Formula
10667 \overset{a}{\maltese}
10672 As seen in the last example, with
10684 symbols and characters can also be accented; with
10690 this is not possible.
10693 \begin_layout Subsection
10694 Accents for several Characters
10695 \begin_inset Index idx
10698 \begin_layout Plain Layout
10699 Accents ! for several characters
10707 \begin_layout Standard
10708 \begin_inset space \hfill{}
10712 \begin_inset Tabular
10713 <lyxtabular version="3" rows="5" columns="2">
10714 <features tabularvalignment="middle">
10715 <column alignment="center" valignment="top" width="0pt">
10716 <column alignment="center" valignment="top" width="0pt">
10718 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10721 \begin_layout Plain Layout
10727 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10730 \begin_layout Plain Layout
10732 \begin_inset Note Note
10735 \begin_layout Plain Layout
10742 is only used as spacer.
10754 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10757 \begin_layout Plain Layout
10764 \begin_layout Plain Layout
10778 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10781 \begin_layout Plain Layout
10782 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
10792 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10795 \begin_layout Plain Layout
10802 \begin_layout Plain Layout
10816 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10819 \begin_layout Plain Layout
10820 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
10830 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10833 \begin_layout Plain Layout
10840 \begin_layout Plain Layout
10854 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10857 \begin_layout Plain Layout
10858 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
10868 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10871 \begin_layout Plain Layout
10874 underleftrightarrow
10878 \begin_layout Plain Layout
10892 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10895 \begin_layout Plain Layout
10896 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
10910 \begin_inset space \hfill{}
10914 \begin_inset Tabular
10915 <lyxtabular version="3" rows="5" columns="2">
10916 <features tabularvalignment="middle">
10917 <column alignment="center" valignment="top" width="0pt">
10918 <column alignment="center" valignment="top" width="0pt">
10920 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10923 \begin_layout Plain Layout
10929 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10932 \begin_layout Plain Layout
10940 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10943 \begin_layout Plain Layout
10950 \begin_layout Plain Layout
10964 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10967 \begin_layout Plain Layout
10968 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
10978 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10981 \begin_layout Plain Layout
10988 \begin_layout Plain Layout
11002 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11005 \begin_layout Plain Layout
11006 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
11016 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11019 \begin_layout Plain Layout
11026 \begin_layout Plain Layout
11040 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11043 \begin_layout Plain Layout
11044 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
11054 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11057 \begin_layout Plain Layout
11064 \begin_layout Plain Layout
11078 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11081 \begin_layout Plain Layout
11082 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
11096 \begin_inset space \hfill{}
11102 \begin_layout Standard
11103 \begin_inset VSpace medskip
11106 With these commands as many characters as you like can be accented.
11119 will only be set in the output with a length of three characters, as shown
11120 in the following example:
11121 \begin_inset Formula
11123 \widetilde{A+B=C-D}
11131 \begin_layout Standard
11139 \begin_inset Index idx
11142 \begin_layout Plain Layout
11157 \begin_inset Index idx
11160 \begin_layout Plain Layout
11168 described in the previous subsection it is also possible to accent several
11178 \begin_layout Plain Layout
11188 \begin_inset Formula $\downarrow$
11194 \begin_inset Formula
11196 \underset{***}{A=B}
11204 \begin_layout Section
11206 \begin_inset CommandInset label
11213 \begin_inset Index idx
11216 \begin_layout Plain Layout
11225 \begin_layout Subsection
11227 \begin_inset CommandInset label
11229 name "sub:Predefined-Space"
11234 \begin_inset Index idx
11237 \begin_layout Plain Layout
11238 Space ! horizontal ! predefined
11246 \begin_layout Standard
11247 Sometimes it is necessary to insert horizontal space into a formula.
11248 This is done by inserting a protected space (shortcut
11251 arg "command-alternatives space-insert protected ; math-space"
11256 \begin_inset Quotes eld
11265 \begin_layout Plain Layout
11277 \begin_inset Quotes erd
11280 appears and by pressing
11284 several times one can select one of eight different space sizes.
11285 The spaces can also be inserted using the math toolbar button
11286 \begin_inset Graphics
11287 filename ../images/math/space.png
11292 or special commands.
11293 Independent from the inserted command, one can select the size again by
11301 \begin_layout Standard
11304 \begin_inset VSpace -5mm
11308 \begin_inset Tabular
11309 <lyxtabular version="3" rows="3" columns="7">
11310 <features tabularvalignment="middle">
11311 <column alignment="center" valignment="middle" width="6.8cm">
11312 <column alignment="center" valignment="top" width="0">
11313 <column alignment="center" valignment="top" width="0">
11314 <column alignment="center" valignment="top" width="0">
11315 <column alignment="center" valignment="top" width="0">
11316 <column alignment="center" valignment="top" width="0">
11317 <column alignment="center" valignment="top" width="0">
11319 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11322 \begin_layout Plain Layout
11328 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11331 \begin_layout Plain Layout
11339 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11342 \begin_layout Plain Layout
11350 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11353 \begin_layout Plain Layout
11361 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11364 \begin_layout Plain Layout
11372 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11375 \begin_layout Plain Layout
11383 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11386 \begin_layout Plain Layout
11396 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11399 \begin_layout Plain Layout
11404 keystrokes after inserting the protected space
11409 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11412 \begin_layout Plain Layout
11418 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11421 \begin_layout Plain Layout
11427 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11430 \begin_layout Plain Layout
11436 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11439 \begin_layout Plain Layout
11445 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11448 \begin_layout Plain Layout
11454 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11457 \begin_layout Plain Layout
11465 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11468 \begin_layout Plain Layout
11474 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11477 \begin_layout Plain Layout
11478 \begin_inset Formula $A\, B$
11486 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11489 \begin_layout Plain Layout
11490 \begin_inset Formula $A\: B$
11498 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11501 \begin_layout Plain Layout
11502 \begin_inset Formula $A\; B$
11510 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11513 \begin_layout Plain Layout
11514 \begin_inset Formula $A\quad B$
11522 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11525 \begin_layout Plain Layout
11526 \begin_inset Formula $A\qquad B$
11534 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11537 \begin_layout Plain Layout
11538 \begin_inset Formula $A\! B$
11554 \begin_layout Standard
11555 The last size seem to produce no space.
11556 It is displayed red in LyX contrary to the other sizes, because it is a
11558 There are two more negative spaces:
11561 \begin_layout Standard
11563 \begin_inset Tabular
11564 <lyxtabular version="3" rows="3" columns="3">
11565 <features tabularvalignment="middle">
11566 <column alignment="center" valignment="middle" width="6.8cm">
11567 <column alignment="center" valignment="top" width="0pt">
11568 <column alignment="center" valignment="top" width="0pt">
11570 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11573 \begin_layout Plain Layout
11579 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11582 \begin_layout Plain Layout
11590 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11593 \begin_layout Plain Layout
11603 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11606 \begin_layout Plain Layout
11611 keystrokes after inserting the protected space
11616 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11619 \begin_layout Plain Layout
11625 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11628 \begin_layout Plain Layout
11636 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11639 \begin_layout Plain Layout
11645 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11648 \begin_layout Plain Layout
11649 \begin_inset Formula $A\negmedspace B$
11657 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11660 \begin_layout Plain Layout
11661 \begin_inset Formula $A\negthickspace B$
11677 \begin_layout Standard
11678 Negative spaces can lead to characters overlapping each other.
11679 Thus they can be used to enforce ligatures, which are e.
11680 \begin_inset space \thinspace{}
11684 \begin_inset space \space{}
11687 useful for summation operators:
11690 \begin_layout Standard
11692 \begin_inset Tabular
11693 <lyxtabular version="3" rows="3" columns="2">
11694 <features tabularvalignment="middle">
11695 <column alignment="center" valignment="top" width="0">
11696 <column alignment="center" valignment="top" width="0">
11698 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11701 \begin_layout Plain Layout
11707 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11710 \begin_layout Plain Layout
11712 \begin_inset Note Note
11715 \begin_layout Plain Layout
11722 is only used as spacer.
11734 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11737 \begin_layout Plain Layout
11746 \begin_layout Plain Layout
11760 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11763 \begin_layout Plain Layout
11764 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
11774 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11777 \begin_layout Plain Layout
11788 \begin_layout Plain Layout
11802 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11805 \begin_layout Plain Layout
11806 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
11822 \begin_layout Standard
11823 Relations like for example equal signs, are always surrounded by space.
11824 To suppress this, the equal sign is placed into a TeX-brace.
11825 The following example demonstrates this:
11828 \begin_layout Standard
11830 \begin_inset Tabular
11831 <lyxtabular version="3" rows="2" columns="2">
11832 <features tabularvalignment="middle">
11833 <column alignment="center" valignment="top" width="0pt">
11834 <column alignment="center" valignment="top" width="0pt">
11836 <cell alignment="center" valignment="top" usebox="none">
11839 \begin_layout Plain Layout
11845 <cell alignment="center" valignment="top" usebox="none">
11848 \begin_layout Plain Layout
11849 \begin_inset Formula $A=B$
11859 <cell alignment="center" valignment="top" usebox="none">
11862 \begin_layout Plain Layout
11863 \begin_inset Note Note
11866 \begin_layout Plain Layout
11873 is only used as spacer.
11879 \begin_inset Formula $\raisebox{5mm}{}$
11882 equation without space
11887 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11890 \begin_layout Plain Layout
11891 \begin_inset Formula $A{=}B$
11907 \begin_layout Standard
11909 The command for the last formula is:
11914 \begin_inset Formula $\to$
11920 \begin_layout Standard
11921 \begin_inset VSpace bigskip
11924 Spaces are needed for physical units, because the space between the value
11925 and the unit is the smallest one and not a normal space.
11926 For units in text, the smallest space is inserted via the menu
11928 Insert\SpecialChar \menuseparator
11929 Formatting\SpecialChar \menuseparator
11931 \begin_inset space ~
11939 arg "space-insert thin"
11945 \begin_layout Standard
11946 An example to visualize the difference:
11949 \begin_layout Standard
11950 \begin_inset Tabular
11951 <lyxtabular version="3" rows="2" columns="2">
11952 <features tabularvalignment="middle">
11953 <column alignment="left" valignment="top" width="0">
11954 <column alignment="left" valignment="top" width="0">
11956 <cell alignment="center" valignment="top" usebox="none">
11959 \begin_layout Plain Layout
11961 \begin_inset Formula $\cdot$
11969 <cell alignment="center" valignment="top" usebox="none">
11972 \begin_layout Plain Layout
11973 space between value and unit
11980 <cell alignment="center" valignment="top" usebox="none">
11983 \begin_layout Plain Layout
11985 \begin_inset space \thinspace{}
11989 \begin_inset Formula $\cdot$
11997 <cell alignment="center" valignment="top" usebox="none">
12000 \begin_layout Plain Layout
12001 smallest space between value and unit
12014 \begin_layout Subsection
12019 \begin_layout Plain Layout
12032 \begin_layout Plain Layout
12033 for vertical space in formulas see
12034 \begin_inset CommandInset ref
12036 reference "sub:Line-Separation"
12049 \begin_layout Plain Layout
12057 \begin_inset Note Note
12060 \begin_layout Plain Layout
12063 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
12066 \begin_layout Plain Layout
12069 texorpdfstring is in section
12070 \begin_inset CommandInset ref
12072 reference "sub:Formulas-in-Section"
12082 \begin_inset CommandInset label
12084 name "sub:Variable-Space"
12089 \begin_inset Index idx
12092 \begin_layout Plain Layout
12093 Space ! horizontal ! variable
12101 \begin_layout Standard
12102 Space with a defined length can be inserted with the command
12109 \begin_inset Index idx
12112 \begin_layout Plain Layout
12122 \begin_inset Quotes eld
12131 \begin_layout Plain Layout
12143 \begin_inset Quotes erd
12147 The length can be specified by left-clicking on the
12148 \begin_inset Quotes eld
12157 \begin_layout Plain Layout
12169 \begin_inset Quotes erd
12173 The length may also be negative.
12174 To insert as much space as is available, the command
12181 \begin_inset Index idx
12184 \begin_layout Plain Layout
12195 \begin_layout Standard
12196 \begin_inset VSpace -1mm
12202 \begin_layout Standard
12204 \begin_inset Tabular
12205 <lyxtabular version="3" rows="4" columns="2">
12206 <features tabularvalignment="middle">
12207 <column alignment="center" valignment="top" width="0">
12208 <column alignment="center" valignment="top" width="0">
12210 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12213 \begin_layout Plain Layout
12221 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12224 \begin_layout Plain Layout
12232 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12235 \begin_layout Plain Layout
12242 \begin_layout Plain Layout
12252 \begin_inset Formula $\to$
12258 \begin_inset space \thinspace{}
12266 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12269 \begin_layout Plain Layout
12270 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
12280 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12283 \begin_layout Plain Layout
12290 \begin_layout Plain Layout
12300 \begin_inset Formula $\to$
12306 \begin_inset space \thinspace{}
12314 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12317 \begin_layout Plain Layout
12318 \begin_inset Formula $A\hspace{-1mm}A\not=A$
12328 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12331 \begin_layout Plain Layout
12338 \begin_layout Plain Layout
12352 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12355 \begin_layout Plain Layout
12356 \begin_inset Formula $A=A\hfill B=B$
12372 \begin_layout Standard
12373 In the last example the available space is given by the longest column entry
12375 In an inline formula the space depends on the length of the line in which
12383 Thus, when the line uses the full width, no space will be created.
12390 only has an effect on displayed formulas when the formula style
12395 (Formula styles are explained in
12396 \begin_inset CommandInset ref
12398 reference "sec:Formula-Styles"
12405 \begin_layout Standard
12412 , there are the commands
12424 that fill the space with a pattern, see
12425 \begin_inset CommandInset ref
12427 reference "sub:Ellipses"
12434 \begin_layout Standard
12435 For text, variable space can be inserted via the menu
12437 Insert\SpecialChar \menuseparator
12438 Formatting\SpecialChar \menuseparator
12440 \begin_inset space ~
12448 \begin_layout Standard
12449 This is a line with
12450 \begin_inset space \hspace{}
12455 \begin_inset space \thinspace{}
12461 \begin_layout Standard
12462 This is a line with
12463 \begin_inset space \hfill{}
12469 \begin_layout Subsection
12470 Space besides inline Formulas
12471 \begin_inset Index idx
12474 \begin_layout Plain Layout
12475 Space ! besides inline formulas
12483 \begin_layout Standard
12484 The space that surrounds inline formulas can be adjusted with the length
12492 \begin_inset Index idx
12495 \begin_layout Plain Layout
12504 The value of a length is set with the command
12511 \begin_inset Index idx
12514 \begin_layout Plain Layout
12522 which has the following scheme:
12525 \begin_layout Standard
12530 setlength{length name}{value}
12533 \begin_layout Standard
12541 \begin_inset space \thinspace{}
12547 \begin_layout Standard
12557 \begin_layout Standard
12558 is inserted in TeX-mode.
12560 \begin_inset space \thinspace{}
12563 mm space will now be set around all inline formulas:
12567 \begin_layout Plain Layout
12581 \begin_layout Standard
12582 This is a line with an inline formula
12583 \begin_inset Formula $A=B$
12587 \begin_inset space \thinspace{}
12590 mm surrounding space.
12594 \begin_layout Plain Layout
12608 \begin_layout Standard
12609 To return to the predefined value,
12615 is set to the value 0
12616 \begin_inset space \thinspace{}
12622 \begin_layout Section
12624 \begin_inset Index idx
12627 \begin_layout Plain Layout
12634 \begin_inset Index idx
12637 \begin_layout Plain Layout
12642 \begin_layout Plain Layout
12653 \begin_layout Plain Layout
12668 \begin_layout Standard
12669 Boxes for text are described in chapter
12676 \begin_inset space ~
12684 \begin_layout Subsection
12686 \begin_inset CommandInset label
12688 name "sub:Boxes-with-Frame"
12693 \begin_inset Index idx
12696 \begin_layout Plain Layout
12705 \begin_layout Standard
12706 It is possible to frame a formula or part of one with the commands
12713 \begin_inset Index idx
12716 \begin_layout Plain Layout
12731 \begin_inset Index idx
12734 \begin_layout Plain Layout
12745 \begin_layout Standard
12746 When one of these commands is inserted in a formula, a blue box appears
12747 within a frame to enter formula parts.
12754 an additional formula has to be created by
12758 within this box, because the box content will otherwise be treated as mathemati
12766 is used, a new formula is automatically created inside the frame.
12769 \begin_layout Standard
12776 is not suitable to frame displayed formulas because the formula will always
12777 be set in the size of the text.
12784 is in contrary not suitable to frame inline formulas, because the formula
12785 will always be set in the size of a displayed formula.
12788 \begin_layout Standard
12802 \begin_inset Index idx
12805 \begin_layout Plain Layout
12813 where additionally the frame width and the alignment can be specified.
12820 is used in the following scheme:
12823 \begin_layout Standard
12828 framebox[frame width][position]{box content}
12831 \begin_layout Standard
12832 The position can either be
12849 right aligns the formula in the box.
12850 When no position is given, the formula will be centered.
12851 \begin_inset Newline newline
12854 If no width is given, also no position can be given.
12855 In this case the frame width is adjusted to the box content like for
12864 \begin_layout Standard
12871 is inserted, a box appears containing three blue boxes.
12872 The first two boxes are surrounded by brackets and denote the two optional
12874 The third box is for formula parts like for
12883 \begin_layout Standard
12885 \begin_inset Tabular
12886 <lyxtabular version="3" rows="5" columns="2">
12887 <features tabularvalignment="middle">
12888 <column alignment="center" valignment="top" width="0">
12889 <column alignment="center" valignment="top" width="0">
12891 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12894 \begin_layout Plain Layout
12900 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12903 \begin_layout Plain Layout
12905 \begin_inset Note Note
12908 \begin_layout Plain Layout
12915 is only used as spacer.
12927 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12930 \begin_layout Plain Layout
12937 \begin_layout Plain Layout
12956 \begin_layout Plain Layout
12970 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12973 \begin_layout Plain Layout
12974 \begin_inset Formula $\raisebox{6mm}{}\fbox{\ensuremath{\int A=B}}\raisebox{-4mm}{}$
12984 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12987 \begin_layout Plain Layout
12994 \begin_layout Plain Layout
13009 \begin_layout Plain Layout
13023 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13026 \begin_layout Plain Layout
13027 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
13037 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13040 \begin_layout Plain Layout
13047 \begin_layout Plain Layout
13061 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13064 \begin_layout Plain Layout
13065 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
13075 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13078 \begin_layout Plain Layout
13085 \begin_layout Plain Layout
13095 \begin_inset Formula $\to$
13099 \begin_inset Formula $\to$
13112 \begin_layout Plain Layout
13122 \begin_inset Formula $\downarrow$
13130 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13133 \begin_layout Plain Layout
13134 \begin_inset Formula $\raisebox{6mm}{}$
13138 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
13142 \begin_inset Formula $\raisebox{-4mm}{}$
13158 \begin_layout Standard
13159 The frame thickness can also be adjusted.
13160 To do this the following commands have to be inserted in TeX-mode before
13164 \begin_layout Standard
13174 \begin_inset Quotes eld
13178 \begin_inset Quotes erd
13192 \begin_inset Quotes eld
13196 \begin_inset Quotes erd
13202 \begin_layout Standard
13203 \begin_inset Quotes eld
13207 \begin_inset Quotes erd
13210 specifies the minimal distance between the frame and the first character
13212 An example for this is the following framed formula:
13216 \begin_layout Plain Layout
13228 \begin_inset Formula
13235 Before this formula the commands
13238 \begin_layout Standard
13260 \begin_layout Standard
13261 were inserted in TeX-mode.
13262 The given values are used for all following boxes.
13265 \begin_layout Standard
13266 To return to the standard frame size, the command
13269 \begin_layout Standard
13294 \begin_layout Plain Layout
13308 \begin_layout Standard
13309 is inserted in TeX-mode before the next formula.
13312 \begin_layout Subsection
13313 Boxes without Frame
13314 \begin_inset CommandInset label
13316 name "sub:Boxes-without-Frame"
13321 \begin_inset Index idx
13324 \begin_layout Plain Layout
13325 Boxes ! without frame
13333 \begin_layout Standard
13334 For boxes without a frame there are the following box commands:
13341 \begin_inset Index idx
13344 \begin_layout Plain Layout
13359 \begin_inset Index idx
13362 \begin_layout Plain Layout
13377 \begin_inset Index idx
13380 \begin_layout Plain Layout
13391 \begin_layout Standard
13398 a box can be super- or subscripted.
13399 But in contrary to normal super- and subscripting, the characters in the
13400 box keep their font size.
13407 is used in the following scheme:
13410 \begin_layout Standard
13415 raisebox{height}{box content}
13418 \begin_layout Standard
13419 When the box should contain a formula, an extra formula is needed like for
13430 \begin_inset Note Greyedout
13433 \begin_layout Plain Layout
13444 this extra formula is created by pressing
13448 twice instead of once because LyX doesn't yet support
13462 \begin_layout Standard
13464 \begin_inset Tabular
13465 <lyxtabular version="3" rows="4" columns="2">
13466 <features tabularvalignment="middle">
13467 <column alignment="center" valignment="top" width="0">
13468 <column alignment="center" valignment="top" width="0">
13470 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13473 \begin_layout Plain Layout
13479 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13482 \begin_layout Plain Layout
13490 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13493 \begin_layout Plain Layout
13497 \begin_inset Formula $\to$
13503 \begin_inset Formula $\to$
13511 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13514 \begin_layout Plain Layout
13515 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13525 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13528 \begin_layout Plain Layout
13532 \begin_inset Formula $\to$
13538 \begin_inset Formula $\to$
13546 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13549 \begin_layout Plain Layout
13550 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13560 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13563 \begin_layout Plain Layout
13567 \begin_inset Formula $\to$
13586 \begin_layout Plain Layout
13600 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13603 \begin_layout Plain Layout
13604 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
13620 \begin_layout Standard
13645 , with the difference that there is no frame.
13648 \begin_layout Subsection
13650 \begin_inset CommandInset label
13652 name "sub:Colored-Boxes"
13657 \begin_inset Index idx
13660 \begin_layout Plain Layout
13669 \begin_layout Standard
13670 To be able to use all commands explained in this section, the LaTeX-package
13679 \begin_layout Plain Layout
13684 is part of every LaTeX standard installation.
13690 \begin_inset Index idx
13693 \begin_layout Plain Layout
13699 has to be loaded in the LaTeX-preamble with the line
13703 \begin_layout Plain Layout
13704 When text is colored somewhere in the document with a predefined color,
13705 LyX loads the LaTeX-package
13710 Thus it is possible that the package is loaded twice, but this does not
13717 \begin_inset Note Note
13720 \begin_layout Plain Layout
13721 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
13730 \begin_layout Standard
13738 \begin_layout Standard
13739 \begin_inset VSpace medskip
13742 To color boxes, the command
13749 \begin_inset Index idx
13752 \begin_layout Plain Layout
13760 is used in the following scheme:
13763 \begin_layout Standard
13768 colorbox{color}{box content}
13771 \begin_layout Standard
13772 The box content can also be a box and a
13778 can also be part of another box (see the 2nd and 3rd example).
13779 When the box should contain a formula, an extra formula has to be created,
13780 the same way as for
13790 \begin_layout Plain Layout
13791 This also applies for the command
13805 \begin_layout Standard
13806 One of the following predefined colors can be chosen:
13809 \begin_layout Standard
13843 \begin_layout Standard
13845 \begin_inset Tabular
13846 <lyxtabular version="3" rows="4" columns="2">
13847 <features tabularvalignment="middle">
13848 <column alignment="center" valignment="top" width="0">
13849 <column alignment="center" valignment="top" width="0">
13851 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13854 \begin_layout Plain Layout
13860 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13863 \begin_layout Plain Layout
13865 \begin_inset Note Note
13868 \begin_layout Plain Layout
13875 is only used as spacer.
13887 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13890 \begin_layout Plain Layout
13894 \begin_inset Formula $\to$
13904 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13907 \begin_layout Plain Layout
13908 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
13918 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13921 \begin_layout Plain Layout
13925 \begin_inset Formula $\to$
13936 \begin_layout Plain Layout
13950 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13953 \begin_layout Plain Layout
13954 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
13964 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13967 \begin_layout Plain Layout
13974 \begin_layout Plain Layout
13986 \begin_inset Formula $\to$
14005 \begin_layout Plain Layout
14019 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14022 \begin_layout Plain Layout
14023 \begin_inset Formula $\raisebox{7mm}{}\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}\raisebox{-5mm}{}$
14039 \begin_layout Standard
14046 only colors the box but not the characters in the box.
14047 To color all characters, the whole formula is highlighted and the desired
14048 color is chosen in the
14051 \begin_inset space ~
14057 The dialog can be called with the toolbar button
14058 \begin_inset Graphics
14059 filename ../images/dialog-show_character.png
14066 Edit\SpecialChar \menuseparator
14068 \begin_inset space ~
14071 Style\SpecialChar \menuseparator
14075 The formula number then has the same color as the formula.
14076 When the formula number should get another color than the formula characters,
14077 the color must be changed within the formula.
14080 \begin_layout Standard
14084 \begin_layout Standard
14087 \begin_inset Formula
14089 \int A=B\label{eq:red}
14097 \begin_inset Formula
14099 \textcolor{red}{\int A=B}\label{eq:redgreen}
14107 \begin_layout Standard
14109 \begin_inset CommandInset ref
14115 is completely colored red.
14116 \begin_inset Newline newline
14120 \begin_inset CommandInset ref
14122 reference "eq:redgreen"
14126 was first completely colored green to set the color for the formula number.
14127 Subsequently the formula characters were colored red.
14130 \begin_layout Standard
14131 \begin_inset VSpace bigskip
14134 To color the frame different than the rest of the box, the command
14141 \begin_inset Index idx
14144 \begin_layout Plain Layout
14152 is used in the following scheme:
14155 \begin_layout Standard
14160 fcolorbox{frame color}{color}{box content}
14163 \begin_layout Standard
14170 is an extension of the command
14177 The frame width is set, like for
14200 \begin_layout Plain Layout
14212 \begin_inset Formula
14214 \fcolorbox{cyan}{magenta}{A=B}
14223 \begin_layout Plain Layout
14237 \begin_layout Standard
14238 This formula was created with the command
14239 \begin_inset Newline newline
14247 \begin_inset Formula $\to$
14253 \begin_inset Formula $\to$
14263 \begin_layout Standard
14264 \begin_inset VSpace bigskip
14267 To use other colors than the predefined ones, they have to be defined first.
14270 \begin_layout Standard
14271 One can for example define the color
14272 \begin_inset Quotes eld
14280 \begin_inset Quotes erd
14283 with the LaTeX-preamble line:
14286 \begin_layout Standard
14291 definecolor{darkgreen}{cmyk}{0.5,
14306 \begin_inset Index idx
14309 \begin_layout Plain Layout
14320 \begin_layout Standard
14325 is the color space that denotes the colors
14342 The four comma separated numbers are the portion factor for the corresponding
14343 colors of the color space.
14344 The factors can be in the range of 0
14345 \begin_inset space \thinspace{}
14349 \begin_inset space \thinspace{}
14357 also the color space
14361 can be used for definitions.
14378 , so that there are in this case three portion factors for the corresponding
14380 Furthermore there is the color space
14384 with one portion factor for the gray value.
14387 \begin_layout Standard
14388 As example a framed box with the new defined color
14392 where the characters have been colored
14397 \begin_inset Formula
14399 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}
14407 \begin_layout Standard
14408 Self-defined colors can also be used for text with the help of the command
14416 \begin_inset Index idx
14419 \begin_layout Plain Layout
14428 \begin_layout Standard
14432 \begin_layout Plain Layout
14436 textcolor{darkgreen}{
14442 \begin_inset Quotes eld
14446 \begin_inset Quotes erd
14453 \begin_layout Plain Layout
14463 \begin_layout Standard
14471 \begin_inset Index idx
14474 \begin_layout Plain Layout
14482 is used in the scheme
14486 textcolor{color}{characters to color}
14491 \begin_layout Subsection
14493 \begin_inset CommandInset label
14495 name "sub:Paragraph-Boxes"
14500 \begin_inset Index idx
14503 \begin_layout Plain Layout
14504 Boxes ! as paragraph
14512 \begin_layout Standard
14513 A box that can contain several lines and paragraphs, a so-called paragraph
14514 box (parbox), can be created with the menu
14516 Insert\SpecialChar \menuseparator
14519 or the toolbar button
14520 \begin_inset Graphics
14521 filename ../images/box-insert.png
14529 \begin_layout Standard
14530 The following example shows a framed parbox in a line:
14533 \begin_layout Standard
14534 \begin_inset VSpace medskip
14538 \begin_inset Box Boxed
14548 height_special "totalheight"
14551 \begin_layout Plain Layout
14552 This is a paragraph box.
14554 \begin_inset space \thinspace{}
14557 cm long and can also contain formulas:
14558 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14569 \begin_layout Standard
14570 \begin_inset VSpace medskip
14576 \begin_layout Standard
14577 Such a box is created by right-clicking on the gray box inset.
14578 A dialog pops up showing the box properties.
14592 \begin_inset space \thinspace{}
14597 Vertical Box Alignment
14602 \begin_layout Standard
14603 \begin_inset VSpace medskip
14606 In LaTeX a parbox is created with the command
14613 \begin_inset Index idx
14616 \begin_layout Plain Layout
14624 which has the following scheme:
14627 \begin_layout Standard
14632 parbox[position]{width}{box content}
14635 \begin_layout Standard
14650 \begin_inset Quotes eld
14654 \begin_inset Quotes erd
14657 means that the box is aligned within the surrounding text with its last
14664 \begin_inset Quotes eld
14668 \begin_inset Quotes erd
14671 this is done with the first line.
14672 When no position is given, the box will be vertically centered, see section
14680 \begin_inset space ~
14685 manual for examples.
14688 \begin_layout Standard
14689 \begin_inset VSpace bigskip
14692 To frame formulas completely, including the formula number, the formula
14693 must be set into a parbox.
14694 To do this, the command
14708 is inserted in TeX-mode before the formula.
14716 \begin_inset Index idx
14719 \begin_layout Plain Layout
14727 is hereby the line width set for the document.
14728 Because the frame is outside the parbox, 2
14729 \begin_inset space \thinspace{}
14732 times the frame separation and the frame thickness must be subtracted from
14734 As this is not automatically done by LyX due to a bug
14738 \begin_layout Plain Layout
14739 \begin_inset CommandInset href
14741 name "LyX-bug #4483"
14742 target "http://www.lyx.org/trac/ticket/4483"
14751 , TeX-mode has to be used.
14752 To be able to multiply and subtract in arguments, the LaTeX-package
14760 \begin_layout Plain Layout
14765 is part of every LaTeX standard installation.
14771 \begin_inset Index idx
14774 \begin_layout Plain Layout
14780 must be loaded in the LaTeX-preamble with the line
14783 \begin_layout Standard
14791 \begin_layout Standard
14792 Behind the formula both boxes are closed by entering
14797 Here is an example:
14801 \begin_layout Plain Layout
14815 \begin_layout Standard
14819 \begin_layout Plain Layout
14837 \begin_inset Formula
14839 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}
14848 \begin_layout Plain Layout
14859 \begin_layout Plain Layout
14873 \begin_layout Standard
14874 \begin_inset VSpace medskip
14877 As a parbox is used as the argument of
14883 , there is in this case no difference between
14898 \begin_layout Standard
14899 \begin_inset VSpace bigskip
14902 Paragraph boxes are very useful to comment formulas directly.
14909 is used in combination with the command
14923 \begin_inset CommandInset ref
14925 reference "sub:User-defined-Numbering"
14932 \begin_layout Standard
14933 An example of a formula commented with
14942 \begin_layout Standard
14946 \begin_layout Plain Layout
14959 This is a description.
14960 It is distinctly separated from the formula and multiline.
14964 \begin_layout Plain Layout
14976 \begin_layout Standard
14977 Such a formula must be inserted completely in TeX-mode because LyX does
14978 not yet support the command
14985 The formula is created with the following command sequence:
14988 \begin_layout Standard
15001 is inserted in TeX-mode.
15005 \begin_layout Plain Layout
15006 When the formula style
15018 can also be replaced by
15025 (formula styles see
15026 \begin_inset CommandInset ref
15028 reference "sec:Formula-Styles"
15037 Then the description follows as normal text and finally
15043 is inserted in TeX-mode.
15056 hereby create a displayed formula.
15059 \begin_layout Standard
15066 can be seen in this example that was
15067 \begin_inset Quotes eld
15071 \begin_inset Quotes erd
15074 using the mathematical textmode:
15075 \begin_inset Formula
15077 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}
15085 \begin_layout Section
15087 \begin_inset Index idx
15090 \begin_layout Plain Layout
15099 \begin_layout Subsection
15101 \begin_inset CommandInset label
15103 name "sub:Big-Operators"
15108 \begin_inset Index idx
15111 \begin_layout Plain Layout
15118 \begin_inset Index idx
15121 \begin_layout Plain Layout
15128 \begin_inset Index idx
15131 \begin_layout Plain Layout
15140 \begin_layout Standard
15141 To be able to use all integral operators listed here, the option
15143 Use esint package automatically
15145 must be set in the document settings under
15148 \begin_inset space ~
15156 \begin_layout Standard
15157 \begin_inset space \hfill{}
15161 \begin_inset Tabular
15162 <lyxtabular version="3" rows="11" columns="2">
15163 <features tabularvalignment="middle">
15164 <column alignment="center" valignment="top" width="0pt">
15165 <column alignment="center" valignment="top" width="0pt">
15167 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15170 \begin_layout Plain Layout
15176 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15179 \begin_layout Plain Layout
15187 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15190 \begin_layout Plain Layout
15194 \begin_inset Index idx
15197 \begin_layout Plain Layout
15210 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15213 \begin_layout Plain Layout
15214 \begin_inset Formula $\int$
15224 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15227 \begin_layout Plain Layout
15235 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15238 \begin_layout Plain Layout
15239 \begin_inset Formula $\oint$
15249 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15252 \begin_layout Plain Layout
15260 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15263 \begin_layout Plain Layout
15264 \begin_inset Formula $\ointctrclockwise$
15274 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15277 \begin_layout Plain Layout
15285 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15288 \begin_layout Plain Layout
15289 \begin_inset Formula $\ointclockwise$
15299 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15302 \begin_layout Plain Layout
15310 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15313 \begin_layout Plain Layout
15314 \begin_inset Formula $\sqint$
15324 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15327 \begin_layout Plain Layout
15335 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15338 \begin_layout Plain Layout
15340 \begin_inset Formula $\fint$
15350 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15353 \begin_layout Plain Layout
15361 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15364 \begin_layout Plain Layout
15366 \begin_inset Formula $\landupint$
15376 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15379 \begin_layout Plain Layout
15387 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15390 \begin_layout Plain Layout
15392 \begin_inset Formula $\landdownint$
15402 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15405 \begin_layout Plain Layout
15413 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15416 \begin_layout Plain Layout
15417 \begin_inset Formula $\bigcap$
15427 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15430 \begin_layout Plain Layout
15438 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15441 \begin_layout Plain Layout
15442 \begin_inset Formula $\bigcup$
15456 \begin_inset space \hfill{}
15460 \begin_inset Tabular
15461 <lyxtabular version="3" rows="11" columns="2">
15462 <features tabularvalignment="middle">
15463 <column alignment="center" valignment="top" width="0pt">
15464 <column alignment="center" valignment="top" width="0pt">
15466 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15469 \begin_layout Plain Layout
15475 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15478 \begin_layout Plain Layout
15486 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15489 \begin_layout Plain Layout
15493 \begin_inset Index idx
15496 \begin_layout Plain Layout
15509 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15512 \begin_layout Plain Layout
15513 \begin_inset Formula $\sum$
15523 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15526 \begin_layout Plain Layout
15530 \begin_inset Index idx
15533 \begin_layout Plain Layout
15546 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15549 \begin_layout Plain Layout
15550 \begin_inset Formula $\prod$
15560 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15563 \begin_layout Plain Layout
15571 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15574 \begin_layout Plain Layout
15575 \begin_inset Formula $\coprod$
15585 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15588 \begin_layout Plain Layout
15596 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15599 \begin_layout Plain Layout
15600 \begin_inset Formula $\bigodot$
15610 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15613 \begin_layout Plain Layout
15621 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15624 \begin_layout Plain Layout
15625 \begin_inset Formula $\bigotimes$
15635 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15638 \begin_layout Plain Layout
15646 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15649 \begin_layout Plain Layout
15650 \begin_inset Formula $\bigoplus$
15660 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15663 \begin_layout Plain Layout
15671 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15674 \begin_layout Plain Layout
15675 \begin_inset Formula $\bigwedge$
15685 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15688 \begin_layout Plain Layout
15696 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15699 \begin_layout Plain Layout
15700 \begin_inset Formula $\bigvee$
15710 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15713 \begin_layout Plain Layout
15721 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15724 \begin_layout Plain Layout
15725 \begin_inset Formula $\bigsqcup$
15735 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15738 \begin_layout Plain Layout
15746 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15749 \begin_layout Plain Layout
15750 \begin_inset Formula $\biguplus$
15764 \begin_inset space \hfill{}
15770 \begin_layout Standard
15771 All big operators can also be inserted via the math toolbar button
15772 \begin_inset Graphics
15773 filename ../images/math/intop.png
15781 \begin_layout Standard
15782 The operators are called big because they are bigger than the sometimes
15783 equal looking binary operators.
15784 All big operators can have limits as described in the next subsection.
15787 \begin_layout Standard
15788 For all integral operators there is a second version available, ending in
15806 These operators are different from
15813 \begin_inset space \space{}
15816 in the style the operator limits are displayed, see
15817 \begin_inset CommandInset ref
15819 reference "sub:Operator-Limits"
15827 \begin_layout Subsubsection*
15828 Advice for Integrals
15831 \begin_layout Standard
15836 in an integral is an operator, that therefore has to be set upright.
15837 This is done by highlighting the
15841 and using the keyboard shortcut
15851 \begin_layout Plain Layout
15857 \begin_inset CommandInset ref
15859 reference "sub:Font-Styles"
15869 Finally the smallest space is inserted before the
15873 , as this is usual for operators.
15877 \begin_layout Standard
15879 \begin_inset Formula $\int A(x)dx$
15883 \begin_inset Newline newline
15887 \begin_inset Phantom HPhantom
15890 \begin_layout Plain Layout
15897 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15903 \begin_layout Standard
15904 For multiple integrals there are the following commands:
15905 \begin_inset VSpace medskip
15911 \begin_layout Standard
15912 \begin_inset space \hfill{}
15916 \begin_inset Tabular
15917 <lyxtabular version="3" rows="4" columns="2">
15918 <features tabularvalignment="middle">
15919 <column alignment="center" valignment="top" width="0">
15920 <column alignment="center" valignment="top" width="0">
15922 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15925 \begin_layout Plain Layout
15931 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15934 \begin_layout Plain Layout
15936 \begin_inset Note Note
15939 \begin_layout Plain Layout
15946 is only used as spacer.
15958 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15961 \begin_layout Plain Layout
15969 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15972 \begin_layout Plain Layout
15973 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
15983 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15986 \begin_layout Plain Layout
15994 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15997 \begin_layout Plain Layout
15998 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
16008 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16011 \begin_layout Plain Layout
16019 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16022 \begin_layout Plain Layout
16023 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
16037 \begin_inset space \hfill{}
16041 \begin_inset Tabular
16042 <lyxtabular version="3" rows="4" columns="2">
16043 <features tabularvalignment="middle">
16044 <column alignment="center" valignment="top" width="0">
16045 <column alignment="center" valignment="top" width="0">
16047 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16050 \begin_layout Plain Layout
16056 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16059 \begin_layout Plain Layout
16067 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16070 \begin_layout Plain Layout
16078 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16081 \begin_layout Plain Layout
16082 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
16092 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16095 \begin_layout Plain Layout
16103 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16106 \begin_layout Plain Layout
16107 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
16117 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16120 \begin_layout Plain Layout
16128 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16131 \begin_layout Plain Layout
16132 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
16146 \begin_inset space \hfill{}
16152 \begin_layout Subsection
16154 \begin_inset CommandInset label
16156 name "sub:Operator-Limits"
16161 \begin_inset Index idx
16164 \begin_layout Plain Layout
16173 \begin_layout Standard
16174 Limits are created by super- and subscripts:
16177 \begin_layout Standard
16179 \begin_inset Tabular
16180 <lyxtabular version="3" rows="2" columns="2">
16181 <features tabularvalignment="middle">
16182 <column alignment="center" valignment="top" width="0pt">
16183 <column alignment="center" valignment="top" width="0pt">
16185 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16188 \begin_layout Plain Layout
16194 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16197 \begin_layout Plain Layout
16199 \begin_inset Note Note
16202 \begin_layout Plain Layout
16209 is only used as spacer.
16221 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16224 \begin_layout Plain Layout
16233 \begin_layout Plain Layout
16243 \begin_inset Formula $\to$
16247 \begin_inset Formula $\to$
16255 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16258 \begin_layout Plain Layout
16259 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
16275 \begin_layout Standard
16276 Limits of inline formulas are set right beside the operator.
16277 Limits in displayed formulas are set above or below the operator, except
16278 for integral limits.
16281 \begin_layout Standard
16282 To force that the limits are set beside the operator, the cursor is set
16283 directly behind the operator and the limits type is changed with the menu
16286 Edit\SpecialChar \menuseparator
16287 Math\SpecialChar \menuseparator
16306 \begin_layout Standard
16307 The default limits type is this:
16308 \begin_inset Formula
16310 \sum_{x=0}^{\infty}\frac{1}{x^{2}}
16315 This is how it looks when the limits type was changed to
16322 \begin_inset Formula
16324 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}
16329 For integrals, except those ending with
16345 etc., the limits are by default set beside the operator.
16346 But for multiple integrals the limits are often set below the operator.
16347 In the following example the limits type was therefore set to
16351 and so set below the integrals:
16352 \begin_inset Formula
16354 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}
16362 \begin_layout Standard
16363 \begin_inset VSpace medskip
16366 To specify conditions for limits, the commands
16373 \begin_inset Index idx
16376 \begin_layout Plain Layout
16391 \begin_inset Index idx
16394 \begin_layout Plain Layout
16403 To create for example this expression
16404 \begin_inset Formula
16406 \sum_{\begin{subarray}{c}
16410 \end{subarray}}^{n}k^{-2}\label{eq:substack}
16418 \begin_layout Standard
16419 the following has to be done:
16420 \begin_inset Newline newline
16435 \begin_layout Plain Layout
16447 One is now in a blue box under the summation operator and insert there
16456 \begin_layout Plain Layout
16468 The blue box is now within a purple box and now several lines can be written
16470 A new line is created by inserting a line break (
16473 arg "newline-insert newline"
16478 \begin_inset Newline newline
16483 0<k<1000 Ctrl+Return
16484 \begin_inset Newline newline
16489 is typed in, a new box appears below for the new line.
16492 \begin_layout Standard
16493 The alignment of the lines can be changed to left aligned with the
16503 Edit\SpecialChar \menuseparator
16507 To get right alignment,
16515 \begin_layout Plain Layout
16526 is inserted at the beginning of the line.
16529 \begin_layout Standard
16542 with the difference that the lines are always centered.
16545 \begin_layout Standard
16546 \begin_inset VSpace bigskip
16550 \begin_inset CommandInset ref
16552 reference "eq:substack"
16556 there can be too much space beside an operator, because the characters
16557 following the operator are set beside the limits.
16560 \begin_layout Standard
16561 To avoid this, the following macro can be used in the LaTeX-preamble:
16564 \begin_layout Standard
16578 \begin_inset Newline newline
16590 \begin_inset Newline newline
16597 mathclapinternal #1#2{
16601 mathsurround =0pt #1{#2}$}}
16604 \begin_layout Standard
16605 This defines the command
16612 \begin_inset Index idx
16615 \begin_layout Plain Layout
16623 that sets the width of the limit to 0
16624 \begin_inset space \thinspace{}
16628 The command scheme is
16631 \begin_layout Standard
16639 \begin_layout Standard
16640 where the limit can consist of several conditions.
16643 \begin_layout Standard
16645 \begin_inset CommandInset ref
16647 reference "eq:substack"
16651 , one uses the command
16654 \begin_layout Standard
16667 \begin_layout Plain Layout
16676 0<k<1000 Ctrl+Return
16679 \begin_layout Standard
16680 to create the lower limit.
16681 The summand is now directly behind the summation operator:
16682 \begin_inset Formula
16684 \sum_{\mathclap{\substack{0<k<1000\\
16696 \begin_layout Standard
16697 \begin_inset VSpace bigskip
16700 How to use one limit for several operators is described in
16701 \begin_inset CommandInset ref
16703 reference "sub:Self-defined-Operators"
16710 \begin_layout Standard
16711 \begin_inset Newpage newpage
16717 \begin_layout Subsection
16719 \begin_inset CommandInset label
16721 name "sub:Binary-Operators"
16726 \begin_inset Index idx
16729 \begin_layout Plain Layout
16738 \begin_layout Standard
16739 Binary operators are surrounded by space when there is a character before
16741 \begin_inset VSpace medskip
16747 \begin_layout Standard
16748 \begin_inset space \hfill{}
16752 \begin_inset Tabular
16753 <lyxtabular version="3" rows="13" columns="2">
16754 <features tabularvalignment="middle">
16755 <column alignment="center" valignment="top" width="0pt">
16756 <column alignment="center" valignment="top" width="0pt">
16758 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16761 \begin_layout Plain Layout
16763 \begin_inset Note Note
16766 \begin_layout Plain Layout
16773 is only used as spacer.
16783 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16786 \begin_layout Plain Layout
16794 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16797 \begin_layout Plain Layout
16803 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16806 \begin_layout Plain Layout
16807 \begin_inset Formula $+$
16817 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16820 \begin_layout Plain Layout
16826 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16829 \begin_layout Plain Layout
16830 \begin_inset Formula $-$
16840 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16843 \begin_layout Plain Layout
16851 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16854 \begin_layout Plain Layout
16855 \begin_inset Formula $\pm$
16865 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16868 \begin_layout Plain Layout
16876 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16879 \begin_layout Plain Layout
16880 \begin_inset Formula $\mp$
16890 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16893 \begin_layout Plain Layout
16901 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16904 \begin_layout Plain Layout
16905 \begin_inset Formula $\cdot$
16915 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16918 \begin_layout Plain Layout
16926 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16929 \begin_layout Plain Layout
16930 \begin_inset Formula $\times$
16940 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16943 \begin_layout Plain Layout
16951 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16954 \begin_layout Plain Layout
16955 \begin_inset Formula $\div$
16965 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16968 \begin_layout Plain Layout
16972 \begin_layout Plain Layout
16985 \begin_layout Plain Layout
16997 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17000 \begin_layout Plain Layout
17001 \begin_inset Formula $*$
17011 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17014 \begin_layout Plain Layout
17022 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17025 \begin_layout Plain Layout
17026 \begin_inset Formula $\star$
17036 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17039 \begin_layout Plain Layout
17047 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17050 \begin_layout Plain Layout
17051 \begin_inset Formula $\circ$
17061 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17064 \begin_layout Plain Layout
17072 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17075 \begin_layout Plain Layout
17076 \begin_inset Formula $\diamond$
17086 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17089 \begin_layout Plain Layout
17097 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17100 \begin_layout Plain Layout
17101 \begin_inset Formula $\bullet$
17115 \begin_inset space \hfill{}
17119 \begin_inset Tabular
17120 <lyxtabular version="3" rows="13" columns="2">
17121 <features tabularvalignment="middle">
17122 <column alignment="center" valignment="top" width="0pt">
17123 <column alignment="center" valignment="top" width="0pt">
17125 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17128 \begin_layout Plain Layout
17134 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17137 \begin_layout Plain Layout
17145 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17148 \begin_layout Plain Layout
17156 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17159 \begin_layout Plain Layout
17160 \begin_inset Formula $\nabla$
17170 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17173 \begin_layout Plain Layout
17181 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17184 \begin_layout Plain Layout
17185 \begin_inset Formula $\bigtriangledown$
17195 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17198 \begin_layout Plain Layout
17206 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17209 \begin_layout Plain Layout
17210 \begin_inset Formula $\bigtriangleup$
17220 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17223 \begin_layout Plain Layout
17231 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17234 \begin_layout Plain Layout
17235 \begin_inset Formula $\Box$
17245 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17248 \begin_layout Plain Layout
17256 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17259 \begin_layout Plain Layout
17260 \begin_inset Formula $\cap$
17270 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17273 \begin_layout Plain Layout
17281 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17284 \begin_layout Plain Layout
17285 \begin_inset Formula $\cup$
17295 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17298 \begin_layout Plain Layout
17306 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17309 \begin_layout Plain Layout
17310 \begin_inset Formula $\dagger$
17320 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17323 \begin_layout Plain Layout
17331 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17334 \begin_layout Plain Layout
17335 \begin_inset Formula $\ddagger$
17345 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17348 \begin_layout Plain Layout
17356 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17359 \begin_layout Plain Layout
17360 \begin_inset Formula $\wr$
17370 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17373 \begin_layout Plain Layout
17381 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17384 \begin_layout Plain Layout
17385 \begin_inset Formula $\bigcirc$
17395 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17398 \begin_layout Plain Layout
17406 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17409 \begin_layout Plain Layout
17410 \begin_inset Formula $\wedge$
17420 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17423 \begin_layout Plain Layout
17431 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17434 \begin_layout Plain Layout
17435 \begin_inset Formula $\vee$
17449 \begin_inset space \hfill{}
17453 \begin_inset Tabular
17454 <lyxtabular version="3" rows="13" columns="2">
17455 <features tabularvalignment="middle">
17456 <column alignment="center" valignment="top" width="0pt">
17457 <column alignment="center" valignment="top" width="0pt">
17459 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17462 \begin_layout Plain Layout
17468 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17471 \begin_layout Plain Layout
17479 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17482 \begin_layout Plain Layout
17490 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17493 \begin_layout Plain Layout
17494 \begin_inset Formula $\oplus$
17504 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17507 \begin_layout Plain Layout
17515 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17518 \begin_layout Plain Layout
17519 \begin_inset Formula $\ominus$
17529 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17532 \begin_layout Plain Layout
17540 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17543 \begin_layout Plain Layout
17544 \begin_inset Formula $\otimes$
17554 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17557 \begin_layout Plain Layout
17565 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17568 \begin_layout Plain Layout
17569 \begin_inset Formula $\oslash$
17579 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17582 \begin_layout Plain Layout
17590 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17593 \begin_layout Plain Layout
17594 \begin_inset Formula $\odot$
17604 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17607 \begin_layout Plain Layout
17615 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17618 \begin_layout Plain Layout
17619 \begin_inset Formula $\amalg$
17629 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17632 \begin_layout Plain Layout
17640 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17643 \begin_layout Plain Layout
17644 \begin_inset Formula $\uplus$
17654 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17657 \begin_layout Plain Layout
17665 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17668 \begin_layout Plain Layout
17669 \begin_inset Formula $\setminus$
17679 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17682 \begin_layout Plain Layout
17690 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17693 \begin_layout Plain Layout
17694 \begin_inset Formula $\sqcap$
17704 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17707 \begin_layout Plain Layout
17715 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17718 \begin_layout Plain Layout
17719 \begin_inset Formula $\sqcup$
17729 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17732 \begin_layout Plain Layout
17740 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17743 \begin_layout Plain Layout
17744 \begin_inset Formula $\triangleleft$
17754 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17757 \begin_layout Plain Layout
17765 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17768 \begin_layout Plain Layout
17769 \begin_inset Formula $\triangleright$
17783 \begin_inset space \hfill{}
17789 \begin_layout Standard
17790 All binary operators can also be inserted via the math toolbar button
17791 \begin_inset Graphics
17792 filename ../images/math/pm.png
17800 \begin_layout Standard
17801 To typeset the Laplace operator also
17818 \begin_inset Formula $\nabla^{2}$
17821 ) can be used instead of
17830 \begin_layout Standard
17837 Insert\SpecialChar \menuseparator
17849 \begin_layout Subsection
17850 Self-defined Operators
17851 \begin_inset CommandInset label
17853 name "sub:Self-defined-Operators"
17858 \begin_inset Index idx
17861 \begin_layout Plain Layout
17862 Operators ! self-defined
17870 \begin_layout Standard
17871 With the help of the command
17875 DeclareMathOperator
17878 \begin_inset Index idx
17881 \begin_layout Plain Layout
17886 DeclareMathOperator
17891 custom operators can be defined in the LaTeX-preamble.
17892 Its command scheme is:
17895 \begin_layout Standard
17900 DeclareMathOperator{new command}{display}
17903 \begin_layout Standard
17904 Display can be characters or symbols that define how the operator looks
17906 To define a big operator a * is set behind the command.
17907 All self-defined big operators can have limits as described in
17908 \begin_inset CommandInset ref
17910 reference "sub:Operator-Limits"
17917 \begin_layout Standard
17918 For example the LaTeX-preamble line
17921 \begin_layout Standard
17926 DeclareMathOperator*{
17933 \begin_layout Standard
17934 defines the command
17940 , that inserts a big operator consisting of the lozenge symbol from
17941 \begin_inset CommandInset ref
17943 reference "sub:Miscellaneous-Symbols"
17948 \begin_inset Formula
17950 \Lozenge_{n=1}^{\infty}
17955 The command for this formula is:
17966 \begin_inset Formula $\to$
17972 \begin_layout Standard
17973 \begin_inset VSpace bigskip
17976 When self-defined operators are not used several times in the document,
17977 they can also be defined with the commands
17984 \begin_inset Index idx
17987 \begin_layout Plain Layout
18002 \begin_inset Index idx
18005 \begin_layout Plain Layout
18013 , which have the following scheme:
18016 \begin_layout Standard
18030 \begin_layout Standard
18037 defines big operators,
18046 \begin_layout Standard
18054 \begin_inset space \thinspace{}
18058 \begin_inset space \space{}
18061 be used to use one limit for several operators:
18064 \begin_layout Standard
18065 \begin_inset Formula
18067 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
18075 \begin_layout Standard
18076 The command for the formula above is:
18077 \begin_inset Newline newline
18096 \begin_layout Plain Layout
18108 \begin_inset Formula $\to$
18117 \begin_layout Plain Layout
18131 \begin_layout Section
18133 \begin_inset Index idx
18136 \begin_layout Plain Layout
18145 \begin_layout Subsection
18147 \begin_inset CommandInset label
18149 name "sub:Font-Styles"
18154 \begin_inset Index idx
18157 \begin_layout Plain Layout
18166 \begin_layout Standard
18167 Latin letters in formulas can be set in one of the following font styles:
18168 \begin_inset VSpace -2mm
18174 \begin_layout Standard
18176 \begin_inset Tabular
18177 <lyxtabular version="3" rows="7" columns="3">
18178 <features tabularvalignment="middle">
18179 <column alignment="center" valignment="top" width="0">
18180 <column alignment="center" valignment="top" width="0">
18181 <column alignment="center" valignment="top" width="0">
18183 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18186 \begin_layout Plain Layout
18192 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18195 \begin_layout Plain Layout
18201 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18204 \begin_layout Plain Layout
18212 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18215 \begin_layout Plain Layout
18224 \begin_layout Plain Layout
18240 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18243 \begin_layout Plain Layout
18244 \begin_inset Formula $\mathbb{ABC}$
18252 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18255 \begin_layout Plain Layout
18268 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18271 \begin_layout Plain Layout
18280 \begin_layout Plain Layout
18296 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18299 \begin_layout Plain Layout
18300 \begin_inset Formula $\mathbf{AbC}$
18308 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18311 \begin_layout Plain Layout
18324 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18327 \begin_layout Plain Layout
18336 \begin_layout Plain Layout
18352 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18355 \begin_layout Plain Layout
18356 \begin_inset Formula $\boldsymbol{AbC}$
18364 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18367 \begin_layout Plain Layout
18370 arg "font-boldsymbol"
18380 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18383 \begin_layout Plain Layout
18392 \begin_layout Plain Layout
18408 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18411 \begin_layout Plain Layout
18412 \begin_inset Formula $\mathcal{ABC}$
18420 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18423 \begin_layout Plain Layout
18436 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18439 \begin_layout Plain Layout
18448 \begin_layout Plain Layout
18464 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18467 \begin_layout Plain Layout
18468 \begin_inset Formula $\mathfrak{AbC}$
18476 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18479 \begin_layout Plain Layout
18487 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18490 \begin_layout Plain Layout
18499 \begin_layout Plain Layout
18515 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18518 \begin_layout Plain Layout
18519 \begin_inset Formula $\mathscr{AbC}$
18527 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18530 \begin_layout Plain Layout
18544 \begin_layout Standard
18546 \begin_inset Tabular
18547 <lyxtabular version="3" rows="5" columns="3">
18548 <features tabularvalignment="middle">
18549 <column alignment="center" valignment="top" width="0">
18550 <column alignment="center" valignment="top" width="0">
18551 <column alignment="center" valignment="top" width="0">
18553 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18556 \begin_layout Plain Layout
18562 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18565 \begin_layout Plain Layout
18571 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18574 \begin_layout Plain Layout
18582 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18585 \begin_layout Plain Layout
18594 \begin_layout Plain Layout
18610 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18613 \begin_layout Plain Layout
18614 \begin_inset Formula $\mathit{AbC}$
18622 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18625 \begin_layout Plain Layout
18633 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18636 \begin_layout Plain Layout
18645 \begin_layout Plain Layout
18661 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18664 \begin_layout Plain Layout
18665 \begin_inset Formula $\mathrm{AbC}$
18673 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18676 \begin_layout Plain Layout
18689 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18692 \begin_layout Plain Layout
18701 \begin_layout Plain Layout
18717 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18720 \begin_layout Plain Layout
18721 \begin_inset Formula $\mathsf{AbC}$
18729 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18732 \begin_layout Plain Layout
18745 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18748 \begin_layout Plain Layout
18757 \begin_layout Plain Layout
18773 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18776 \begin_layout Plain Layout
18777 \begin_inset Formula $\mathtt{AbC}$
18785 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18788 \begin_layout Plain Layout
18791 arg "font-typewriter"
18807 \begin_layout Standard
18808 \begin_inset Note Greyedout
18811 \begin_layout Plain Layout
18828 can only be used for big letters.
18836 \begin_layout Standard
18837 Predefined is the style
18846 \begin_layout Standard
18847 The style commands work also for letters in mathematical constructs:
18848 \begin_inset Formula
18850 \mathfrak{A=\frac{b}{C}}
18858 \begin_layout Standard
18859 Characters in mathematical text don't appear in a math font style but in
18860 the text font style
18867 That their style can't be set correctly via the text style dialog is a
18872 \begin_layout Plain Layout
18873 \begin_inset CommandInset href
18875 name "LyX-bug #4629"
18876 target "http://www.lyx.org/trac/ticket/4629"
18888 \begin_layout Standard
18889 Instead of the style commands the dialog
18891 Edit\SpecialChar \menuseparator
18892 Math\SpecialChar \menuseparator
18895 or the toolbar button
18896 \begin_inset Graphics
18897 filename ../images/math/font.png
18905 \begin_layout Subsection
18907 \begin_inset CommandInset label
18909 name "sub:Bold-Formulas"
18914 \begin_inset Index idx
18917 \begin_layout Plain Layout
18926 \begin_layout Standard
18927 To make a complete formula bold, the command
18933 from the previous subsection cannot be used, because it doesn't work for
18934 small Greek letters.
18935 Furthermore it prints Latin letters always upright, like in the following
18939 \begin_layout Standard
18940 \begin_inset Formula
18942 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
18950 \begin_layout Standard
18951 To display the formula correctly, the command
18958 \begin_inset Formula
18960 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
18965 It is also possible to set the formula in a
18967 boldmath environment
18970 This environment is created by inserting the command
18977 \begin_inset Index idx
18980 \begin_layout Plain Layout
18989 To end the environment, the command
18996 \begin_inset Index idx
18999 \begin_layout Plain Layout
19007 is inserted in TeX-mode.
19011 \begin_layout Plain Layout
19021 \begin_inset Formula
19023 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
19032 \begin_layout Plain Layout
19044 \begin_layout Subsection
19046 \begin_inset Index idx
19049 \begin_layout Plain Layout
19058 \begin_layout Standard
19059 Formulas can be colored like normal text: Highlight a formula or a formula
19065 Here is a formula in magenta:
19066 \begin_inset Formula
19068 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
19076 \begin_layout Standard
19077 You can also define your own colors as described in
19078 \begin_inset CommandInset ref
19080 reference "sub:Colored-Boxes"
19085 They can be used with the TeX code command
19092 \begin_inset Index idx
19095 \begin_layout Plain Layout
19106 \begin_layout Standard
19111 textcolor{color}{characters or formula}
19114 \begin_layout Standard
19115 The following example was colored completely dark green and partly red:
19118 \begin_layout Standard
19122 \begin_layout Plain Layout
19126 textcolor{darkgreen}{
19132 \begin_inset Formula
19134 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
19143 \begin_layout Plain Layout
19153 \begin_layout Standard
19154 Due to a bug in LyX only complete formulas can be colored with self-defined
19159 \begin_layout Plain Layout
19160 \begin_inset CommandInset href
19162 name "LyX-bug #5269"
19163 target "http://www.lyx.org/trac/ticket/5269"
19175 \begin_layout Subsection
19177 \begin_inset CommandInset label
19179 name "sub:Font-Sizes"
19184 \begin_inset Index idx
19187 \begin_layout Plain Layout
19196 \begin_layout Standard
19197 For characters in formulas there are, analog to characters in text, the
19198 following size commands:
19201 \begin_layout Standard
19245 \begin_inset Newline newline
19267 \begin_layout Standard
19268 The size produced by the commands depends on the document font size, which
19269 corresponds to the command
19276 The other commands produce smaller or larger sizes than
19283 The font size can however not exceed a certain value.
19284 Is for example the document font size 12
19285 \begin_inset space \thinspace{}
19294 switches to the same size as
19304 \begin_layout Standard
19305 A size command is inserted in TeX-mode before the formula and sets the size
19306 for all following formula and text characters.
19307 To switch back to the initial size, the command
19313 is inserted behind the formula in TeX-mode.
19316 \begin_layout Standard
19317 Within a formula the size can be changed using the following size commands:
19320 \begin_layout Standard
19323 \begin_inset Tabular
19324 <lyxtabular version="3" rows="5" columns="2">
19325 <features tabularvalignment="middle">
19326 <column alignment="center" valignment="top" width="0">
19327 <column alignment="center" valignment="top" width="0">
19329 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19332 \begin_layout Plain Layout
19338 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19341 \begin_layout Plain Layout
19343 \begin_inset Note Note
19346 \begin_layout Plain Layout
19353 is only used as spacer.
19365 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19368 \begin_layout Plain Layout
19372 \begin_inset Index idx
19375 \begin_layout Plain Layout
19388 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19391 \begin_layout Plain Layout
19392 \begin_inset Formula $\raisebox{6.5mm}{}{\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-5.5mm}{}$
19402 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19405 \begin_layout Plain Layout
19413 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19416 \begin_layout Plain Layout
19417 \begin_inset Formula $\raisebox{4.5mm}{}{\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-4mm}{}$
19427 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19430 \begin_layout Plain Layout
19438 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19441 \begin_layout Plain Layout
19442 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
19452 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19455 \begin_layout Plain Layout
19463 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19466 \begin_layout Plain Layout
19467 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
19483 \begin_layout Standard
19484 After entering these commands, a blue box appears in which the formula parts
19488 \begin_layout Standard
19489 There is a further method to change the font size, that though only works
19490 for symbols or letters in mathematical text.
19491 To use it, one of the above text size commands is inserted in mathematical
19493 All following characters until the end of the mathematical text or until
19494 another size command will have the selected size.
19496 \begin_inset VSpace -2mm
19502 \begin_layout Standard
19506 \begin_layout Plain Layout
19516 \begin_inset Formula
19518 A=\frac{B}{c}\cdot\maltese
19524 \begin_inset Formula
19526 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
19535 \begin_layout Plain Layout
19547 \begin_layout Standard
19548 \begin_inset VSpace medskip
19551 Before both formulas the command
19558 The command for the second formula is:
19559 \begin_inset Newline newline
19570 \begin_layout Plain Layout
19585 \begin_layout Plain Layout
19600 \begin_layout Plain Layout
19615 \begin_layout Plain Layout
19625 \begin_inset Formula $\to$
19629 \begin_inset Formula $\to$
19633 \begin_inset Newline newline
19637 \begin_inset space \hspace*{}
19651 \begin_layout Plain Layout
19666 \begin_layout Plain Layout
19681 \begin_layout Plain Layout
19693 \begin_layout Standard
19694 If a symbol cannot be displayed in different sizes, it will always be displayed
19695 in the default size.
19698 \begin_layout Section
19700 \begin_inset Index idx
19703 \begin_layout Plain Layout
19712 \begin_layout Standard
19713 Greek letters can also be inserted via the toolbar button
19714 \begin_inset Graphics
19715 filename ../images/math/alpha.png
19721 All international typesetting norms purport that Greek letters in math
19722 have to be typeset italic/slanted.
19723 In some languages, like French or Russian, they are nevertheless sometimes
19727 \begin_layout Subsection
19729 \begin_inset Index idx
19732 \begin_layout Plain Layout
19733 Greek letters ! small
19741 \begin_layout Standard
19742 \begin_inset space \hfill{}
19746 \begin_inset Tabular
19747 <lyxtabular version="3" rows="11" columns="2">
19748 <features tabularvalignment="middle">
19749 <column alignment="center" valignment="top" width="0pt">
19750 <column alignment="center" valignment="top" width="0pt">
19752 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19755 \begin_layout Plain Layout
19761 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19764 \begin_layout Plain Layout
19772 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19775 \begin_layout Plain Layout
19783 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19786 \begin_layout Plain Layout
19787 \begin_inset Formula $\alpha$
19797 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19800 \begin_layout Plain Layout
19808 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19811 \begin_layout Plain Layout
19812 \begin_inset Formula $\beta$
19822 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19825 \begin_layout Plain Layout
19833 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19836 \begin_layout Plain Layout
19837 \begin_inset Formula $\gamma$
19847 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19850 \begin_layout Plain Layout
19858 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19861 \begin_layout Plain Layout
19862 \begin_inset Formula $\delta$
19872 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19875 \begin_layout Plain Layout
19883 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19886 \begin_layout Plain Layout
19887 \begin_inset Formula $\epsilon$
19897 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19900 \begin_layout Plain Layout
19908 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19911 \begin_layout Plain Layout
19912 \begin_inset Formula $\varepsilon$
19922 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19925 \begin_layout Plain Layout
19933 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19936 \begin_layout Plain Layout
19937 \begin_inset Formula $\zeta$
19947 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19950 \begin_layout Plain Layout
19958 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19961 \begin_layout Plain Layout
19962 \begin_inset Formula $\eta$
19972 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19975 \begin_layout Plain Layout
19983 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19986 \begin_layout Plain Layout
19987 \begin_inset Formula $\theta$
19997 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20000 \begin_layout Plain Layout
20008 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20011 \begin_layout Plain Layout
20012 \begin_inset Formula $\vartheta$
20026 \begin_inset space \hfill{}
20030 \begin_inset Tabular
20031 <lyxtabular version="3" rows="12" columns="2">
20032 <features tabularvalignment="middle">
20033 <column alignment="center" valignment="top" width="0pt">
20034 <column alignment="center" valignment="top" width="0pt">
20036 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20039 \begin_layout Plain Layout
20045 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20048 \begin_layout Plain Layout
20056 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20059 \begin_layout Plain Layout
20067 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20070 \begin_layout Plain Layout
20071 \begin_inset Formula $\iota$
20081 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20084 \begin_layout Plain Layout
20092 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20095 \begin_layout Plain Layout
20096 \begin_inset Formula $\kappa$
20106 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20109 \begin_layout Plain Layout
20117 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20120 \begin_layout Plain Layout
20121 \begin_inset Formula $\varkappa$
20131 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20134 \begin_layout Plain Layout
20142 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20145 \begin_layout Plain Layout
20146 \begin_inset Formula $\lambda$
20156 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20159 \begin_layout Plain Layout
20167 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20170 \begin_layout Plain Layout
20171 \begin_inset Formula $\mu$
20181 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20184 \begin_layout Plain Layout
20192 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20195 \begin_layout Plain Layout
20196 \begin_inset Formula $\nu$
20206 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20209 \begin_layout Plain Layout
20217 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20220 \begin_layout Plain Layout
20221 \begin_inset Formula $\xi$
20231 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20234 \begin_layout Plain Layout
20240 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20243 \begin_layout Plain Layout
20244 \begin_inset Formula $o$
20254 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20257 \begin_layout Plain Layout
20265 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20268 \begin_layout Plain Layout
20269 \begin_inset Formula $\pi$
20279 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20282 \begin_layout Plain Layout
20290 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20293 \begin_layout Plain Layout
20294 \begin_inset Formula $\varpi$
20304 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20307 \begin_layout Plain Layout
20315 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20318 \begin_layout Plain Layout
20319 \begin_inset Formula $\rho$
20333 \begin_inset space \hfill{}
20337 \begin_inset Tabular
20338 <lyxtabular version="3" rows="11" columns="2">
20339 <features tabularvalignment="middle">
20340 <column alignment="center" valignment="top" width="0pt">
20341 <column alignment="center" valignment="top" width="0pt">
20343 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20346 \begin_layout Plain Layout
20352 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20355 \begin_layout Plain Layout
20363 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20366 \begin_layout Plain Layout
20374 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20377 \begin_layout Plain Layout
20378 \begin_inset Formula $\varrho$
20388 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20391 \begin_layout Plain Layout
20399 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20402 \begin_layout Plain Layout
20403 \begin_inset Formula $\sigma$
20413 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20416 \begin_layout Plain Layout
20424 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20427 \begin_layout Plain Layout
20428 \begin_inset Formula $\varsigma$
20438 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20441 \begin_layout Plain Layout
20449 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20452 \begin_layout Plain Layout
20453 \begin_inset Formula $\tau$
20463 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20466 \begin_layout Plain Layout
20474 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20477 \begin_layout Plain Layout
20478 \begin_inset Formula $\upsilon$
20488 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20491 \begin_layout Plain Layout
20499 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20502 \begin_layout Plain Layout
20503 \begin_inset Formula $\phi$
20513 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20516 \begin_layout Plain Layout
20524 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20527 \begin_layout Plain Layout
20528 \begin_inset Formula $\varphi$
20538 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20541 \begin_layout Plain Layout
20549 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20552 \begin_layout Plain Layout
20553 \begin_inset Formula $\chi$
20563 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20566 \begin_layout Plain Layout
20574 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20577 \begin_layout Plain Layout
20578 \begin_inset Formula $\psi$
20588 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20591 \begin_layout Plain Layout
20599 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20602 \begin_layout Plain Layout
20603 \begin_inset Formula $\omega$
20617 \begin_inset space \hfill{}
20623 \begin_layout Standard
20624 \begin_inset VSpace medskip
20630 \begin_layout Standard
20631 How to create special upright Greek letters is explained in
20632 \begin_inset CommandInset ref
20634 reference "sub:Upright-small-Greek"
20641 \begin_layout Subsection
20643 \begin_inset Index idx
20646 \begin_layout Plain Layout
20647 Greek letters ! big
20655 \begin_layout Standard
20656 \begin_inset space \hfill{}
20660 \begin_inset Tabular
20661 <lyxtabular version="3" rows="7" columns="2">
20662 <features tabularvalignment="middle">
20663 <column alignment="center" valignment="top" width="0pt">
20664 <column alignment="center" valignment="top" width="0pt">
20666 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20669 \begin_layout Plain Layout
20675 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20678 \begin_layout Plain Layout
20686 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20689 \begin_layout Plain Layout
20697 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20700 \begin_layout Plain Layout
20701 \begin_inset Formula $\Gamma$
20711 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20714 \begin_layout Plain Layout
20722 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20725 \begin_layout Plain Layout
20726 \begin_inset Formula $\Delta$
20736 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20739 \begin_layout Plain Layout
20747 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20750 \begin_layout Plain Layout
20751 \begin_inset Formula $\Theta$
20761 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20764 \begin_layout Plain Layout
20772 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20775 \begin_layout Plain Layout
20776 \begin_inset Formula $\Lambda$
20786 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20789 \begin_layout Plain Layout
20797 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20800 \begin_layout Plain Layout
20801 \begin_inset Formula $\Xi$
20811 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20814 \begin_layout Plain Layout
20822 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20825 \begin_layout Plain Layout
20826 \begin_inset Formula $\Pi$
20840 \begin_inset space \hfill{}
20844 \begin_inset Tabular
20845 <lyxtabular version="3" rows="6" columns="2">
20846 <features tabularvalignment="middle">
20847 <column alignment="center" valignment="top" width="0pt">
20848 <column alignment="center" valignment="top" width="0pt">
20850 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20853 \begin_layout Plain Layout
20859 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20862 \begin_layout Plain Layout
20870 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20873 \begin_layout Plain Layout
20881 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20884 \begin_layout Plain Layout
20885 \begin_inset Formula $\Sigma$
20895 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20898 \begin_layout Plain Layout
20906 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20909 \begin_layout Plain Layout
20910 \begin_inset Formula $\Upsilon$
20920 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20923 \begin_layout Plain Layout
20931 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20934 \begin_layout Plain Layout
20935 \begin_inset Formula $\Phi$
20945 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20948 \begin_layout Plain Layout
20956 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20959 \begin_layout Plain Layout
20960 \begin_inset Formula $\Psi$
20970 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20973 \begin_layout Plain Layout
20981 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20984 \begin_layout Plain Layout
20985 \begin_inset Formula $\Omega$
20999 \begin_inset space \hfill{}
21005 \begin_layout Standard
21006 \begin_inset VSpace medskip
21009 That the big Greek letters appear upright is caused by a design bug when
21011 To get correct italic big letters, begin every command with
21016 For example the command
21023 \begin_inset Formula $\varGamma$
21027 Another way is to load the package
21035 \begin_layout Plain Layout
21040 is part of the LaTeX-package
21045 \begin_inset Index idx
21048 \begin_layout Plain Layout
21053 \begin_layout Plain Layout
21073 \begin_inset Index idx
21076 \begin_layout Plain Layout
21082 with the LaTeX-preamble line
21085 \begin_layout Standard
21090 usepackage{fixmath}
21093 \begin_layout Standard
21094 Then all big Greek letters in a document will automatically be typeset italic.
21097 \begin_layout Subsection
21099 \begin_inset Index idx
21102 \begin_layout Plain Layout
21103 Greek letters ! bold
21111 \begin_layout Standard
21112 Greek letters cannot be set with different font styles like Latin letters.
21113 They can only be made bold with the command
21120 \begin_inset Index idx
21123 \begin_layout Plain Layout
21134 \begin_layout Standard
21136 \begin_inset Tabular
21137 <lyxtabular version="3" rows="3" columns="2">
21138 <features tabularvalignment="middle">
21139 <column alignment="center" valignment="top" width="0">
21140 <column alignment="center" valignment="top" width="0">
21142 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21145 \begin_layout Plain Layout
21151 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21154 \begin_layout Plain Layout
21162 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21165 \begin_layout Plain Layout
21177 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21180 \begin_layout Plain Layout
21181 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
21191 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21194 \begin_layout Plain Layout
21206 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21209 \begin_layout Plain Layout
21210 \begin_inset Formula $\theta\boldsymbol{\theta}$
21226 \begin_layout Standard
21227 \begin_inset Newpage newpage
21233 \begin_layout Section
21238 \begin_layout Plain Layout
21251 \begin_layout Plain Layout
21252 A list with all symbols of most of the LaTeX-packages can be found in
21253 \begin_inset CommandInset citation
21268 \begin_layout Plain Layout
21276 \begin_inset Note Note
21279 \begin_layout Plain Layout
21282 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
21285 \begin_layout Plain Layout
21288 texorpdfstring is in section
21289 \begin_inset CommandInset ref
21291 reference "sub:Formulas-in-Section"
21301 \begin_inset Index idx
21304 \begin_layout Plain Layout
21313 \begin_layout Standard
21314 Many of the symbols listed in this section can also be inserted via the
21316 \begin_inset Graphics
21317 filename ../images/math/nabla.png
21323 \begin_inset Graphics
21324 filename ../images/math/digamma.png
21332 \begin_layout Subsection
21333 Mathematical Symbols
21334 \begin_inset CommandInset label
21336 name "sub:Mathematical-Symbols"
21341 \begin_inset Index idx
21344 \begin_layout Plain Layout
21345 Symbols ! mathematical
21353 \begin_layout Standard
21354 \begin_inset space \hfill{}
21358 \begin_inset Tabular
21359 <lyxtabular version="3" rows="10" columns="2">
21360 <features tabularvalignment="middle">
21361 <column alignment="center" valignment="top" width="0pt">
21362 <column alignment="center" valignment="top" width="0pt">
21364 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21367 \begin_layout Plain Layout
21373 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21376 \begin_layout Plain Layout
21384 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21387 \begin_layout Plain Layout
21395 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21398 \begin_layout Plain Layout
21399 \begin_inset Formula $\neg$
21409 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21412 \begin_layout Plain Layout
21420 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21423 \begin_layout Plain Layout
21424 \begin_inset Formula $\Im$
21434 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21437 \begin_layout Plain Layout
21445 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21448 \begin_layout Plain Layout
21449 \begin_inset Formula $\Re$
21459 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21462 \begin_layout Plain Layout
21470 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21473 \begin_layout Plain Layout
21474 \begin_inset Formula $\aleph$
21484 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21487 \begin_layout Plain Layout
21495 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21498 \begin_layout Plain Layout
21499 \begin_inset Formula $\partial$
21509 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21512 \begin_layout Plain Layout
21520 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21523 \begin_layout Plain Layout
21524 \begin_inset Formula $\infty$
21534 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21537 \begin_layout Plain Layout
21545 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21548 \begin_layout Plain Layout
21549 \begin_inset Formula $\wp$
21559 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21562 \begin_layout Plain Layout
21570 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21573 \begin_layout Plain Layout
21574 \begin_inset Formula $\imath$
21584 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21587 \begin_layout Plain Layout
21595 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21598 \begin_layout Plain Layout
21599 \begin_inset Formula $\jmath$
21613 \begin_inset space \hfill{}
21617 \begin_inset Tabular
21618 <lyxtabular version="3" rows="10" columns="2">
21619 <features tabularvalignment="middle">
21620 <column alignment="center" valignment="top" width="0pt">
21621 <column alignment="center" valignment="top" width="0pt">
21623 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21626 \begin_layout Plain Layout
21632 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21635 \begin_layout Plain Layout
21637 \begin_inset Note Note
21640 \begin_layout Plain Layout
21647 is only used as spacer.
21659 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21662 \begin_layout Plain Layout
21670 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21673 \begin_layout Plain Layout
21674 \begin_inset Formula $\forall$
21684 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21687 \begin_layout Plain Layout
21695 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21698 \begin_layout Plain Layout
21699 \begin_inset Formula $\exists$
21709 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21712 \begin_layout Plain Layout
21720 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21723 \begin_layout Plain Layout
21724 \begin_inset Formula $\nexists$
21734 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21737 \begin_layout Plain Layout
21745 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21748 \begin_layout Plain Layout
21749 \begin_inset Formula $\emptyset$
21759 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21762 \begin_layout Plain Layout
21770 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21773 \begin_layout Plain Layout
21774 \begin_inset Formula $\varnothing$
21784 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21787 \begin_layout Plain Layout
21795 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21798 \begin_layout Plain Layout
21799 \begin_inset Formula $\dag$
21809 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21812 \begin_layout Plain Layout
21820 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21823 \begin_layout Plain Layout
21824 \begin_inset Formula $\ddag$
21834 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21837 \begin_layout Plain Layout
21845 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21848 \begin_layout Plain Layout
21852 \begin_layout Plain Layout
21862 \begin_inset Formula $\complement$
21869 \begin_layout Plain Layout
21883 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21886 \begin_layout Plain Layout
21894 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21897 \begin_layout Plain Layout
21898 \begin_inset Formula $\Bbbk$
21912 \begin_inset space \hfill{}
21916 \begin_inset Tabular
21917 <lyxtabular version="3" rows="10" columns="2">
21918 <features tabularvalignment="middle">
21919 <column alignment="center" valignment="top" width="0pt">
21920 <column alignment="center" valignment="top" width="0pt">
21922 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21925 \begin_layout Plain Layout
21931 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21934 \begin_layout Plain Layout
21942 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21945 \begin_layout Plain Layout
21953 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21956 \begin_layout Plain Layout
21957 \begin_inset Formula $\prime$
21967 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21970 \begin_layout Plain Layout
21978 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21981 \begin_layout Plain Layout
21982 \begin_inset Formula $\backprime$
21992 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21995 \begin_layout Plain Layout
22003 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22006 \begin_layout Plain Layout
22007 \begin_inset Formula $\mho$
22017 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22020 \begin_layout Plain Layout
22028 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22031 \begin_layout Plain Layout
22032 \begin_inset Formula $\triangle$
22042 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22045 \begin_layout Plain Layout
22053 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22056 \begin_layout Plain Layout
22057 \begin_inset Formula $\angle$
22067 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22070 \begin_layout Plain Layout
22078 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22081 \begin_layout Plain Layout
22082 \begin_inset Formula $\measuredangle$
22092 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22095 \begin_layout Plain Layout
22103 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22106 \begin_layout Plain Layout
22107 \begin_inset Formula $\sphericalangle$
22117 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22120 \begin_layout Plain Layout
22128 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22131 \begin_layout Plain Layout
22132 \begin_inset Formula $\top$
22142 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22145 \begin_layout Plain Layout
22153 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22156 \begin_layout Plain Layout
22157 \begin_inset Formula $\bot$
22171 \begin_inset space \hfill{}
22177 \begin_layout Subsection
22178 Miscellaneous Symbols
22179 \begin_inset CommandInset label
22181 name "sub:Miscellaneous-Symbols"
22186 \begin_inset Index idx
22189 \begin_layout Plain Layout
22190 Symbols ! miscellaneous
22198 \begin_layout Standard
22201 \begin_inset Tabular
22202 <lyxtabular version="3" rows="10" columns="2">
22203 <features tabularvalignment="middle">
22204 <column alignment="center" valignment="top" width="0pt">
22205 <column alignment="center" valignment="top" width="0pt">
22207 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22210 \begin_layout Plain Layout
22216 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22219 \begin_layout Plain Layout
22227 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22230 \begin_layout Plain Layout
22238 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22241 \begin_layout Plain Layout
22242 \begin_inset Formula $\flat$
22252 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22255 \begin_layout Plain Layout
22263 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22266 \begin_layout Plain Layout
22267 \begin_inset Formula $\natural$
22277 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22280 \begin_layout Plain Layout
22288 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22291 \begin_layout Plain Layout
22292 \begin_inset Formula $\sharp$
22302 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22305 \begin_layout Plain Layout
22313 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22316 \begin_layout Plain Layout
22317 \begin_inset Formula $\surd$
22327 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22330 \begin_layout Plain Layout
22338 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22341 \begin_layout Plain Layout
22342 \begin_inset Formula $\checkmark$
22352 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22355 \begin_layout Plain Layout
22363 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22366 \begin_layout Plain Layout
22367 \begin_inset Formula $\yen$
22377 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22380 \begin_layout Plain Layout
22388 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22391 \begin_layout Plain Layout
22392 \begin_inset Formula $\pounds$
22402 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22405 \begin_layout Plain Layout
22411 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22414 \begin_layout Plain Layout
22415 \begin_inset Formula $\$$
22425 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22428 \begin_layout Plain Layout
22434 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22437 \begin_layout Plain Layout
22438 \begin_inset Formula $§$
22452 \begin_inset Tabular
22453 <lyxtabular version="3" rows="10" columns="2">
22454 <features tabularvalignment="middle">
22455 <column alignment="center" valignment="top" width="0">
22456 <column alignment="center" valignment="top" width="0">
22458 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22461 \begin_layout Plain Layout
22467 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22470 \begin_layout Plain Layout
22478 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22481 \begin_layout Plain Layout
22489 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22492 \begin_layout Plain Layout
22493 \begin_inset Formula $\hbar$
22503 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22506 \begin_layout Plain Layout
22514 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22517 \begin_layout Plain Layout
22518 \begin_inset Formula $\hslash$
22528 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22531 \begin_layout Plain Layout
22539 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22542 \begin_layout Plain Layout
22543 \begin_inset Formula $\clubsuit$
22553 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22556 \begin_layout Plain Layout
22564 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22567 \begin_layout Plain Layout
22568 \begin_inset Formula $\spadesuit$
22578 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22581 \begin_layout Plain Layout
22589 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22592 \begin_layout Plain Layout
22593 \begin_inset Formula $\bigstar$
22603 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22606 \begin_layout Plain Layout
22614 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22617 \begin_layout Plain Layout
22618 \begin_inset Formula $\blacklozenge$
22628 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22631 \begin_layout Plain Layout
22639 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22642 \begin_layout Plain Layout
22643 \begin_inset Formula $\blacktriangle$
22653 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22656 \begin_layout Plain Layout
22664 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22667 \begin_layout Plain Layout
22668 \begin_inset Formula $\blacktriangledown$
22678 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22681 \begin_layout Plain Layout
22689 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22692 \begin_layout Plain Layout
22693 \begin_inset Formula $\bullet$
22707 \begin_inset Tabular
22708 <lyxtabular version="3" rows="10" columns="2">
22709 <features tabularvalignment="middle">
22710 <column alignment="center" valignment="top" width="0pt">
22711 <column alignment="center" valignment="top" width="0pt">
22713 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22716 \begin_layout Plain Layout
22722 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22725 \begin_layout Plain Layout
22733 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22736 \begin_layout Plain Layout
22744 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22747 \begin_layout Plain Layout
22748 \begin_inset Formula $\diamondsuit$
22758 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22761 \begin_layout Plain Layout
22769 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22772 \begin_layout Plain Layout
22773 \begin_inset Formula $\Diamond$
22783 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22786 \begin_layout Plain Layout
22794 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22797 \begin_layout Plain Layout
22798 \begin_inset Formula $\heartsuit$
22808 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22811 \begin_layout Plain Layout
22819 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22822 \begin_layout Plain Layout
22823 \begin_inset Formula $\P$
22833 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22836 \begin_layout Plain Layout
22844 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22847 \begin_layout Plain Layout
22848 \begin_inset Formula $\copyright$
22858 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22861 \begin_layout Plain Layout
22869 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22872 \begin_layout Plain Layout
22873 \begin_inset Formula $\circledR$
22883 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22886 \begin_layout Plain Layout
22894 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22897 \begin_layout Plain Layout
22898 \begin_inset Formula $\maltese$
22908 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22911 \begin_layout Plain Layout
22919 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22922 \begin_layout Plain Layout
22923 \begin_inset Formula $\diagup$
22933 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22936 \begin_layout Plain Layout
22944 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22947 \begin_layout Plain Layout
22948 \begin_inset Formula $\diagdown$
22964 \begin_layout Standard
22965 \begin_inset VSpace medskip
22968 More symbols are listed in
22969 \begin_inset CommandInset ref
22971 reference "sub:Miscellaneous-special-Characters"
22978 \begin_layout Standard
22979 Some symbols can be displayed in different sizes, see
22980 \begin_inset CommandInset ref
22982 reference "sub:Font-Sizes"
22989 \begin_layout Subsection
22991 \begin_inset Index idx
22994 \begin_layout Plain Layout
22995 Symbols ! Euro-symbol
23001 \begin_inset Index idx
23004 \begin_layout Plain Layout
23011 \begin_layout Plain Layout
23028 \begin_layout Standard
23029 To use the Euro symbol in formulas, the LaTeX-package
23034 \begin_inset Index idx
23037 \begin_layout Plain Layout
23043 must be installed and loaded with the LaTeX-preamble line
23046 \begin_layout Standard
23051 usepackage[gennarrow]{eurosym}
23054 \begin_layout Standard
23055 The Euro symbol can now be inserted with the command
23062 \begin_inset Index idx
23065 \begin_layout Plain Layout
23076 \begin_layout Standard
23077 The Euro symbol can directly be inserted with the € key in mathematical
23078 text, without having
23093 can also be inserted in TeX-mode.
23094 The official currency symbol can then be inserted with the command
23101 \begin_inset Index idx
23104 \begin_layout Plain Layout
23112 , that is only available in TeX-mode.
23115 \begin_layout Standard
23119 \begin_layout Plain Layout
23129 \begin_inset Note Note
23132 \begin_layout Plain Layout
23133 The following table will only be displayed when the LaTeX-package
23145 \begin_layout Standard
23146 An overview about the different Euro symbols:
23149 \begin_layout Standard
23151 \begin_inset Tabular
23152 <lyxtabular version="3" rows="4" columns="3">
23153 <features tabularvalignment="middle">
23154 <column alignment="center" valignment="top" width="0pt">
23155 <column alignment="center" valignment="top" width="0pt">
23156 <column alignment="center" valignment="top" width="0pt">
23158 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
23161 \begin_layout Plain Layout
23167 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23170 \begin_layout Plain Layout
23176 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23179 \begin_layout Plain Layout
23187 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23190 \begin_layout Plain Layout
23196 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23199 \begin_layout Plain Layout
23207 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23210 \begin_layout Plain Layout
23211 \begin_inset Formula $\euro$
23221 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23224 \begin_layout Plain Layout
23230 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23233 \begin_layout Plain Layout
23239 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23242 \begin_layout Plain Layout
23243 \begin_inset Formula $\mbox{€}$
23253 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23256 \begin_layout Plain Layout
23262 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23265 \begin_layout Plain Layout
23273 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23276 \begin_layout Plain Layout
23280 \begin_layout Plain Layout
23302 \begin_layout Standard
23306 \begin_layout Plain Layout
23316 \begin_inset Note Note
23319 \begin_layout Plain Layout
23320 The following will be displayed when the LaTeX-package
23332 \begin_layout Standard
23333 You need to install the LaTeX-package
23337 to see the rest of this subsection in the output.
23340 \begin_layout Standard
23344 \begin_layout Plain Layout
23356 \begin_layout Section
23358 \begin_inset CommandInset label
23360 name "sec:Relations"
23365 \begin_inset Index idx
23368 \begin_layout Plain Layout
23375 \begin_inset Index idx
23378 \begin_layout Plain Layout
23383 \begin_layout Plain Layout
23394 \begin_layout Plain Layout
23409 \begin_layout Standard
23410 All relations can also be inserted via the toolbar button
23411 \begin_inset Graphics
23412 filename ../images/math/leq.png
23420 \begin_layout Standard
23421 \begin_inset space \hfill{}
23425 \begin_inset Tabular
23426 <lyxtabular version="3" rows="17" columns="2">
23427 <features tabularvalignment="middle">
23428 <column alignment="center" valignment="top" width="0pt">
23429 <column alignment="center" valignment="top" width="0pt">
23431 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23434 \begin_layout Plain Layout
23440 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23443 \begin_layout Plain Layout
23451 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23454 \begin_layout Plain Layout
23460 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23463 \begin_layout Plain Layout
23464 \begin_inset Formula $<$
23474 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23477 \begin_layout Plain Layout
23485 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23488 \begin_layout Plain Layout
23489 \begin_inset Formula $\le$
23499 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23502 \begin_layout Plain Layout
23510 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23513 \begin_layout Plain Layout
23514 \begin_inset Formula $\ll$
23524 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23527 \begin_layout Plain Layout
23535 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23538 \begin_layout Plain Layout
23539 \begin_inset Formula $\prec$
23549 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23552 \begin_layout Plain Layout
23560 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23563 \begin_layout Plain Layout
23564 \begin_inset Formula $\preceq$
23574 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23577 \begin_layout Plain Layout
23585 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23588 \begin_layout Plain Layout
23589 \begin_inset Formula $\subset$
23599 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23602 \begin_layout Plain Layout
23610 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23613 \begin_layout Plain Layout
23614 \begin_inset Formula $\subseteq$
23624 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23627 \begin_layout Plain Layout
23635 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23638 \begin_layout Plain Layout
23639 \begin_inset Formula $\sqsubseteq$
23649 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23652 \begin_layout Plain Layout
23660 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23663 \begin_layout Plain Layout
23664 \begin_inset Formula $\in$
23674 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23677 \begin_layout Plain Layout
23685 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23688 \begin_layout Plain Layout
23689 \begin_inset Formula $\vdash$
23699 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23702 \begin_layout Plain Layout
23710 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23713 \begin_layout Plain Layout
23714 \begin_inset Formula $\smile$
23724 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23727 \begin_layout Plain Layout
23735 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23738 \begin_layout Plain Layout
23739 \begin_inset Formula $\lhd$
23749 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23752 \begin_layout Plain Layout
23760 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23763 \begin_layout Plain Layout
23764 \begin_inset Formula $\unlhd$
23774 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23777 \begin_layout Plain Layout
23785 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23788 \begin_layout Plain Layout
23789 \begin_inset Formula $\gtrless$
23799 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23802 \begin_layout Plain Layout
23810 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23813 \begin_layout Plain Layout
23814 \begin_inset Formula $\mid$
23824 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23827 \begin_layout Plain Layout
23835 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23838 \begin_layout Plain Layout
23839 \begin_inset Formula $\nmid$
23853 \begin_inset space \hfill{}
23857 \begin_inset Tabular
23858 <lyxtabular version="3" rows="17" columns="2">
23859 <features tabularvalignment="middle">
23860 <column alignment="center" valignment="top" width="0pt">
23861 <column alignment="center" valignment="top" width="0pt">
23863 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23866 \begin_layout Plain Layout
23872 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23875 \begin_layout Plain Layout
23883 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23886 \begin_layout Plain Layout
23892 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23895 \begin_layout Plain Layout
23896 \begin_inset Formula $=$
23906 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23909 \begin_layout Plain Layout
23917 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23920 \begin_layout Plain Layout
23921 \begin_inset Formula $\not=$
23931 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23934 \begin_layout Plain Layout
23942 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23945 \begin_layout Plain Layout
23946 \begin_inset Formula $\equiv$
23956 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23959 \begin_layout Plain Layout
23967 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23970 \begin_layout Plain Layout
23971 \begin_inset Formula $\sim$
23981 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23984 \begin_layout Plain Layout
23992 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23995 \begin_layout Plain Layout
23996 \begin_inset Formula $\simeq$
24006 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24009 \begin_layout Plain Layout
24017 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24020 \begin_layout Plain Layout
24021 \begin_inset Formula $\approx$
24031 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24034 \begin_layout Plain Layout
24042 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24045 \begin_layout Plain Layout
24046 \begin_inset Formula $\cong$
24056 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24059 \begin_layout Plain Layout
24067 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24070 \begin_layout Plain Layout
24071 \begin_inset Formula $\bowtie$
24081 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24084 \begin_layout Plain Layout
24092 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24095 \begin_layout Plain Layout
24096 \begin_inset Formula $\notin$
24106 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24109 \begin_layout Plain Layout
24117 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24120 \begin_layout Plain Layout
24121 \begin_inset Formula $\perp$
24131 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24134 \begin_layout Plain Layout
24142 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24145 \begin_layout Plain Layout
24146 \begin_inset Formula $\propto$
24156 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24159 \begin_layout Plain Layout
24167 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24170 \begin_layout Plain Layout
24171 \begin_inset Formula $\asymp$
24181 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24184 \begin_layout Plain Layout
24192 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24195 \begin_layout Plain Layout
24196 \begin_inset Formula $\doteq$
24206 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24209 \begin_layout Plain Layout
24217 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24220 \begin_layout Plain Layout
24221 \begin_inset Formula $\circeq$
24231 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24234 \begin_layout Plain Layout
24242 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24245 \begin_layout Plain Layout
24246 \begin_inset Formula $\models$
24256 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24259 \begin_layout Plain Layout
24267 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24270 \begin_layout Plain Layout
24271 \begin_inset Formula $\widehat{=}$
24285 \begin_inset space \hfill{}
24289 \begin_inset Tabular
24290 <lyxtabular version="3" rows="17" columns="2">
24291 <features tabularvalignment="middle">
24292 <column alignment="center" valignment="top" width="0pt">
24293 <column alignment="center" valignment="top" width="0pt">
24295 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24298 \begin_layout Plain Layout
24304 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24307 \begin_layout Plain Layout
24315 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24318 \begin_layout Plain Layout
24324 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24327 \begin_layout Plain Layout
24328 \begin_inset Formula $>$
24338 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24341 \begin_layout Plain Layout
24349 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24352 \begin_layout Plain Layout
24353 \begin_inset Formula $\ge$
24363 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24366 \begin_layout Plain Layout
24374 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24377 \begin_layout Plain Layout
24378 \begin_inset Formula $\gg$
24388 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24391 \begin_layout Plain Layout
24399 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24402 \begin_layout Plain Layout
24403 \begin_inset Formula $\succ$
24413 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24416 \begin_layout Plain Layout
24424 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24427 \begin_layout Plain Layout
24428 \begin_inset Formula $\succeq$
24438 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24441 \begin_layout Plain Layout
24449 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24452 \begin_layout Plain Layout
24453 \begin_inset Formula $\supset$
24463 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24466 \begin_layout Plain Layout
24474 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24477 \begin_layout Plain Layout
24478 \begin_inset Formula $\supseteq$
24488 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24491 \begin_layout Plain Layout
24499 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24502 \begin_layout Plain Layout
24503 \begin_inset Formula $\sqsupseteq$
24513 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24516 \begin_layout Plain Layout
24524 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24527 \begin_layout Plain Layout
24528 \begin_inset Formula $\ni$
24538 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24541 \begin_layout Plain Layout
24549 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24552 \begin_layout Plain Layout
24553 \begin_inset Formula $\dashv$
24563 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24566 \begin_layout Plain Layout
24574 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24577 \begin_layout Plain Layout
24578 \begin_inset Formula $\frown$
24588 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24591 \begin_layout Plain Layout
24599 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24602 \begin_layout Plain Layout
24603 \begin_inset Formula $\rhd$
24613 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24616 \begin_layout Plain Layout
24624 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24627 \begin_layout Plain Layout
24628 \begin_inset Formula $\unrhd$
24638 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24641 \begin_layout Plain Layout
24649 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24652 \begin_layout Plain Layout
24653 \begin_inset Formula $\lessgtr$
24663 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24666 \begin_layout Plain Layout
24674 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24677 \begin_layout Plain Layout
24678 \begin_inset Formula $\parallel$
24688 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24691 \begin_layout Plain Layout
24699 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24702 \begin_layout Plain Layout
24703 \begin_inset Formula $\nparallel$
24717 \begin_inset space \hfill{}
24723 \begin_layout Standard
24724 \begin_inset VSpace medskip
24739 are bigger than the equal looking operators
24754 \begin_layout Standard
24755 Relations are, in contrary to symbols, always surrounded by space.
24758 \begin_layout Standard
24759 Relations with labels can be created with the command
24766 \begin_inset Index idx
24769 \begin_layout Plain Layout
24780 \begin_layout Standard
24782 \begin_inset Tabular
24783 <lyxtabular version="3" rows="2" columns="2">
24784 <features tabularvalignment="middle">
24785 <column alignment="center" valignment="top" width="0">
24786 <column alignment="center" valignment="top" width="0">
24788 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24791 \begin_layout Plain Layout
24797 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24800 \begin_layout Plain Layout
24802 \begin_inset Note Note
24805 \begin_layout Plain Layout
24812 is only used as spacer.
24824 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24827 \begin_layout Plain Layout
24834 \begin_layout Plain Layout
24851 \begin_layout Plain Layout
24861 \begin_inset Formula $\downarrow$
24870 \begin_layout Plain Layout
24883 \begin_layout Plain Layout
24897 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24900 \begin_layout Plain Layout
24901 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
24917 \begin_layout Section
24921 \begin_layout Subsection
24922 Predefined Functions
24923 \begin_inset CommandInset label
24925 name "sub:Predefined-Functions"
24930 \begin_inset Index idx
24933 \begin_layout Plain Layout
24934 Functions ! predefined
24942 \begin_layout Standard
24943 In general, variables are set
24947 in mathematical expressions, but not function names, because
24948 \begin_inset Formula $sin$
24951 could be misunderstood as
24952 \begin_inset Formula $s\cdot i\cdot n$
24956 Therefore there are predefined functionswhich are additionally a bit separated
24958 They are inserted as commands starting with a backslash before their name.
24961 \begin_layout Standard
24963 \begin_inset Tabular
24964 <lyxtabular version="3" rows="2" columns="4">
24965 <features tabularvalignment="middle">
24966 <column alignment="center" valignment="top" width="0pt">
24967 <column alignment="center" valignment="top" width="0pt">
24968 <column alignment="center" valignment="top" width="0pt">
24969 <column alignment="center" valignment="top" width="0pt">
24971 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24974 \begin_layout Plain Layout
24980 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24983 \begin_layout Plain Layout
24989 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24992 \begin_layout Plain Layout
24998 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25001 \begin_layout Plain Layout
25009 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25012 \begin_layout Plain Layout
25018 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25021 \begin_layout Plain Layout
25022 \begin_inset Formula $Asin(x)+B$
25030 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25033 \begin_layout Plain Layout
25041 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25044 \begin_layout Plain Layout
25045 \begin_inset Formula $A\sin(x)+B$
25061 \begin_layout Standard
25062 The following functions are predefined:
25065 \begin_layout Standard
25066 \begin_inset VSpace -2mm
25072 \begin_layout Standard
25074 \begin_inset Tabular
25075 <lyxtabular version="3" rows="9" columns="4">
25076 <features tabularvalignment="middle">
25077 <column alignment="center" valignment="top" width="0pt">
25078 <column alignment="center" valignment="top" width="0pt">
25079 <column alignment="center" valignment="top" width="0pt">
25080 <column alignment="center" valignment="top" width="0pt">
25082 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25085 \begin_layout Plain Layout
25091 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25094 \begin_layout Plain Layout
25100 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25103 \begin_layout Plain Layout
25109 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25112 \begin_layout Plain Layout
25120 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25123 \begin_layout Plain Layout
25131 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25134 \begin_layout Plain Layout
25142 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25145 \begin_layout Plain Layout
25153 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25156 \begin_layout Plain Layout
25166 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25169 \begin_layout Plain Layout
25177 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25180 \begin_layout Plain Layout
25188 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25191 \begin_layout Plain Layout
25199 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25202 \begin_layout Plain Layout
25212 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25215 \begin_layout Plain Layout
25223 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25226 \begin_layout Plain Layout
25234 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25237 \begin_layout Plain Layout
25245 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25248 \begin_layout Plain Layout
25258 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25261 \begin_layout Plain Layout
25269 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25272 \begin_layout Plain Layout
25280 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25283 \begin_layout Plain Layout
25291 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25294 \begin_layout Plain Layout
25304 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25307 \begin_layout Plain Layout
25315 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25318 \begin_layout Plain Layout
25326 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25329 \begin_layout Plain Layout
25337 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25340 \begin_layout Plain Layout
25350 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25353 \begin_layout Plain Layout
25361 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25364 \begin_layout Plain Layout
25372 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25375 \begin_layout Plain Layout
25383 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25386 \begin_layout Plain Layout
25396 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25399 \begin_layout Plain Layout
25407 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25410 \begin_layout Plain Layout
25418 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25421 \begin_layout Plain Layout
25429 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25432 \begin_layout Plain Layout
25442 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25445 \begin_layout Plain Layout
25453 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25456 \begin_layout Plain Layout
25464 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25467 \begin_layout Plain Layout
25475 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25478 \begin_layout Plain Layout
25494 \begin_layout Standard
25495 They can also be inserted with the math toolbar button
25496 \begin_inset Graphics
25497 filename ../images/math/functions.png
25505 \begin_layout Subsection
25506 Self-defined Functions
25507 \begin_inset Index idx
25510 \begin_layout Plain Layout
25511 Functions ! self-defined
25519 \begin_layout Standard
25520 To use a function that is not predefined, like for example the sign function
25521 sgn(x), there are two possibilities:
25524 \begin_layout Itemize
25525 Define the function by inserting the following line to the LaTeX-preamble
25529 \begin_layout Plain Layout
25534 DeclareMathOperator
25537 \begin_inset CommandInset ref
25539 reference "sub:Self-defined-Operators"
25549 \begin_inset Newline newline
25553 \begin_inset VSpace -3mm
25557 \begin_inset Newline newline
25564 DeclareMathOperator{
25569 \begin_inset Index idx
25572 \begin_layout Plain Layout
25577 DeclareMathOperator
25583 \begin_inset Newline newline
25587 \begin_inset VSpace -2mm
25591 \begin_inset Newline newline
25594 Now the new defined function can be called with the command
25603 \begin_layout Itemize
25604 Write the formula as usual, mark the formula name, in our example the letters
25609 , and change it to mathematical text.
25610 Finally, a space is inserted between prefactor and function.
25613 \begin_layout Standard
25614 The result is the same with both methods as with a predefined function
25618 \begin_layout Plain Layout
25619 In LyX self-defined functions are displayed red, predefined ones black.
25627 \begin_layout Standard
25629 \begin_inset Tabular
25630 <lyxtabular version="3" rows="3" columns="2">
25631 <features tabularvalignment="middle">
25632 <column alignment="center" valignment="top" width="0pt">
25633 <column alignment="center" valignment="top" width="0pt">
25635 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25638 \begin_layout Plain Layout
25644 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25647 \begin_layout Plain Layout
25655 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25658 \begin_layout Plain Layout
25666 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25669 \begin_layout Plain Layout
25670 \begin_inset Formula $A\sgn(x)+B$
25680 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25683 \begin_layout Plain Layout
25687 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
25695 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25698 \begin_layout Plain Layout
25699 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
25715 \begin_layout Standard
25716 The first method is more suitable when the self-defined function should
25717 be used several times.
25720 \begin_layout Subsection
25722 \begin_inset Index idx
25725 \begin_layout Plain Layout
25734 \begin_layout Standard
25735 For limits, in addition to the commands
25742 \begin_inset Index idx
25745 \begin_layout Plain Layout
25765 the following functions are defined:
25768 \begin_layout Standard
25770 \begin_inset Tabular
25771 <lyxtabular version="3" rows="5" columns="2">
25772 <features tabularvalignment="middle">
25773 <column alignment="center" valignment="top" width="0">
25774 <column alignment="center" valignment="top" width="0">
25776 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25779 \begin_layout Plain Layout
25785 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25788 \begin_layout Plain Layout
25790 \begin_inset Note Note
25793 \begin_layout Plain Layout
25800 is only used as spacer.
25812 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25815 \begin_layout Plain Layout
25823 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25826 \begin_layout Plain Layout
25827 \begin_inset Formula $\varliminf$
25837 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25840 \begin_layout Plain Layout
25848 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25851 \begin_layout Plain Layout
25852 \begin_inset Formula $\varlimsup$
25862 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25865 \begin_layout Plain Layout
25873 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25876 \begin_layout Plain Layout
25877 \begin_inset Formula $\varprojlim$
25887 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25890 \begin_layout Plain Layout
25898 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25901 \begin_layout Plain Layout
25902 \begin_inset Formula $\varinjlim$
25906 \begin_inset Formula $\raisebox{-2.5mm}{}$
25922 \begin_layout Standard
25923 \begin_inset VSpace medskip
25926 The limit is created by inserting a subscript.
25927 It is set right beside the function in an inline formula:
25930 \begin_layout Standard
25932 \begin_inset Tabular
25933 <lyxtabular version="3" rows="2" columns="2">
25934 <features tabularvalignment="middle">
25935 <column alignment="center" valignment="top" width="0pt">
25936 <column alignment="center" valignment="top" width="0pt">
25938 <cell alignment="center" valignment="top" usebox="none">
25941 \begin_layout Plain Layout
25947 <cell alignment="center" valignment="top" usebox="none">
25950 \begin_layout Plain Layout
25951 \begin_inset space \hspace{}
25956 \begin_inset Note Note
25959 \begin_layout Plain Layout
25966 are used here as spacer.
25978 <cell alignment="center" valignment="top" usebox="none">
25981 \begin_layout Plain Layout
25990 \begin_layout Plain Layout
26003 \begin_layout Plain Layout
26017 <cell alignment="center" valignment="top" usebox="none">
26020 \begin_layout Plain Layout
26021 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
26037 \begin_layout Standard
26038 In a displayed formula the limit is set below the formula, as usual:
26039 \begin_inset Formula
26049 \begin_layout Subsection
26051 \begin_inset Index idx
26054 \begin_layout Plain Layout
26055 Functions ! modulo-
26063 \begin_layout Standard
26064 The modulo-function is special, because it exists in four variants.
26065 The variants in a displayed formula are:
26066 \begin_inset Formula
26068 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
26069 \mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
26070 \mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
26071 \mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
26072 \mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b
26080 \begin_layout Standard
26081 In an inline formula less space is set before the function names for all
26083 By default the modulo-functions take only the first following character
26085 To use more than one character, one has to put them into TeX-braces:
26086 \begin_inset Formula
26088 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
26089 \mathrm{a\backslash pod\textrm{\spce}bcd} & & a\pod bcd\\
26090 \mathrm{a\backslash pod\backslash\{bc\to d} & & a\pod{bc}d
26098 \begin_layout Section
26100 \begin_inset Index idx
26103 \begin_layout Plain Layout
26112 \begin_layout Subsection
26113 Special Characters in Mathematical Text
26116 \begin_layout Standard
26117 The following commands can only be used in mathematical text or in TeX-mode:
26120 \begin_layout Standard
26121 \begin_inset space \hfill{}
26125 \begin_inset Tabular
26126 <lyxtabular version="3" rows="8" columns="2">
26127 <features tabularvalignment="middle">
26128 <column alignment="block" valignment="top" width="0">
26129 <column alignment="block" valignment="top" width="0">
26131 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26134 \begin_layout Plain Layout
26140 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26143 \begin_layout Plain Layout
26151 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26154 \begin_layout Plain Layout
26162 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26165 \begin_layout Plain Layout
26166 \begin_inset Formula $\textrm{œ}$
26176 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26179 \begin_layout Plain Layout
26187 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26190 \begin_layout Plain Layout
26191 \begin_inset Formula $\textrm{Œ}$
26201 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26204 \begin_layout Plain Layout
26212 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26215 \begin_layout Plain Layout
26216 \begin_inset Formula $\textrm{æ}$
26226 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26229 \begin_layout Plain Layout
26237 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26240 \begin_layout Plain Layout
26241 \begin_inset Formula $\textrm{Æ}$
26251 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26254 \begin_layout Plain Layout
26262 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26265 \begin_layout Plain Layout
26266 \begin_inset Formula $\textrm{\aa}$
26276 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26279 \begin_layout Plain Layout
26283 \begin_inset Index idx
26286 \begin_layout Plain Layout
26293 \begin_layout Plain Layout
26314 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26317 \begin_layout Plain Layout
26318 \begin_inset Formula $\textrm{Å}$
26328 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26331 \begin_layout Plain Layout
26339 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26342 \begin_layout Plain Layout
26343 \begin_inset Formula $\textrm{ı}$
26357 \begin_inset space \hfill{}
26361 \begin_inset Tabular
26362 <lyxtabular version="3" rows="8" columns="2">
26363 <features tabularvalignment="middle">
26364 <column alignment="block" valignment="top" width="0">
26365 <column alignment="center" valignment="top" width="0">
26367 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26370 \begin_layout Plain Layout
26372 \begin_inset Note Note
26375 \begin_layout Plain Layout
26377 \begin_inset space \thinspace{}
26380 mm is used for separation, because otherwise the output will be ¡ and ¿
26391 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26394 \begin_layout Plain Layout
26402 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26405 \begin_layout Plain Layout
26413 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26416 \begin_layout Plain Layout
26417 \begin_inset Formula $\textrm{ø}$
26427 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26430 \begin_layout Plain Layout
26438 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26441 \begin_layout Plain Layout
26442 \begin_inset Formula $\textrm{Ø}$
26452 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26455 \begin_layout Plain Layout
26463 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26466 \begin_layout Plain Layout
26467 \begin_inset Formula $\textrm{ł}$
26477 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26480 \begin_layout Plain Layout
26488 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26491 \begin_layout Plain Layout
26492 \begin_inset Formula $\textrm{Ł}$
26502 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26505 \begin_layout Plain Layout
26507 \begin_inset space \hspace{}
26515 \begin_layout Plain Layout
26529 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26532 \begin_layout Plain Layout
26533 \begin_inset Formula $\textrm{!`}$
26543 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26546 \begin_layout Plain Layout
26548 \begin_inset space \hspace{}
26556 \begin_layout Plain Layout
26570 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26573 \begin_layout Plain Layout
26574 \begin_inset Formula $\textrm{?`}$
26584 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26587 \begin_layout Plain Layout
26595 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26598 \begin_layout Plain Layout
26599 \begin_inset Formula $\textrm{ȷ}$
26613 \begin_inset space \hfill{}
26619 \begin_layout Standard
26621 \begin_inset Formula $\textrm{\textrm{Å}}$
26625 \begin_inset Formula $\textrm{\textrm{Ø}}$
26628 can also be inserted via the math toolbar button
26629 \begin_inset Graphics
26630 filename ../images/math/digamma.png
26638 \begin_layout Standard
26639 An exception are the commands
26642 \begin_inset space \hspace{}
26651 \begin_inset space \hspace{}
26657 , because they can be inserted in LyX directly to text.
26660 \begin_layout Subsection
26662 \begin_inset CommandInset label
26664 name "sub:Accents-in-Text"
26669 \begin_inset Index idx
26672 \begin_layout Plain Layout
26681 \begin_layout Standard
26682 With the following commands all letters can be accented.
26683 The commands must be inserted in TeX-mode.
26686 \begin_layout Standard
26687 \begin_inset space \hfill{}
26691 \begin_inset Tabular
26692 <lyxtabular version="3" rows="8" columns="2">
26693 <features tabularvalignment="middle">
26694 <column alignment="block" valignment="top" width="0">
26695 <column alignment="block" valignment="top" width="0">
26697 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26700 \begin_layout Plain Layout
26706 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26709 \begin_layout Plain Layout
26717 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26720 \begin_layout Plain Layout
26724 \begin_inset Quotes grd
26732 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26735 \begin_layout Plain Layout
26739 \begin_layout Plain Layout
26755 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26758 \begin_layout Plain Layout
26766 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26769 \begin_layout Plain Layout
26773 \begin_layout Plain Layout
26789 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26792 \begin_layout Plain Layout
26799 \begin_layout Plain Layout
26813 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26816 \begin_layout Plain Layout
26820 \begin_layout Plain Layout
26836 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26839 \begin_layout Plain Layout
26847 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26850 \begin_layout Plain Layout
26854 \begin_layout Plain Layout
26870 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26873 \begin_layout Plain Layout
26880 \begin_layout Plain Layout
26894 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26897 \begin_layout Plain Layout
26901 \begin_layout Plain Layout
26917 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26920 \begin_layout Plain Layout
26927 \begin_layout Plain Layout
26941 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26944 \begin_layout Plain Layout
26948 \begin_layout Plain Layout
26964 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26967 \begin_layout Plain Layout
26974 \begin_layout Plain Layout
26988 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26991 \begin_layout Plain Layout
26995 \begin_layout Plain Layout
27015 \begin_inset space \hfill{}
27019 \begin_inset Tabular
27020 <lyxtabular version="3" rows="8" columns="2">
27021 <features tabularvalignment="middle">
27022 <column alignment="block" valignment="top" width="0">
27023 <column alignment="center" valignment="top" width="0">
27025 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27028 \begin_layout Plain Layout
27034 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27037 \begin_layout Plain Layout
27045 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27048 \begin_layout Plain Layout
27055 \begin_layout Plain Layout
27069 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27072 \begin_layout Plain Layout
27076 \begin_layout Plain Layout
27092 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27095 \begin_layout Plain Layout
27103 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27106 \begin_layout Plain Layout
27110 \begin_layout Plain Layout
27126 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27129 \begin_layout Plain Layout
27133 \begin_inset Index idx
27136 \begin_layout Plain Layout
27147 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27150 \begin_layout Plain Layout
27154 \begin_layout Plain Layout
27170 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27173 \begin_layout Plain Layout
27181 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27184 \begin_layout Plain Layout
27188 \begin_layout Plain Layout
27204 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27207 \begin_layout Plain Layout
27214 \begin_layout Plain Layout
27228 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27231 \begin_layout Plain Layout
27235 \begin_layout Plain Layout
27251 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27254 \begin_layout Plain Layout
27261 \begin_layout Plain Layout
27275 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27278 \begin_layout Plain Layout
27282 \begin_layout Plain Layout
27298 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27301 \begin_layout Plain Layout
27308 \begin_layout Plain Layout
27322 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27325 \begin_layout Plain Layout
27329 \begin_layout Plain Layout
27349 \begin_inset space \hfill{}
27355 \begin_layout Standard
27356 \begin_inset VSpace medskip
27365 also two different characters can be accented.
27374 \begin_layout Plain Layout
27389 \begin_layout Plain Layout
27401 \begin_layout Standard
27414 can in combination with vowels directly be inserted with the keyboard without
27416 The same applies for the tilde
27420 \begin_layout Plain Layout
27421 This only applies for keyboards where the tilde is defined as accent.
27430 in combination with
27445 \begin_layout Standard
27488 and accents that are inserted directly with the keyboard are also available
27489 in mathematical text.
27490 For the other accents there are special math commands to be used in formulas,
27492 \begin_inset CommandInset ref
27494 reference "sub:Accents-for-one"
27501 \begin_layout Standard
27502 \begin_inset VSpace bigskip
27505 Furthermore, with the command
27512 \begin_inset Index idx
27515 \begin_layout Plain Layout
27523 all numbers and letters can be set into a circle, quasi accented with a
27524 circle, similar to the copyright symbol.
27527 \begin_layout Standard
27529 \begin_inset Tabular
27530 <lyxtabular version="3" rows="3" columns="2">
27531 <features tabularvalignment="middle">
27532 <column alignment="center" valignment="top" width="0">
27533 <column alignment="center" valignment="top" width="0">
27535 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27538 \begin_layout Plain Layout
27544 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27547 \begin_layout Plain Layout
27549 \begin_inset Note Note
27552 \begin_layout Plain Layout
27559 is only used as spacer.
27571 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27574 \begin_layout Plain Layout
27582 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27585 \begin_layout Plain Layout
27589 \begin_layout Plain Layout
27605 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27608 \begin_layout Plain Layout
27619 raisebox{-1.5pt}{W}}
27624 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27627 \begin_layout Plain Layout
27628 \begin_inset Formula $\raisebox{4.5mm}{}$
27635 \begin_layout Plain Layout
27653 \begin_inset Formula $\raisebox{-2mm}{}$
27669 \begin_layout Standard
27670 One has to take care that the character fits in the circle.
27681 \begin_layout Plain Layout
27683 \begin_inset CommandInset ref
27685 reference "sub:Font-Sizes"
27694 specifies thereby the size of the circle.
27705 \begin_layout Plain Layout
27707 \begin_inset CommandInset ref
27709 reference "sub:Boxes-without-Frame"
27718 the character can be centered.
27721 \begin_layout Subsection
27723 \begin_inset Index idx
27726 \begin_layout Plain Layout
27735 \begin_layout Standard
27736 Old-style figures (also known as old-style numerals) are created with the
27744 \begin_inset Index idx
27747 \begin_layout Plain Layout
27756 The command can be used in formulas and in TeX-mode.
27757 The command scheme is:
27760 \begin_layout Standard
27765 oldstylenums{number}
27768 \begin_layout Standard
27773 oldstylenums{0123456789
27776 \begin_inset Formula $\oldstylenums{0123456789}$
27782 \begin_layout Subsection
27783 Miscellaneous special Characters
27784 \begin_inset CommandInset label
27786 name "sub:Miscellaneous-special-Characters"
27791 \begin_inset Index idx
27794 \begin_layout Plain Layout
27795 Special characters ! miscellaneous
27803 \begin_layout Standard
27804 The following characters can only be inserted to formulas by using commands:
27807 \begin_layout Standard
27809 \begin_inset Tabular
27810 <lyxtabular version="3" rows="4" columns="2">
27811 <features tabularvalignment="middle">
27812 <column alignment="center" valignment="top" width="0">
27813 <column alignment="center" valignment="top" width="0">
27815 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27818 \begin_layout Plain Layout
27824 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27827 \begin_layout Plain Layout
27835 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27838 \begin_layout Plain Layout
27845 \begin_layout Plain Layout
27859 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27862 \begin_layout Plain Layout
27863 \begin_inset Formula $\mathcircumflex$
27873 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27876 \begin_layout Plain Layout
27884 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27887 \begin_layout Plain Layout
27888 \begin_inset Formula $\_$
27898 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27901 \begin_layout Plain Layout
27906 \begin_layout Plain Layout
27918 \begin_inset Index idx
27921 \begin_layout Plain Layout
27934 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27937 \begin_layout Plain Layout
27938 \begin_inset Formula $^{\circ}$
27954 \begin_layout Standard
27955 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
27956 contains the following line
27960 \begin_layout Plain Layout
27961 More about this is described in
27962 \begin_inset CommandInset ref
27964 reference "sub:Text-Characters-in"
27976 \begin_layout Standard
27981 DeclareInputtext{176}{
27994 \begin_layout Standard
27995 \begin_inset Newpage newpage
28001 \begin_layout Section
28003 \begin_inset CommandInset label
28005 name "sec:Formula-Styles"
28010 \begin_inset Index idx
28013 \begin_layout Plain Layout
28022 \begin_layout Itemize
28023 There are two different alignment styles:
28027 \begin_layout Description
28028 Centered is the predefined standard
28031 \begin_layout Description
28032 Indented for this the option
28036 must be inserted in the menu
28038 Document\SpecialChar \menuseparator
28044 \begin_inset space ~
28050 \begin_layout Standard
28055 is used, the indentation can be adjusted with the length
28062 \begin_inset Index idx
28065 \begin_layout Plain Layout
28074 Should the distance be 15
28075 \begin_inset space \thinspace{}
28078 mm, the following command line is inserted in the LaTeX-preamble
28081 \begin_layout Standard
28091 \begin_layout Standard
28092 When no length is specified, the predefined value of 30
28093 \begin_inset space \thinspace{}
28100 \begin_layout Itemize
28101 And two different numbering styles:
28105 \begin_layout Description
28106 Right is the predefined standard
28109 \begin_layout Description
28110 Left for this the option
28114 must be inserted in the menu
28116 Document\SpecialChar \menuseparator
28122 \begin_inset space ~
28129 \begin_layout Standard
28138 can also be used together.
28139 In this case both options are inserted, separated by a comma.
28142 \begin_layout Standard
28143 The chosen styles are used for all displayed formulas of the document.
28144 When both, centered and indented formulas should be created in a document,
28150 The indented formulas are then set in a flalign environment, see
28151 \begin_inset CommandInset ref
28153 reference "sub:Flalign-Environment"
28160 \begin_layout Section
28162 \begin_inset CommandInset label
28164 name "sec:Multiline-Formulas"
28169 \begin_inset Index idx
28172 \begin_layout Plain Layout
28173 Formula ! multiline
28181 \begin_layout Subsection
28185 \begin_layout Standard
28186 In LyX multiline formulas are created by pressing
28191 arg "newline-insert newline"
28197 This creates either an
28199 eqnarray environment
28201 that is described in
28202 \begin_inset CommandInset ref
28204 reference "sub:Eqnarray-Environment"
28208 or, when the option
28210 Use AMS math package
28212 in the document settings is selected, an
28216 that is described in
28217 \begin_inset CommandInset ref
28219 reference "sub:Standard-align-Environment"
28225 \change_inserted -1853239151 1334713000
28226 The align environment is recommended.
28231 \begin_layout Standard
28232 There are other multiline formula environments that can be created via the
28235 Insert\SpecialChar \menuseparator
28239 These environments are described in the following sections.
28242 \begin_layout Standard
28243 In all multiline formula environments a new line is created by pressing
28247 arg "newline-insert newline"
28251 To add or delete lines, the math toolbar buttons
28252 \begin_inset Graphics
28253 filename ../images/tabular-feature_append-row.png
28259 \begin_inset Graphics
28260 filename ../images/tabular-feature_delete-row.png
28265 , respectively, or the menu
28267 Edit\SpecialChar \menuseparator
28273 \begin_layout Subsubsection
28275 \begin_inset CommandInset label
28277 name "sub:Line-Separation"
28282 \begin_inset Index idx
28285 \begin_layout Plain Layout
28286 Formula ! multiline ! Line separation
28294 \begin_layout Standard
28295 There is sometimes not enough space in multiline formulas between the lines:
28296 \begin_inset Formula
28298 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}\\
28299 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
28307 \begin_layout Standard
28308 In LaTeX additional line space is specified as optional argument of the
28310 This is not yet possible in LyX
28314 \begin_layout Plain Layout
28316 \begin_inset CommandInset href
28318 name "LyX-bug #1505"
28319 target "http://www.lyx.org/trac/ticket/1505"
28328 , therefore the whole formula must be inserted in TeX-mode.
28329 To add in our example space, the command
28337 is inserted at the end of the first line.
28342 \begin_layout Plain Layout
28349 \begin_layout Plain Layout
28351 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
28354 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
28361 \begin_layout Plain Layout
28365 left(B^{2}+x_{0}^{2}
28373 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
28378 \begin_layout Plain Layout
28390 \begin_layout Standard
28391 \begin_inset VSpace bigskip
28394 To set the line separation for all lines in a formula, the length
28401 \begin_inset Index idx
28404 \begin_layout Plain Layout
28414 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
28425 \begin_inset space \thinspace{}
28430 \begin_inset space \thinspace{}
28433 mm additional line separation as in the previous example, the command
28436 \begin_layout Standard
28446 \begin_layout Standard
28447 is inserted in TeX-mode before the formula.
28448 This requires that the LaTeX-package
28456 \begin_layout Plain Layout
28461 is part of every LaTeX standard installation.
28467 \begin_inset Index idx
28470 \begin_layout Plain Layout
28476 was loaded in LaTeX-preamble with the line
28479 \begin_layout Standard
28487 \begin_layout Standard
28492 \begin_layout Plain Layout
28504 \begin_inset Formula
28506 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}\\
28507 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
28515 \begin_layout Standard
28519 \begin_layout Plain Layout
28530 To get back to the predefined distance,
28536 is set to the value 3
28537 \begin_inset space \thinspace{}
28543 \begin_layout Subsubsection
28545 \begin_inset CommandInset label
28547 name "sub:Column-Separation"
28552 \begin_inset Index idx
28555 \begin_layout Plain Layout
28556 Formula ! multiline ! Column separation
28564 \begin_layout Standard
28565 Multiline formulas form a matrix.
28566 A formula in the eqnarray environment is for example a matrix with three
28568 By changing the column separation in this environment, the space beside
28569 the relation sign can be changed.
28572 \begin_layout Standard
28573 The column separation is specified with the length
28580 \begin_inset Index idx
28583 \begin_layout Plain Layout
28592 \begin_inset Newline newline
28595 column separation = 2
28596 \begin_inset space \thinspace{}
28606 \begin_inset Newline newline
28612 \begin_layout Standard
28622 \begin_layout Standard
28623 inserted in TeX-mode, sets for all following formulas a column separation
28625 \begin_inset space \thinspace{}
28629 To get back to the predefined distance,
28636 \begin_inset space \thinspace{}
28642 \begin_layout Standard
28644 \begin_inset space \thinspace{}
28647 cm column separation:
28651 \begin_layout Plain Layout
28663 \begin_inset Formula
28671 A formula with the predefined column separation for matrices of 10
28672 \begin_inset space \thinspace{}
28679 \begin_layout Plain Layout
28691 \begin_inset Formula
28702 \begin_layout Subsubsection
28704 \begin_inset Index idx
28707 \begin_layout Plain Layout
28716 \begin_layout Standard
28717 Long formulas can be typeset using these methods:
28720 \begin_layout Itemize
28721 When one side of the equation is much shorter than the line width, this
28722 one is chosen for the left side and the right side is typeset over two
28724 \begin_inset Formula
28726 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 \\
28727 & & -\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:shortlong}
28732 The minus sign at the beginning of the second line does normally not appear
28733 as an operator because it is the first character of the line.
28734 Thus it would not be surrounded by space and could not be distinguished
28735 from the fraction bar.
28737 \begin_inset space \thinspace{}
28740 pt space was inserted behind the minus sign with the command
28750 \begin_layout Plain Layout
28758 \begin_inset CommandInset ref
28760 reference "sub:Variable-Space"
28770 \begin_inset Index idx
28773 \begin_layout Plain Layout
28782 \change_inserted -1853239151 1334712095
28783 Note that the label is only applied to the second line.
28788 \begin_layout Itemize
28789 When both sides of the equation are too long, the command
28796 \begin_inset Index idx
28799 \begin_layout Plain Layout
28808 It is inserted in the first column of the first line and causes all further
28809 insertions to overwrite the following columns:
28810 \begin_inset Formula
28812 \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 \\
28813 & & -\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 \\
28814 & & =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}
28819 After the insertion of
28825 , the cursor is in a purple box that is a bit shifted to the left from the
28827 In this the formula is inserted.
28828 \begin_inset Newline newline
28831 The content of the further lines is inserted to the second or another formula
28833 The greater the column number where it was inserted, the larger the indentation.
28834 \begin_inset VSpace medskip
28838 \begin_inset Newline newline
28842 \begin_inset Note Greyedout
28845 \begin_layout Plain Layout
28846 Note the following when using
28855 \begin_layout Itemize
28856 The formula doesn't use the full page width.
28858 \begin_inset space \thinspace{}
28862 \begin_inset space \space{}
28866 \begin_inset Formula $-B^{2}$
28869 is added to the first line in the above example, it would have been outside
28871 To better use the width, negative space can be inserted at the beginning
28875 \begin_layout Itemize
28876 Due to a bug in LyX the cursor cannot be set with the mouse into the first
28881 \begin_layout Plain Layout
28882 \begin_inset CommandInset href
28884 name "LyX-bug #1429"
28885 target "http://www.lyx.org/trac/ticket/1429"
28894 One can only set the cursor at the beginning of the line and move it with
28903 \begin_layout Itemize
28904 Other methods to set long formulas are offered by the environments described
28906 \begin_inset CommandInset ref
28908 reference "sub:Multline-Environment"
28913 \begin_inset CommandInset ref
28915 reference "sub:Multiline-Formula-Parts"
28922 \begin_layout Subsubsection
28924 \begin_inset CommandInset label
28926 name "sub:Multiline-Brackets"
28931 \begin_inset Index idx
28934 \begin_layout Plain Layout
28935 Brackets ! for multiline expressions
28943 \begin_layout Standard
28944 For brackets spanning multiple lines the following problem occurs:
28945 \begin_inset Formula
28947 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28948 & & \left.\cdots+B-D\right]
28956 \begin_layout Standard
28957 The closing bracket is smaller than the opening bracket because brackets
28958 with variable size may not span multiple lines.
28961 \begin_layout Standard
28962 To set the bracket size for the second line correctly, the first line is
28970 \begin_inset Index idx
28973 \begin_layout Plain Layout
28981 and the second line with
28989 \begin_layout Plain Layout
29003 \begin_inset CommandInset ref
29005 reference "sub:Automatic-Bracket-Size"
29017 \begin_inset Index idx
29020 \begin_layout Plain Layout
29046 \begin_layout Plain Layout
29065 \begin_layout Plain Layout
29084 \begin_layout Plain Layout
29096 \begin_inset Formula $\downarrow$
29102 \begin_inset Index idx
29105 \begin_layout Plain Layout
29113 is inserted, because the multiplication operator with its limits is the
29114 largest symbol in the first line and this should be the size for the bracket
29115 in the second line.
29118 \begin_layout Standard
29119 The result is this:
29120 \begin_inset Formula
29122 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
29123 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
29131 \begin_layout Subsection
29135 \begin_layout Standard
29136 Align environments can be used for every kind of multiline formulas.
29137 They are especially useful to set several formulas side by side.
29140 \begin_layout Standard
29141 Align environments consist of columns.
29142 The odd columns are right aligned, the even ones left aligned.
29143 Every line in an Align environment can be numbered.
29146 \begin_layout Standard
29147 Align environments are created via the menu
29149 Insert\SpecialChar \menuseparator
29155 Edit\SpecialChar \menuseparator
29156 Math\SpecialChar \menuseparator
29157 Change Formula Type
29159 already existing formulas can be converted to Align environments.
29162 \begin_layout Standard
29163 To add or delete columns, the math toolbar buttons
29164 \begin_inset Graphics
29165 filename ../images/tabular-feature_append-column.png
29171 \begin_inset Graphics
29172 filename ../images/tabular-feature_delete-column.png
29177 , respectively, or the menu
29179 Edit\SpecialChar \menuseparator
29185 \begin_layout Subsubsection
29186 Standard align Environment
29187 \begin_inset CommandInset label
29189 name "sub:Standard-align-Environment"
29194 \begin_inset Index idx
29197 \begin_layout Plain Layout
29198 Formula ! multiline ! align environment
29206 \begin_layout Standard
29207 This Align environment is created by presssing
29210 arg "newline-insert newline"
29213 in a formula or by the menu
29215 Insert\SpecialChar \menuseparator
29216 Math\SpecialChar \menuseparator
29217 AMS align Environment
29222 \begin_layout Standard
29223 An example for two formulas set side by side, that are created with a four
29224 column align environment:
29225 \begin_inset Formula
29227 A & =\sin(B) & C & =D\\
29228 C & \ne A & B & \ne D
29233 As it can be seen, the formulas in this environment are placed so as if
29242 \begin_layout Plain Layout
29250 \begin_inset CommandInset ref
29252 reference "sub:Variable-Space"
29263 before the first and after every even column.
29264 When the formula style
29270 \begin_layout Plain Layout
29272 \begin_inset CommandInset ref
29274 reference "sec:Formula-Styles"
29285 is used, the formula is set without the
29291 before the first column.
29294 \begin_layout Subsubsection
29295 Alignat Environment
29296 \begin_inset Index idx
29299 \begin_layout Plain Layout
29300 Formula ! multiline ! alignat environment
29308 \begin_layout Standard
29309 The alignat environment has no predefined column separation.
29310 It can be inserted manually with the spaces that are described
29311 \begin_inset CommandInset ref
29313 reference "sub:Space"
29320 \begin_layout Standard
29321 The above example in the alignat environment where 1
29322 \begin_inset space \thinspace{}
29325 cm space was inserted at the beginning of the second formula:
29326 \begin_inset Formula
29327 \begin{alignat*}{2}
29328 A & =\sin(B) & \hspace{1cm}C & =D\\
29329 C & \ne A & B & \ne D
29334 Because the column separation can be set separately for every column, this
29335 environment is especially suitable to set three and more formulas side
29339 \begin_layout Subsubsection
29340 Flalign Environment
29341 \begin_inset CommandInset label
29343 name "sub:Flalign-Environment"
29348 \begin_inset Index idx
29351 \begin_layout Plain Layout
29352 Formula ! multiline ! flalign environment
29360 \begin_layout Standard
29361 In this environment the first two columns are always set as much as possible
29362 to the left and the last two ones to the right.
29364 \begin_inset Formula
29366 A & =1 & B & =2 & C & =3\\
29367 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
29375 \begin_layout Standard
29376 By creating a flalign environment with an odd number of columns where an
29377 empty TeX-brace is inserted to the last column, several formulas in a document
29378 can be set to the left, although the formula style
29383 As example the indented formula
29384 \begin_inset CommandInset ref
29386 reference "eq:VolInt"
29391 \begin_inset Formula
29393 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}
29398 The first two columns contain the formula.
29399 To indent it as with the formula style
29404 \begin_inset space \thinspace{}
29407 pt space was inserted at the beginning of the first column.
29410 \begin_layout Subsection
29411 Eqnarray Environment
29412 \begin_inset CommandInset label
29414 name "sub:Eqnarray-Environment"
29419 \begin_inset Index idx
29422 \begin_layout Plain Layout
29423 Formula ! multiline ! eqnarray environment
29431 \begin_layout Standard
29432 When this environment has been created, three blue boxes appear.
29433 The content of the first box is right aligned, the content of the last
29435 The content of the middle box appears centered and a bit smaller, because
29436 it is designed to insert there only relation characters.
29437 \begin_inset Formula
29439 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
29449 \begin_layout Subsection
29451 \begin_inset Index idx
29454 \begin_layout Plain Layout
29455 Formula ! multiline ! gather environment
29463 \begin_layout Standard
29464 This environment consists of only one centered column.
29465 Every line can be numbered.
29466 \begin_inset Formula
29477 \begin_layout Subsection
29478 Multline Environment
29479 \begin_inset CommandInset label
29481 name "sub:Multline-Environment"
29486 \begin_inset Index idx
29489 \begin_layout Plain Layout
29490 Formula ! multiline ! multline environment
29498 \begin_layout Standard
29499 The multline environment consists, like the gather environment, of only
29501 But the first line is left aligned, the last one right aligned.
29502 All other lines are centered.
29503 Therefore this environment is suitable for long formulas.
29505 \begin_inset CommandInset ref
29507 reference "eq:lefteqn"
29511 in the multline environment:
29512 \begin_inset Formula
29514 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}\\
29515 -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}\\
29516 =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}}
29524 \begin_layout Standard
29525 In the output only the last (first) line of a multline environment appears
29526 numbered when the document numbering is right (left).
29530 \begin_layout Plain Layout
29531 numbering styles see
29532 \begin_inset CommandInset ref
29534 reference "sec:Formula-Styles"
29546 \begin_layout Standard
29554 \begin_inset Index idx
29557 \begin_layout Plain Layout
29572 \begin_inset Index idx
29575 \begin_layout Plain Layout
29583 a centered line can be right or left aligned, respectively.
29584 The commands are used as follows:
29587 \begin_layout Standard
29592 shoveright{line content}
29598 shoveleft{line content}
29601 \begin_layout Standard
29602 \begin_inset VSpace medskip
29612 \begin_inset Index idx
29615 \begin_layout Plain Layout
29623 specifies the distance of the first line from the left page margin.
29624 Predefined is the length 0
29625 \begin_inset space \thinspace{}
29631 \begin_layout Standard
29632 As example the above formula where the command
29635 \begin_layout Standard
29645 \begin_layout Standard
29646 was inserted in TeX-mode before:
29650 \begin_layout Plain Layout
29662 \begin_inset Formula
29664 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}\\
29665 \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}}\\
29666 =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}}
29675 \begin_layout Plain Layout
29686 The second line was left aligned using
29695 \begin_layout Subsection
29696 Multiline Formula Parts
29697 \begin_inset CommandInset label
29699 name "sub:Multiline-Formula-Parts"
29704 \begin_inset Index idx
29707 \begin_layout Plain Layout
29708 Formula ! multiline ! formula parts
29716 \begin_layout Standard
29717 To display only parts of a formula with multiple lines, one of the following
29718 environments is used:
29735 They can be inserted via the menu
29737 Insert\SpecialChar \menuseparator
29740 or by using the commands described in this section.
29743 \begin_layout Standard
29744 The first three have the same properties as the corresponding multiline
29745 formula environments, but it is possible to set further formula parts beside
29748 \begin_inset Formula
29750 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29751 \Delta E\Delta t & \ge\frac{\hbar}{2}
29753 \right\} \textrm{Uncertainty relations}
29761 \begin_layout Standard
29762 To get this formula, a displayed formula is created where the command
29769 \begin_inset Index idx
29772 \begin_layout Plain Layout
29781 A purple box appears around the blue formula box where now columns and
29782 lines can be added.
29783 Outside the multiline environment other formula parts can be set, like
29787 \begin_layout Standard
29788 The aligned environment is also suitable for long formulas whose lines are
29789 horizontally aligned.
29790 Using aligned in a displayed formula has the advantage that the formula
29791 number is vertically centered behind the lines.
29793 \begin_inset CommandInset ref
29795 reference "eq:shortlong"
29799 in the aligned environment:
29800 \begin_inset Formula
29802 \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}|}\\
29803 & -\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}|}
29812 \begin_layout Standard
29813 To use the environments
29832 \begin_inset Index idx
29835 \begin_layout Plain Layout
29850 \begin_inset Index idx
29853 \begin_layout Plain Layout
29868 \begin_inset Index idx
29871 \begin_layout Plain Layout
29879 are inserted, respectively.
29880 The split environment has the same properties as the aligned environment
29881 but it can only have two columns.
29884 \begin_layout Subsection
29885 Text in multiline Formulas
29886 \begin_inset CommandInset label
29888 name "sub:Text-in-multiline"
29893 \begin_inset Index idx
29896 \begin_layout Plain Layout
29903 \begin_inset Index idx
29906 \begin_layout Plain Layout
29907 Formula ! multiline ! text
29915 \begin_layout Standard
29916 In the Align environments, and the multline and gather environment, text
29917 can be inserted that will appear in a separate line and doesn't affect
29918 the column alignment.
29919 To do this, the command
29926 \begin_inset Index idx
29929 \begin_layout Plain Layout
29937 is used in the following scheme:
29940 \begin_layout Standard
29948 \begin_layout Standard
29949 The text should not be longer than a line because it cannot be hyphenated.
29950 As LyX doesn't yet support
29956 directly, the text is written as mathematical text.
29963 must hereby be at the beginning of a line and appears in the output above
29965 An example where the text was inserted at the beginning of the second line:
29966 \begin_inset Formula
29968 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29969 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29977 \begin_layout Standard
29978 \begin_inset Newpage newpage
29984 \begin_layout Section
29986 \begin_inset Index idx
29989 \begin_layout Plain Layout
29996 \begin_inset Index idx
29999 \begin_layout Plain Layout
30000 Formula ! numbering|see
30004 \begin_layout Plain Layout
30015 \begin_layout Plain Layout
30030 \begin_layout Subsection
30034 \begin_layout Standard
30035 Numbered formulas can be created with the menu
30037 Insert\SpecialChar \menuseparator
30038 Math\SpecialChar \menuseparator
30040 \begin_inset space ~
30048 \begin_inset space ~
30054 Existing formulas can be numbered with the menu
30056 Edit\SpecialChar \menuseparator
30057 Math\SpecialChar \menuseparator
30059 \begin_inset space ~
30067 arg "math-number-toggle"
30071 The formula number is displayed in LyX behind the formula as a number sign
30073 The number sign is replaced in the output by the formula number.
30076 \begin_layout Standard
30077 When numbering is turned on in multiline formulas, all lines will be numbered.
30078 But the numbering can be controlled with the menu
30080 Edit\SpecialChar \menuseparator
30081 Math\SpecialChar \menuseparator
30083 \begin_inset space ~
30087 \begin_inset space ~
30091 \begin_inset space ~
30099 arg "math-number-line-toggle"
30105 \begin_layout Standard
30106 Except for inline formulas, all formulas can be numbered with two different
30108 \begin_inset CommandInset ref
30110 reference "sec:Formula-Styles"
30117 \begin_layout Subsection
30119 \begin_inset Index idx
30122 \begin_layout Plain Layout
30123 Cross-references ! to formulas
30131 \begin_layout Standard
30132 All labeled formulas can be cross-referenced.
30133 A label is added by the menu
30135 Insert\SpecialChar \menuseparator
30138 or the toolbar button
30139 \begin_inset Graphics
30140 filename ../images/label-insert.png
30146 The cursor must hereby be inside a displayed formula.
30147 A dialog pops up displaying the prefix
30152 The label is inserted there behind the prefix.
30153 The predefined prefix means
30154 \begin_inset Quotes eld
30158 \begin_inset Quotes erd
30161 and makes it easier to find labels in large documents because it marks
30162 it as formula label to divide it from e.
30163 \begin_inset space \thinspace{}
30167 \begin_inset space \space{}
30171 To change a label, the menu
30173 Insert\SpecialChar \menuseparator
30177 \change_inserted -1853239151 1334715366
30178 or you can right-click on the formula and click on
30179 \begin_inset Quotes eld
30183 \begin_inset Quotes erd
30191 \begin_layout Standard
30192 The name of the label is displayed in LyX within two parentheses behind
30194 A formula with a label is always numbered.
30197 \begin_layout Standard
30198 Cross-references are inserted via the menu
30200 Insert\SpecialChar \menuseparator
30203 or with the toolbar button
30204 \begin_inset Graphics
30205 filename ../images/dialog-show-new-inset_ref.png
30211 A formula cross-reference appears in the output as formula number.
30212 When in the cross-reference dialog window the format
30216 is chosen, the cross-reference appears in the output as formula number
30218 \begin_inset Newline newline
30221 By right-clicking on a cross-reference in LyX, one jumps to the formula
30222 that is referenced.
30225 \begin_layout Standard
30226 Here are as examples cross-references to formulas of the following subsections:
30227 \begin_inset Note Note
30230 \begin_layout Plain Layout
30231 Note the different cross-reference types.
30239 \begin_layout Standard
30241 \begin_inset CommandInset ref
30248 \begin_inset CommandInset ref
30256 \begin_inset CommandInset ref
30262 ) big Latin letters are used for the numbering in contrary to (
30263 \begin_inset CommandInset ref
30272 \begin_layout Standard
30273 \begin_inset VSpace medskip
30276 When the argument of
30284 \begin_layout Plain Layout
30292 \begin_inset CommandInset ref
30294 reference "sub:User-defined-Numbering"
30305 contains a box like in
30306 \begin_inset CommandInset ref
30308 reference "sub:Paragraph-Boxes"
30312 , the formula cannot be referenced.
30315 \begin_layout Subsection
30317 \begin_inset Index idx
30320 \begin_layout Plain Layout
30321 Formula numbering ! subnumbering
30329 \begin_layout Standard
30330 With the help of the commands
30334 begin{subequations}
30342 formulas can be subnumbered.
30343 Both commands are inserted in TeX-mode.
30346 \begin_layout Standard
30348 \begin_inset Formula
30359 \begin_layout Plain Layout
30363 addtocounter{equation}{-1}
30372 \begin_layout Plain Layout
30376 begin{subequations}
30382 \begin_inset VSpace -5mm
30386 \begin_inset Formula
30394 \begin_inset Formula
30404 \begin_layout Standard
30408 \begin_layout Plain Layout
30420 \begin_layout Standard
30421 To create the example, the following is done:
30424 \begin_layout Enumerate
30425 first formula is inserted
30428 \begin_layout Enumerate
30433 addtocounter{equation}{-1}
30435 begin{subequations}
30436 \begin_inset Index idx
30439 \begin_layout Plain Layout
30448 \begin_inset Newline newline
30453 is inserted after the first formula
30456 \begin_layout Enumerate
30457 second formula is inserted
30460 \begin_layout Enumerate
30461 third formula is inserted
30464 \begin_layout Enumerate
30471 is inserted after the third formula
30474 \begin_layout Standard
30475 Every formula between the commands
30487 is subnumbered as a, b,
30488 \begin_inset Newline linebreak
30491 c, \SpecialChar \ldots{}
30492 For multiline formulas every line will be subnumbered.
30493 All subnumbered formulas are treated as
30498 But as every numbered formula increases the counter
30502 by one, the command
30508 is needed to decrease it.
30509 Otherwise the formulas
30510 \begin_inset CommandInset ref
30517 \begin_inset CommandInset ref
30524 \begin_inset CommandInset ref
30530 would be numbered as
30531 \begin_inset CommandInset ref
30538 \begin_inset CommandInset ref
30545 \begin_inset CommandInset ref
30554 \begin_layout Standard
30555 By inserting the commands in TeX-mode, a space is created between the first
30558 \begin_inset space \thinspace{}
30561 mm vertical space is inserted after the command
30565 begin{subequations}
30568 When the formula style
30574 \begin_layout Plain Layout
30576 \begin_inset CommandInset ref
30578 reference "sec:Formula-Styles"
30590 \begin_inset space \thinspace{}
30593 mm space is inserted instead.
30596 \begin_layout Standard
30597 Here is an example for a multiline formula where the numbering was turned
30598 off for the second line:
30602 \begin_layout Plain Layout
30606 begin{subequations}
30612 \begin_inset Formula
30614 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
30615 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
30616 & = & B^{2}-2BZ+Z^{2}\label{eq:f}
30625 \begin_layout Plain Layout
30637 \begin_layout Subsection
30638 User-defined Numbering
30639 \begin_inset CommandInset label
30641 name "sub:User-defined-Numbering"
30646 \begin_inset Index idx
30649 \begin_layout Plain Layout
30650 Formula numbering ! user-defined
30658 \begin_layout Standard
30659 \begin_inset Index idx
30662 \begin_layout Plain Layout
30663 Formula numbering ! self-defined delimiters
30668 With the standard numbering parentheses are set around the formula number.
30669 To replace the parentheses for example by vertical bars, the following
30670 line is added to the LaTeX-preamble:
30673 \begin_layout Standard
30685 \begin_inset Note Note
30688 \begin_layout Plain Layout
30689 This macro is already declared in the LaTeX-preamble for testing.
30690 To activate it, remove the percent sign at the beginning.
30698 \begin_layout Standard
30699 To use other characters, the vertical bars besides the
30703 are replaced by one ore more characters.
30704 To get only the formula number the vertical bars are omitted.
30707 \begin_layout Standard
30708 \begin_inset VSpace bigskip
30711 When there should be an expression of your choice instead of the consecutive
30712 formula number in parentheses behind the formula, the command
30719 \begin_inset Index idx
30722 \begin_layout Plain Layout
30731 \begin_inset Formula
30733 A+B=C\tag{something}\label{eq:tag}
30738 In this example the command
30746 \begin_layout Plain Layout
30757 was inserted in the formula.
30760 \begin_layout Standard
30769 \begin_layout Plain Layout
30780 is inserted instead, the star prevents the parentheses around the expression:
30781 \begin_inset Formula
30783 A+B=C\tag*{something}
30791 \begin_layout Standard
30792 \begin_inset VSpace bigskip
30795 To restart the formula numbering with new document parts or sections, the
30796 following command is used:
30799 \begin_layout Standard
30804 @addtoreset{equation}{part}
30807 \begin_inset Index idx
30810 \begin_layout Plain Layout
30815 \begin_layout Plain Layout
30826 \begin_layout Plain Layout
30839 \begin_layout Plain Layout
30850 \begin_layout Plain Layout
30863 \begin_inset Newline newline
30867 \begin_inset Newline newline
30874 @addtoreset{equation}{section}
30877 \begin_layout Standard
30878 To be able to use these commands in TeX-mode, the
30879 \begin_inset Quotes eld
30883 \begin_inset Quotes erd
30886 character has to be made
30887 \begin_inset Quotes eld
30891 \begin_inset Quotes erd
30894 for LaTeX using the command
30908 So the command sequence in TeX-mode is:
30911 \begin_layout Standard
30917 \begin_inset Newline newline
30922 @addtoreset{equation}{section}
30923 \begin_inset Newline newline
30931 \begin_layout Standard
30932 In the LaTeX-preamble
30944 can be omitted as they are automatically internally inserted by LyX.
30947 \begin_layout Standard
30962 \begin_layout Plain Layout
30967 is part of the LaTeX-package
30972 \begin_inset Index idx
30975 \begin_layout Plain Layout
30976 Packages ! carlisle
30981 that is part of every LaTeX standard installation.
30987 \begin_inset Index idx
30990 \begin_layout Plain Layout
30991 Packages ! remreset
30996 has to be loaded in the LaTeX-preamble with the line
30999 \begin_layout Standard
31004 usepackage{remreset}
31007 \begin_layout Standard
31015 \begin_inset Index idx
31018 \begin_layout Plain Layout
31023 \begin_layout Plain Layout
31034 \begin_layout Plain Layout
31047 \begin_layout Plain Layout
31058 \begin_layout Plain Layout
31070 can be used with the same scheme as
31079 \begin_layout Standard
31080 \begin_inset VSpace bigskip
31083 Sometimes formulas should be numbered in the following form:
31086 \begin_layout Standard
31089 (section number.formula number)
31092 \begin_layout Standard
31093 The formula number should start with every section with
31094 \begin_inset Quotes eld
31098 \begin_inset Quotes erd
31104 \begin_layout Standard
31105 For this case there is the command
31112 \begin_inset Index idx
31115 \begin_layout Plain Layout
31123 , which is used with the following scheme:
31126 \begin_layout Standard
31131 numberwithin{counter}{sectioning}
31134 \begin_layout Standard
31135 Counter denotes what kind of numbering is affected, sectioning denotes what
31136 number is before the dot.
31139 \begin_layout Standard
31140 Thus in our case the following LaTeX-preamble or TeX code line is used:
31143 \begin_layout Standard
31148 numberwithin{equation}{section}
31151 \begin_layout Standard
31152 This is the result:
31156 \begin_layout Plain Layout
31160 numberwithin{equation}{section}
31166 \begin_inset Formula
31176 \begin_layout Standard
31178 \begin_inset space \thinspace{}
31182 \begin_inset space \space{}
31185 tables so that the number of the part is the sectioning,
31186 \begin_inset Newline newline
31193 numberwithin{table}{part}
31198 \begin_layout Standard
31199 To go back to the standard numbering or to prevent this kind of numbering
31200 when it is defined by the document class, the following command is inserted
31201 as TeX code or to the LaTeX-preamble:
31204 \begin_layout Standard
31214 \begin_inset Index idx
31217 \begin_layout Plain Layout
31231 \begin_layout Plain Layout
31247 \begin_inset Newline newline
31255 \begin_inset Newline newline
31267 \begin_layout Standard
31274 uses internally the command
31280 , described above, that also needs to be reverted.
31284 \begin_layout Plain Layout
31291 \begin_layout Plain Layout
31295 @removefromreset{equation}{section}
31298 \begin_layout Plain Layout
31310 \begin_layout Subsection
31311 Numbering with Roman Numbers and Letters
31312 \begin_inset Index idx
31315 \begin_layout Plain Layout
31316 Formula numbering ! with letters
31322 \begin_inset Index idx
31325 \begin_layout Plain Layout
31326 Formula numbering ! with Roman numbers
31334 \begin_layout Standard
31335 Formulas can also be numbered with Roman numbers and Latin letters.
31336 To number for example with small Roman numbers, the command
31339 \begin_layout Standard
31351 \begin_layout Standard
31352 is inserted before the formula in TeX-mode.
31360 \begin_inset Index idx
31363 \begin_layout Plain Layout
31371 redefines the predefined command
31387 \begin_layout Plain Layout
31394 has the same scheme like the command
31400 that is described in
31401 \begin_inset CommandInset ref
31403 reference "sub:The-Command-newcommand"
31416 is the formula counter.
31423 is used as prefix for a counter, the value of the counter is output as
31425 When a formula is numbered, LaTeX sets internally the command
31431 behind the formula.
31437 \begin_inset Index idx
31440 \begin_layout Plain Layout
31450 outputs the counter as small Roman number.
31453 \begin_layout Standard
31454 All formulas behind the command
31464 are now numbered Roman.
31465 To switch to numbering with big Roman numbers, the command is inserted
31479 \begin_inset Index idx
31482 \begin_layout Plain Layout
31494 \begin_inset Quotes eld
31498 \begin_inset Quotes erd
31501 with small Latin letters there is the command
31508 \begin_inset Index idx
31511 \begin_layout Plain Layout
31519 , for big ones there is the command
31526 \begin_inset Index idx
31529 \begin_layout Plain Layout
31542 \begin_layout Standard
31543 \begin_inset Note Greyedout
31546 \begin_layout Plain Layout
31551 Only maximal 26 formulas can be numbered with Latin letters in one document.
31559 \begin_layout Standard
31563 \begin_layout Plain Layout
31579 \begin_layout Standard
31580 \begin_inset Formula
31582 A=\textrm{small roman}
31591 \begin_layout Plain Layout
31605 \begin_inset Formula
31607 B=\textrm{big Roman}\label{eq:Rom}
31616 \begin_layout Plain Layout
31630 \begin_inset Formula
31632 C=\textrm{small Latin}
31641 \begin_layout Plain Layout
31655 \begin_inset Formula
31657 D=\textrm{big Latin}\label{eq:Lat}
31665 \begin_layout Standard
31666 To switch back to the default numbering, insert the command:
31669 \begin_layout Standard
31679 \begin_inset Index idx
31682 \begin_layout Plain Layout
31693 \begin_layout Standard
31697 \begin_layout Plain Layout
31711 \begin_inset Formula
31721 \begin_layout Standard
31722 \begin_inset VSpace medskip
31725 As you see, formulas are numbered serially independent from the numbering
31727 When then numbering should start with
31728 \begin_inset Quotes eld
31732 \begin_inset Quotes erd
31735 when the style is changed, new equation counters have to be defined.
31736 A description about this can be found in the file
31737 \begin_inset CommandInset href
31739 name "Formula-numbering.lyx"
31740 target "run:Formula-numbering.lyx"
31747 \begin_layout Section
31748 Chemical Symbols and Equations
31749 \begin_inset CommandInset label
31751 name "sub:Chemical-Symbols-and"
31756 \begin_inset Index idx
31759 \begin_layout Plain Layout
31760 Chemical characters ! Symbols
31766 \begin_inset Index idx
31769 \begin_layout Plain Layout
31776 \begin_inset Index idx
31779 \begin_layout Plain Layout
31788 \begin_layout Standard
31789 An example text from chemistry:
31792 \begin_layout Quote
31794 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
31797 -ion reacts with two
31798 \begin_inset Formula $\mathrm{Na^{+}}$
31801 -ions to sodium sulfate
31802 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
31806 The chemical equation for this is:
31807 \begin_inset Formula
31809 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
31817 \begin_layout Standard
31818 This chemical equation can directly be created as formula.
31819 To avoid that the symbols appear italic, everything is highlighted and
31820 changed by the shortcut
31826 to the upright font style.
31830 \begin_layout Plain Layout
31836 \begin_inset CommandInset ref
31838 reference "sub:Font-Styles"
31850 \begin_layout Standard
31851 A more convenient way to typeset chemical formulas is to use the command
31859 \begin_inset Index idx
31862 \begin_layout Plain Layout
31870 that is available when the LaTeX-package
31875 \begin_inset Index idx
31878 \begin_layout Plain Layout
31891 to a formula a new blue box appears where chemical formulas can be inserted
31892 in an intuitive way.
31895 \begin_layout Standard
31897 \begin_inset Tabular
31898 <lyxtabular version="3" rows="9" columns="2">
31899 <features tabularvalignment="middle">
31900 <column alignment="center" valignment="top" width="0">
31901 <column alignment="center" valignment="top" width="0">
31903 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31906 \begin_layout Plain Layout
31912 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31915 \begin_layout Plain Layout
31917 \begin_inset Note Note
31920 \begin_layout Plain Layout
31927 is only used as spacer.
31939 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31942 \begin_layout Plain Layout
31949 \begin_layout Plain Layout
31963 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31966 \begin_layout Plain Layout
31967 \begin_inset Formula $\raisebox{4.5mm}{}\ce{H2CO3}\raisebox{-2mm}{}$
31977 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31980 \begin_layout Plain Layout
31987 \begin_layout Plain Layout
32001 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32004 \begin_layout Plain Layout
32005 \begin_inset Formula $\raisebox{5mm}{}\ce{SO4^{2-}}\raisebox{-2mm}{}$
32015 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32018 \begin_layout Plain Layout
32025 \begin_layout Plain Layout
32039 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32042 \begin_layout Plain Layout
32043 \begin_inset Formula $\raisebox{4.5mm}{}\ce{(NH4)2S}\raisebox{-2mm}{}$
32053 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32056 \begin_layout Plain Layout
32063 \begin_layout Plain Layout
32077 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32080 \begin_layout Plain Layout
32081 \begin_inset Formula $\raisebox{4.5mm}{}\ce{KCr(SO4)2.12H2O}\raisebox{-2mm}{}$
32091 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32094 \begin_layout Plain Layout
32101 \begin_layout Plain Layout
32116 \begin_layout Plain Layout
32131 \begin_layout Plain Layout
32145 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32148 \begin_layout Plain Layout
32149 \begin_inset Formula $\raisebox{4.5mm}{}\ce{A-B\dbond C\tbond D}\raisebox{-2mm}{}$
32159 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32162 \begin_layout Plain Layout
32169 \begin_layout Plain Layout
32179 \begin_inset Formula $\downarrow$
32183 \begin_inset Formula $\to$
32191 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32194 \begin_layout Plain Layout
32195 \begin_inset Formula $\raisebox{5mm}{}\ce{_{90}^{227}Th+}\raisebox{-2mm}{}$
32205 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32208 \begin_layout Plain Layout
32215 \begin_layout Plain Layout
32228 \begin_layout Plain Layout
32241 \begin_layout Plain Layout
32254 \begin_layout Plain Layout
32267 \begin_layout Plain Layout
32281 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32284 \begin_layout Plain Layout
32285 \begin_inset Formula $\raisebox{4.5mm}{}\ce{CO2 + C <=> 2CO}\raisebox{-2mm}{}$
32295 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32298 \begin_layout Plain Layout
32305 \begin_layout Plain Layout
32318 \begin_layout Plain Layout
32331 \begin_layout Plain Layout
32344 \begin_layout Plain Layout
32361 \begin_layout Plain Layout
32375 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32378 \begin_layout Plain Layout
32379 \begin_inset Formula $\raisebox{5mm}{}\ce{CO2 + C ->[\alpha][\beta] 2CO}\raisebox{-4mm}{}$
32395 \begin_layout Standard
32396 \begin_inset Note Greyedout
32399 \begin_layout Plain Layout
32404 Inserting a formula to a
32410 box will lead to LaTeX errors.
32411 In this case TeX code has to be used like for
32425 \begin_layout Plain Layout
32446 \begin_layout Standard
32453 the command for equation
32454 \begin_inset space ~
32458 \begin_inset CommandInset ref
32460 reference "eq:chem-reaction"
32465 \begin_inset Newline newline
32476 \begin_layout Plain Layout
32489 \begin_layout Plain Layout
32502 \begin_layout Plain Layout
32515 \begin_layout Plain Layout
32528 \begin_layout Plain Layout
32541 \begin_layout Plain Layout
32553 \begin_layout Standard
32554 To create multiline chemical equations first a multiline formula is created
32556 \begin_inset CommandInset ref
32558 reference "sec:Multiline-Formulas"
32563 Afterwards the command
32569 is used in every small blue box of the formula.
32571 \begin_inset CommandInset ref
32573 reference "eq:TEOS-reaction-1"
32578 \begin_inset CommandInset ref
32580 reference "eq:TEOS-reaction-2"
32584 are an example of a multi-stage chemical reaction where every equation
32585 has its own number.
32586 \begin_inset Formula
32588 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
32589 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
32597 \begin_layout Standard
32608 package provides the command
32615 \begin_inset Index idx
32618 \begin_layout Plain Layout
32626 that has to be used for special cases.
32627 For more information about
32633 and more examples have a look at the documentation of
32638 \begin_inset CommandInset citation
32647 \begin_layout Section
32651 \begin_layout Standard
32652 LyX supports two types of commutative diagrams:
32660 that are explained in the following.
32663 \begin_layout Subsection
32665 \begin_inset Index idx
32668 \begin_layout Plain Layout
32677 \begin_layout Standard
32678 Diagrams of this type visualize relations by vertical and horizontal lines
32680 \begin_inset Formula
32682 \begin{CD}A@>>>B@>>>C\\
32693 \begin_layout Standard
32694 To get them, the command
32699 \begin_inset Index idx
32702 \begin_layout Plain Layout
32712 is inserted to a formula.
32713 A blue box appears with two dashed lines where further commands can be
32718 arg "newline-insert newline"
32721 a new line is created.
32722 Horizontal relations are inserted in odd, vertical in even formula lines.
32725 \begin_layout Standard
32726 To create the relations there are the following commands:
32729 \begin_layout Itemize
32734 creates a left arrow,
32745 \begin_layout Itemize
32750 creates an up arrow,
32758 a vertical equal sign
32761 \begin_layout Itemize
32767 is a placeholder for non-existent relations
32770 \begin_layout Standard
32771 All arrows can be labeled as follows:
32774 \begin_layout Itemize
32775 If text inserted between the first and second < or >, resp., it is placed
32777 When it is inserted between the second and third one, it appears under
32781 \begin_layout Itemize
32782 When text for vertical arrows is inserted between the first and second A
32783 or V, resp., it is placed left beside the arrow.
32784 When it is inserted between the second and third one, it appears right
32786 If the text contains an A or V, these letters must be set into a TeX-brace.
32789 \begin_layout Standard
32790 As example a diagram with all possible relations:
32793 \begin_layout Standard
32794 \begin_inset Formula
32796 \begin{CD}A@>j>>B@>>k>C@=F\\
32807 \begin_layout Standard
32808 The command for this is:
32809 \begin_inset Newline newline
32820 \begin_layout Plain Layout
32829 A@>j>>B@>>k>C@=F Ctrl+Return
32830 \begin_inset Newline newline
32834 \begin_inset Phantom HPhantom
32837 \begin_layout Plain Layout
32846 \begin_layout Plain Layout
32865 \begin_inset Formula $\to$
32871 \begin_inset Newline newline
32875 \begin_inset Phantom HPhantom
32878 \begin_layout Plain Layout
32887 \begin_layout Plain Layout
32904 \begin_layout Subsection
32906 \begin_inset Index idx
32909 \begin_layout Plain Layout
32910 Diagrams ! xymatrix
32918 \begin_layout Standard
32919 To be able to use xymatrices, the LaTeX-package
32924 A xymatrix is created by inserting the command
32931 Then you are able to add new matrix columns and rows like for normal matrices,
32933 \begin_inset CommandInset ref
32935 reference "sec:Matrices"
32942 \begin_layout Standard
32943 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
32945 All possibilities to create commutative diagrams and decorations are explained
32950 that you find in the menu
32952 Help\SpecialChar \menuseparator
32954 \begin_inset space ~
32962 \begin_layout Subsection
32968 \begin_inset Index idx
32971 \begin_layout Plain Layout
32980 \begin_layout Standard
32985 -diagrams, the LaTeX-package
32994 -diagram is created by inserting the command
33001 Then you are able to add new matrix columns and rows like for normal matrices,
33003 \begin_inset CommandInset ref
33005 reference "sec:Matrices"
33012 \begin_layout Standard
33013 Examples how to create
33017 diagrams in LyX is given in the
33019 Feynman-diagram manual
33021 that you find in the menu
33023 Help\SpecialChar \menuseparator
33025 \begin_inset space ~
33033 \begin_layout Section
33034 User-defined Commands
33035 \begin_inset Index idx
33038 \begin_layout Plain Layout
33039 User-defined commands
33047 \begin_layout Standard
33048 \begin_inset Note Greyedout
33051 \begin_layout Plain Layout
33056 The names of user-defined commands and macros may only consist of Latin
33065 \begin_layout Subsection
33069 \begin_inset CommandInset label
33071 name "sub:The-Command-newcommand"
33076 \begin_inset Index idx
33079 \begin_layout Plain Layout
33080 User-defined commands !
33088 \begin_inset Index idx
33091 \begin_layout Plain Layout
33102 \begin_layout Standard
33103 Many LaTeX-commands are too long to be used frequently.
33104 But it is possible to define with the command
33110 new shorter commands.
33113 \begin_layout Standard
33114 The command scheme of
33123 \begin_layout Standard
33128 newcommand{new command name}[number of arguments][optional
33133 \begin_inset Newline newline
33137 \begin_inset Phantom HPhantom
33140 \begin_layout Plain Layout
33150 {command definition}
33153 \begin_layout Standard
33154 \begin_inset Note Greyedout
33157 \begin_layout Plain Layout
33162 Assure that the name of the new command is not already used in your document
33163 or by LaTeX-packages that you use.
33164 When you for example define the command
33176 , you get an error message because
33182 is already defined as command for
33183 \begin_inset Quotes eld
33187 \begin_inset Formula $\le$
33191 \begin_inset Quotes erd
33202 \begin_layout Standard
33203 The number of arguments is an integer in the range 0
33204 \begin_inset space \thinspace{}
33208 \begin_inset space \thinspace{}
33211 9 and specifies how many arguments the new command should have.
33212 With the optional value a value for an optional argument can be predefined.
33213 When this is done, the
33221 rgument of the new command is automatically an optional one.
33224 \begin_layout Standard
33225 Here are some examples:
33228 \begin_layout Itemize
33229 To define the command
33241 , the LaTeX-preamble line is:
33242 \begin_inset VSpace medskip
33246 \begin_inset Newline newline
33260 \begin_layout Itemize
33261 To define the command
33273 , the argument (that should be underlined) must be taken into account.
33274 For this the preamble line is:
33275 \begin_inset VSpace medskip
33279 \begin_inset Newline newline
33293 \begin_inset VSpace medskip
33297 \begin_inset Newline newline
33304 acts as argument placeholder, the
33308 behind it denotes that it is the placeholder for the first argument.
33311 \begin_layout Itemize
33319 \begin_inset space \thinspace{}
33323 \begin_inset space \space{}
33333 \begin_inset VSpace medskip
33337 \begin_inset Newline newline
33348 framebox#1#2{$#3$}}
33351 \begin_inset VSpace medskip
33355 \begin_inset Newline newline
33358 The two Dollar signs creates the extra formula needed for
33365 \begin_inset CommandInset ref
33367 reference "sub:Boxes-with-Frame"
33374 \begin_layout Itemize
33375 To create a new command for
33381 where the color for the box need not be specified, the argument for the
33382 color is defined optional:
33383 \begin_inset VSpace medskip
33387 \begin_inset Newline newline
33398 fcolorbox{#2}{#1}{$#3$}}
33401 \begin_inset VSpace medskip
33405 \begin_inset Newline newline
33408 When the color is not specified when using
33414 , the predefined color
33421 \begin_layout Standard
33422 A test of the new defined commands:
33425 \begin_layout Standard
33427 \begin_inset Tabular
33428 <lyxtabular version="3" rows="6" columns="2">
33429 <features tabularvalignment="middle">
33430 <column alignment="center" valignment="top" width="0">
33431 <column alignment="center" valignment="top" width="0">
33433 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33436 \begin_layout Plain Layout
33442 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33445 \begin_layout Plain Layout
33447 \begin_inset Note Note
33450 \begin_layout Plain Layout
33457 is only used as spacer.
33469 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33472 \begin_layout Plain Layout
33479 \begin_layout Plain Layout
33493 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33496 \begin_layout Plain Layout
33497 \begin_inset Formula $A\gr B$
33507 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33510 \begin_layout Plain Layout
33518 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33521 \begin_layout Plain Layout
33522 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
33532 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33535 \begin_layout Plain Layout
33539 \begin_inset Formula $\to$
33545 \begin_inset Formula $\to$
33556 \begin_layout Plain Layout
33570 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33573 \begin_layout Plain Layout
33574 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
33584 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33587 \begin_layout Plain Layout
33591 \begin_inset Formula $\to$
33602 \begin_layout Plain Layout
33616 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33619 \begin_layout Plain Layout
33620 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
33630 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33633 \begin_layout Plain Layout
33639 \begin_inset Formula $\to$
33650 \begin_layout Plain Layout
33664 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33667 \begin_layout Plain Layout
33668 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
33684 \begin_layout Subsection
33686 \begin_inset Index idx
33689 \begin_layout Plain Layout
33690 User-defined commands! Math macros
33696 \begin_inset Index idx
33699 \begin_layout Plain Layout
33708 \begin_layout Standard
33709 User-defined commands are especially convenient for complex expressions.
33710 When you are for example dealing with a document that has quadratic equations,
33711 the same solution type occurs several times.
33712 The general form of a quadratic equation is
33713 \begin_inset Formula
33715 0=\lambda^{2}+p\lambda+q
33720 The general form of the solution is
33721 \begin_inset Formula
33723 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
33731 \begin_layout Standard
33732 To define a command for the solution formula where only the three parameters
33734 \begin_inset Formula $\lambda$
33738 \begin_inset Formula $p$
33742 \begin_inset Formula $q$
33745 need to be specified and the index of
33746 \begin_inset Formula $\lambda$
33749 can be given optionally, the LaTeX-preamble line is
33750 \begin_inset Newline newline
33766 \begin_inset Newline newline
33770 \begin_inset Phantom HPhantom
33773 \begin_layout Plain Layout
33787 frac{#3^{2}}{4}-#4}}
33790 \begin_layout Standard
33791 To create with this the solution formula, the command
33792 \begin_inset Newline newline
33802 \begin_inset Formula $\to$
33808 \begin_inset Formula $\to$
33815 is inserted to a formula
33820 \begin_layout Standard
33821 The definition of the new command is unintuitive because one has to know
33822 the schemes of all used LaTeX commands, e.
33823 \begin_inset space \thinspace{}
33827 \begin_inset space \space{}
33830 that a fraction is inserted in LaTeX as
33834 frac{numerator}{denominator}
33837 Furthermore one can easily forget a brace in the definition and cannot
33838 see in LyX what the new command is doing.
33839 To avoid these problems LyX offers the possibility to use math macros instead
33849 \begin_layout Standard
33850 A math macro is created by using the menu
33852 Insert\SpecialChar \menuseparator
33853 Math\SpecialChar \menuseparator
33856 or the toolbar button
33857 \begin_inset Graphics
33858 filename ../images/math-macro_newmacroname_newcommand.png
33864 The math macro toolbar appears together with the following box where the
33866 \begin_inset Newline newline
33870 \begin_inset space \hspace*{\fill}
33874 \begin_inset Graphics
33875 filename clipart/macrobox.png
33880 \begin_inset space \hspace*{\fill}
33884 \begin_inset Newline newline
33888 \begin_inset FormulaMacro
33889 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
33894 newmacroname is the default name of the macro that should be changed to
33895 something sensible.
33896 The wanted formula is inserted in the first blue box.
33897 An argument placeholder is inserted with the command
33904 \begin_inset space \thinspace{}
33908 \begin_inset space \space{}
33917 or by using the macro toolbar button
33918 \begin_inset Graphics
33919 filename ../images/math-macro-add-param.png
33925 Argument placeholders are displayed red.
33927 \begin_inset space ~
33930 arguments are possible.
33931 Optional arguments are created with the toolbar button
33932 \begin_inset Graphics
33933 filename ../images/math-macro-add-optional-param.png
33939 The first non-optional argument can be transformed to an optional one with
33941 \begin_inset Graphics
33942 filename ../images/math-macro-make-optional.png
33948 In the second blue box the appearance of the macro in LyX can be defined.
33949 Normally you want to see it as it is defined, so the box is kept empty.
33950 But when you have created a macro that needs lot of space on the screen,
33951 you can insert in the box for example
33952 \begin_inset Newline newline
33982 \begin_inset Newline newline
33987 For the macro only the arguments with the macro name in front of them will
33988 then be displayed in LyX, leading to a better overview.
33989 The formula appears in the output as defined in the first box.
33990 \begin_inset Newline newline
33993 The appearance of macros in formulas can furthermore be changed for single
33994 macros by setting the cursor in the macro and using the menu
33996 View\SpecialChar \menuseparator
33998 \begin_inset space ~
34002 \begin_inset space ~
34010 \begin_layout Standard
34011 To use a macro, the macro name is inserted as command to a formula, in our
34019 Our macro looks in LyX like this:
34020 \begin_inset Newline newline
34024 \begin_inset space \hspace*{\fill}
34028 \begin_inset Graphics
34029 filename clipart/macrouse.png
34034 \begin_inset space \hspace*{\fill}
34038 \begin_inset Newline newline
34041 Here is our macro example with the arguments
34042 \begin_inset Formula $x$
34046 \begin_inset Formula $\ln(x)$
34050 \begin_inset Formula $B$
34056 \begin_layout Standard
34057 \begin_inset Formula
34067 \begin_layout Standard
34068 LyX offers in the menu
34070 Tools\SpecialChar \menuseparator
34071 Preferences\SpecialChar \menuseparator
34072 Editing\SpecialChar \menuseparator
34075 different styles to edit macros.
34076 To find the style that suits you the most, choose a style and set the cursor
34077 in a macro formula to see the difference.
34080 \begin_layout Standard
34081 A math macro is transformed internally to a
34087 command when exporting the document.
34094 command is not placed in the LaTeX-preamble, therefore macros can only
34095 be used in formulas that are in the document below the macro definition
34099 \begin_layout Standard
34100 Math macros can also be directly created from a
34107 When writing for example the command
34110 \begin_inset Newline newline
34119 xleftarrow[#2]{#1}}
34120 \begin_inset Newline newline
34125 in LyX as normal text, highlighting it completely and using then the shortcut
34130 , the command will be transformed to a math macro.
34131 Using this method you need to be careful that the
34137 command is typed correctly, otherwise you get a faulty macro leading to
34141 \begin_layout Standard
34142 Math macros currently have the problem that further formulas in macro definition
34143 s are handled wrongly.
34144 Therefore the example
34151 \begin_inset CommandInset ref
34153 reference "sub:The-Command-newcommand"
34157 cannot be created as macro.
34160 \begin_layout Standard
34161 When the cursor is in a macro definition box, you will see the macro toolbar
34165 \begin_layout Standard
34166 \begin_inset VSpace defskip
34172 \begin_layout Standard
34173 \begin_inset Graphics
34174 filename clipart/MacroToolbar.png
34179 \begin_inset Index idx
34182 \begin_layout Plain Layout
34191 \begin_layout Standard
34192 \begin_inset VSpace defskip
34198 \begin_layout Standard
34199 The macro toolbar contains from left to right the following buttons:
34202 \begin_layout Standard
34203 \begin_inset VSpace defskip
34209 \begin_layout Standard
34210 \begin_inset Tabular
34211 <lyxtabular version="3" rows="9" columns="2">
34212 <features islongtable="true" longtabularalignment="center">
34213 <column alignment="left" valignment="top" width="0">
34214 <column alignment="left" valignment="top" width="85col%">
34215 <row interlinespace="2.5mm">
34216 <cell alignment="center" valignment="top" usebox="none">
34219 \begin_layout Plain Layout
34220 \begin_inset Graphics
34221 filename ../images/math-macro-remove-param.png
34222 rotateOrigin center
34231 <cell alignment="center" valignment="top" usebox="none">
34234 \begin_layout Plain Layout
34237 Edit\SpecialChar \menuseparator
34238 Math\SpecialChar \menuseparator
34240 \begin_inset space ~
34243 Definition\SpecialChar \menuseparator
34244 Remove Last Argument
34250 <row interlinespace="2.5mm">
34251 <cell alignment="center" valignment="top" usebox="none">
34254 \begin_layout Plain Layout
34255 \begin_inset Graphics
34256 filename ../images/math-macro-add-param.png
34257 rotateOrigin center
34266 <cell alignment="center" valignment="top" usebox="none">
34269 \begin_layout Plain Layout
34272 Edit\SpecialChar \menuseparator
34273 Math\SpecialChar \menuseparator
34275 \begin_inset space ~
34278 Definition\SpecialChar \menuseparator
34285 <row interlinespace="2.5mm">
34286 <cell alignment="center" valignment="top" usebox="none">
34289 \begin_layout Plain Layout
34290 \begin_inset Graphics
34291 filename ../images/math-macro-make-optional.png
34292 rotateOrigin center
34301 <cell alignment="center" valignment="top" usebox="none">
34304 \begin_layout Plain Layout
34307 Edit\SpecialChar \menuseparator
34308 Math\SpecialChar \menuseparator
34310 \begin_inset space ~
34313 Definition\SpecialChar \menuseparator
34314 Make First Non-Optional into
34315 \begin_inset Newline newline
34319 \begin_inset Phantom HPhantom
34322 \begin_layout Plain Layout
34325 Edit\SpecialChar \menuseparator
34326 Math\SpecialChar \menuseparator
34328 \begin_inset space ~
34331 Definition\SpecialChar \menuseparator
34343 <row interlinespace="2.5mm">
34344 <cell alignment="center" valignment="top" usebox="none">
34347 \begin_layout Plain Layout
34348 \begin_inset Graphics
34349 filename ../images/math-macro-make-nonoptional.png
34350 rotateOrigin center
34359 <cell alignment="center" valignment="top" usebox="none">
34362 \begin_layout Plain Layout
34365 Edit\SpecialChar \menuseparator
34366 Math\SpecialChar \menuseparator
34368 \begin_inset space ~
34371 Definition\SpecialChar \menuseparator
34372 Make Last Optional into
34373 \begin_inset Newline newline
34377 \begin_inset Phantom HPhantom
34380 \begin_layout Plain Layout
34383 Edit\SpecialChar \menuseparator
34384 Math\SpecialChar \menuseparator
34386 \begin_inset space ~
34389 Definition\SpecialChar \menuseparator
34395 Non-Optional Argument
34401 <row interlinespace="2.5mm">
34402 <cell alignment="center" valignment="top" usebox="none">
34405 \begin_layout Plain Layout
34406 \begin_inset Graphics
34407 filename ../images/math-macro-remove-optional-param.png
34408 rotateOrigin center
34417 <cell alignment="center" valignment="top" usebox="none">
34420 \begin_layout Plain Layout
34423 Edit\SpecialChar \menuseparator
34424 Math\SpecialChar \menuseparator
34426 \begin_inset space ~
34429 Definition\SpecialChar \menuseparator
34430 Remove Optional Argument
34436 <row interlinespace="2.5mm">
34437 <cell alignment="center" valignment="top" usebox="none">
34440 \begin_layout Plain Layout
34441 \begin_inset Graphics
34442 filename ../images/math-macro-add-optional-param.png
34443 rotateOrigin center
34452 <cell alignment="center" valignment="top" usebox="none">
34455 \begin_layout Plain Layout
34458 Edit\SpecialChar \menuseparator
34459 Math\SpecialChar \menuseparator
34461 \begin_inset space ~
34464 Definition\SpecialChar \menuseparator
34465 Insert Optional Argument
34471 <row interlinespace="2.5mm">
34472 <cell alignment="center" valignment="top" usebox="none">
34475 \begin_layout Plain Layout
34476 \begin_inset Graphics
34477 filename ../images/math-macro-remove-greedy-param.png
34478 rotateOrigin center
34487 <cell alignment="center" valignment="top" usebox="none">
34490 \begin_layout Plain Layout
34493 Edit\SpecialChar \menuseparator
34494 Math\SpecialChar \menuseparator
34496 \begin_inset space ~
34499 Definition\SpecialChar \menuseparator
34500 Remove Last Argument
34501 \begin_inset Newline newline
34505 \begin_inset Phantom HPhantom
34508 \begin_layout Plain Layout
34511 Edit\SpecialChar \menuseparator
34512 Math\SpecialChar \menuseparator
34514 \begin_inset space ~
34517 Definition\SpecialChar \menuseparator
34523 Spitting Out To The Right
34529 <row interlinespace="2.5mm">
34530 <cell alignment="center" valignment="top" usebox="none">
34533 \begin_layout Plain Layout
34534 \begin_inset Graphics
34535 filename ../images/math-macro-append-greedy-param.png
34536 rotateOrigin center
34545 <cell alignment="center" valignment="top" usebox="none">
34548 \begin_layout Plain Layout
34551 Edit\SpecialChar \menuseparator
34552 Math\SpecialChar \menuseparator
34554 \begin_inset space ~
34557 Definition\SpecialChar \menuseparator
34559 \begin_inset Newline newline
34563 \begin_inset Phantom HPhantom
34566 \begin_layout Plain Layout
34569 Edit\SpecialChar \menuseparator
34570 Math\SpecialChar \menuseparator
34572 \begin_inset space ~
34575 Definition\SpecialChar \menuseparator
34581 Eating From The Right
34587 <row interlinespace="2.5mm">
34588 <cell alignment="center" valignment="top" usebox="none">
34591 \begin_layout Plain Layout
34592 \begin_inset Graphics
34593 filename ../images/math-macro-add-greedy-optional-param.png
34594 rotateOrigin center
34603 <cell alignment="center" valignment="top" usebox="none">
34606 \begin_layout Plain Layout
34609 Edit\SpecialChar \menuseparator
34610 Math\SpecialChar \menuseparator
34612 \begin_inset space ~
34615 Definition\SpecialChar \menuseparator
34616 Append Optional Argument
34617 \begin_inset Newline newline
34621 \begin_inset Phantom HPhantom
34624 \begin_layout Plain Layout
34627 Edit\SpecialChar \menuseparator
34628 Math\SpecialChar \menuseparator
34630 \begin_inset space ~
34633 Definition\SpecialChar \menuseparator
34639 Eating From The Right
34652 \begin_layout Section
34653 Computer Algebra Systems
34656 \begin_layout Standard
34657 LyX offers the exchange between mathematical expressions written in LyX's
34658 math editor and external applications or user defined scripts.
34659 Currently supported applications are
34676 Note that the set of supported mathematical constructs is limited only
34677 to very simple cases.
34680 \begin_layout Subsection
34684 \begin_layout Standard
34685 Write some expression in a formula, go to the
34687 Edit\SpecialChar \menuseparator
34688 Math\SpecialChar \menuseparator
34689 Use Computer Algebra System
34691 menu and choose the application you have installed on the computer.
34692 After that the result of computation should show on the right side of the
34693 expression together with the
34694 \begin_inset Quotes eld
34698 \begin_inset Quotes erd
34704 \begin_layout Standard
34705 Here are few simple examples (with results from
34709 ) to show what kind of computations can be performed:
34712 \begin_layout Itemize
34713 \begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$
34719 \begin_layout Itemize
34720 \begin_inset Formula $\frac{37.0}{3}=12.33333333333333$
34726 \begin_layout Itemize
34727 \begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$
34733 \begin_layout Itemize
34734 \begin_inset Formula $\det\left[\begin{array}{ccc}
34738 \end{array}\right]=-56$
34744 \begin_layout Itemize
34745 \begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$
34751 \begin_layout Subsection
34755 \begin_layout Standard
34756 Currently there is no keyboard shortcut for calling the algebra applications.
34757 One can easily bind a shortcut to the
34761 LyX function (see the
34769 \begin_inset space \thinspace{}
34773 \begin_inset space ~
34780 key inside the math editor.
34785 one would use this shortcut definition command:
34788 \begin_layout Standard
34791 command-alternatives break-paragraph;math-extern maxima
34794 \begin_layout Standard
34795 \begin_inset Newpage newpage
34801 \begin_layout Section
34803 \begin_inset Index idx
34806 \begin_layout Plain Layout
34815 \begin_layout Subsection
34817 \begin_inset Index idx
34820 \begin_layout Plain Layout
34829 \begin_layout Standard
34830 Negative numbers often look ugly in formulas because the minus sign before
34831 the number is set with the same length as the minus operator sign.
34832 When writing the negative number in normal text, the minus sign appears
34836 \begin_layout Standard
34837 Thus, the problem disappears when converting the minus sign to mathematical
34841 \begin_layout Standard
34842 An example to visualize the problem:
34845 \begin_layout Standard
34847 \begin_inset Tabular
34848 <lyxtabular version="3" rows="3" columns="2">
34849 <features tabularvalignment="middle">
34850 <column alignment="right" valignment="top" width="0">
34851 <column alignment="left" valignment="top" width="0">
34853 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34856 \begin_layout Plain Layout
34862 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
34865 \begin_layout Plain Layout
34873 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34876 \begin_layout Plain Layout
34882 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34885 \begin_layout Plain Layout
34886 \begin_inset Formula $x=-2$
34896 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34899 \begin_layout Plain Layout
34905 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34908 \begin_layout Plain Layout
34909 \begin_inset Formula $x=\textrm{-}2$
34925 \begin_layout Subsection
34926 Comma as decimal Separator
34927 \begin_inset Index idx
34930 \begin_layout Plain Layout
34939 \begin_layout Standard
34940 In LaTeX a comma inside a formula is used, according to the English convention,
34941 as number group separator.
34942 So there will be space added behind all commas in formulas.
34945 \begin_layout Standard
34946 To avoid this, the comma is highlighted and changed to mathematical text
34956 \begin_layout Standard
34957 To use all formula commas in the document as decimal separator, the file
34966 \begin_layout Plain Layout
34971 is part of the LaTeX-package
34976 \begin_inset Index idx
34979 \begin_layout Plain Layout
34984 \begin_layout Plain Layout
35004 \begin_inset Index idx
35007 \begin_layout Plain Layout
35013 is loaded with the LaTeX-preamble line
35016 \begin_layout Standard
35024 \begin_layout Subsection
35026 \begin_inset CommandInset label
35028 name "sub:Physical-Vectors"
35033 \begin_inset Index idx
35036 \begin_layout Plain Layout
35045 \begin_layout Standard
35046 Predefined vectors are offered by the LaTeX-package
35051 \begin_inset Index idx
35054 \begin_layout Plain Layout
35060 that is loaded with the LaTeX-preamble line
35063 \begin_layout Standard
35071 \begin_layout Standard
35075 \begin_layout Plain Layout
35085 \begin_inset Note Note
35088 \begin_layout Plain Layout
35089 The following table will only be displayed when the LaTeX-package
35101 \begin_layout Standard
35102 The following commands are defined:
35105 \begin_layout Standard
35107 \begin_inset Tabular
35108 <lyxtabular version="3" rows="4" columns="2">
35109 <features tabularvalignment="middle">
35110 <column alignment="center" valignment="top" width="0">
35111 <column alignment="center" valignment="top" width="0">
35113 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35116 \begin_layout Plain Layout
35122 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35125 \begin_layout Plain Layout
35133 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35136 \begin_layout Plain Layout
35146 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35149 \begin_layout Plain Layout
35150 \begin_inset Formula $\Bra{\psi}$
35160 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35163 \begin_layout Plain Layout
35173 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35176 \begin_layout Plain Layout
35177 \begin_inset Formula $\Ket{\psi}$
35187 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35190 \begin_layout Plain Layout
35202 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35205 \begin_layout Plain Layout
35206 \begin_inset Formula $\Braket{\psi|\phi}$
35222 \begin_layout Standard
35229 assures that all vertical bars are set in the size of the surrounding brackets:
35230 \begin_inset Formula
35232 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}
35241 \begin_layout Plain Layout
35251 \begin_inset Note Note
35254 \begin_layout Plain Layout
35255 The following will be displayed when the LaTeX-package
35267 \begin_layout Standard
35268 You need to install the LaTeX-package
35272 to see the rest of this subsection in the output.
35275 \begin_layout Standard
35279 \begin_layout Plain Layout
35291 \begin_layout Standard
35298 can also be achieved using the command
35304 , that is described in
35305 \begin_inset CommandInset ref
35307 reference "sub:Automatic-Bracket-Size"
35314 \begin_layout Subsection
35315 Self-defined Fractions
35316 \begin_inset CommandInset label
35318 name "sub:Self-defined-Fractions"
35323 \begin_inset Index idx
35326 \begin_layout Plain Layout
35327 Fractions ! self-defined
35335 \begin_layout Standard
35336 To define custom commands for fractions, the command
35343 \begin_inset Index idx
35346 \begin_layout Plain Layout
35354 is used in the following scheme:
35357 \begin_layout Standard
35370 bracket}{fraction bar thickness}{style}
35371 \begin_inset Newline newline
35375 \begin_inset Phantom HPhantom
35378 \begin_layout Plain Layout
35388 {numerator}{denominator}
35391 \begin_layout Standard
35392 The style is a number in the range of 0
35393 \begin_inset space \thinspace{}
35397 \begin_inset space \thinspace{}
35403 \begin_layout Standard
35405 \begin_inset Tabular
35406 <lyxtabular version="3" rows="5" columns="2">
35407 <features tabularvalignment="middle">
35408 <column alignment="center" valignment="top" width="0">
35409 <column alignment="center" valignment="top" width="0">
35411 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35414 \begin_layout Plain Layout
35420 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35423 \begin_layout Plain Layout
35431 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35434 \begin_layout Plain Layout
35440 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35443 \begin_layout Plain Layout
35444 display style formula
35451 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35454 \begin_layout Plain Layout
35460 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35463 \begin_layout Plain Layout
35471 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35474 \begin_layout Plain Layout
35480 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35483 \begin_layout Plain Layout
35491 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35494 \begin_layout Plain Layout
35500 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35503 \begin_layout Plain Layout
35517 \begin_layout Standard
35518 When no style is given, the size is adjusted to the surrounding environment
35519 like for the command
35528 \begin_layout Standard
35529 When no fraction bar thickness is given, the predefined value of 0.4
35530 \begin_inset space \thinspace{}
35536 \begin_layout Standard
35537 \begin_inset VSpace medskip
35540 For example, the commands
35553 \begin_inset CommandInset ref
35555 reference "sub:Fractions"
35559 are defined with the commands
35562 \begin_layout Standard
35571 genfrac{}{}{}{0}{#1}{#2}}
35574 \begin_layout Standard
35578 \begin_layout Standard
35587 genfrac{(}{)}{0pt}{1}{#1}{#2}}
35590 \begin_layout Standard
35591 \begin_inset VSpace medskip
35594 To define a fraction where the fraction bar thickness can be given as optional
35595 argument, the following line is inserted to the LaTeX-preamble:
35598 \begin_layout Standard
35607 genfrac{}{}{#1}{}{#2}{#3}}
35610 \begin_layout Standard
35611 \begin_inset Newpage newpage
35617 \begin_layout Standard
35619 \begin_inset Formula
35621 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
35622 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
35627 As one can see, the distance of the numerator and the denominator to the
35628 fraction bar is round about three times the bar thickness.
35631 \begin_layout Subsection
35633 \begin_inset Index idx
35636 \begin_layout Plain Layout
35645 \begin_layout Standard
35646 To cancel formulas or formula parts, the LaTeX-package
35651 \begin_inset Index idx
35654 \begin_layout Plain Layout
35660 has to be loaded with the LaTeX-preamble line
35663 \begin_layout Standard
35671 \begin_layout Standard
35675 \begin_layout Plain Layout
35685 \begin_inset Note Note
35688 \begin_layout Plain Layout
35689 The following table will only be displayed when the LaTeX-package
35701 \begin_layout Standard
35702 There are four ways to cancel formulas:
35705 \begin_layout Standard
35707 \begin_inset Tabular
35708 <lyxtabular version="3" rows="5" columns="2">
35709 <features tabularvalignment="middle">
35710 <column alignment="center" valignment="top" width="0">
35711 <column alignment="center" valignment="top" width="0">
35713 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35716 \begin_layout Plain Layout
35722 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35725 \begin_layout Plain Layout
35727 \begin_inset Note Note
35730 \begin_layout Plain Layout
35737 are used here as spacer.
35749 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35752 \begin_layout Plain Layout
35761 \begin_layout Plain Layout
35775 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35778 \begin_layout Plain Layout
35779 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
35789 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35792 \begin_layout Plain Layout
35801 \begin_layout Plain Layout
35815 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35818 \begin_layout Plain Layout
35819 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
35829 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35832 \begin_layout Plain Layout
35841 \begin_layout Plain Layout
35855 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35858 \begin_layout Plain Layout
35859 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
35869 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35872 \begin_layout Plain Layout
35876 \begin_inset Formula $\to$
35887 \begin_layout Plain Layout
35901 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35904 \begin_layout Plain Layout
35905 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
35921 \begin_layout Standard
35928 is especially suitable to visualize the reduction of fractions within formulas:
35929 \begin_inset Formula
35931 \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}}}
35939 \begin_layout Standard
35940 To change the size of
35947 \begin_inset Quotes eld
35951 \begin_inset Quotes erd
35954 value one can load the package
35958 with either the option
35962 which leads to the same size as for the canceled value or with the option
35967 which makes is it a bit smaller than the size one gets without using a
35973 was loaded with this line:
35976 \begin_layout Standard
35981 usepackage[samesize]{cancel}
35984 \begin_layout Standard
35985 To color the cancellation bar one adds this command as TeX code:
35988 \begin_layout Standard
36000 \begin_layout Standard
36005 can be replaced by a color of your choice.
36008 \begin_layout Standard
36012 \begin_layout Plain Layout
36028 \begin_layout Standard
36029 \begin_inset Formula
36031 \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}}}
36039 \begin_layout Standard
36043 \begin_layout Plain Layout
36057 \begin_inset Note Note
36060 \begin_layout Plain Layout
36069 \begin_layout Standard
36070 For further customizations, see the documentation of the package
36075 \begin_inset CommandInset citation
36084 \begin_layout Standard
36088 \begin_layout Plain Layout
36098 \begin_inset Note Note
36101 \begin_layout Plain Layout
36102 The following will be displayed when the LaTeX-package
36114 \begin_layout Standard
36115 You need to install the LaTeX-package
36119 to see the rest of this subsection in the output.
36122 \begin_layout Standard
36126 \begin_layout Plain Layout
36138 \begin_layout Subsection
36139 Formulas in Section Headings
36140 \begin_inset CommandInset label
36142 name "sub:Formulas-in-Section"
36147 \begin_inset Index idx
36150 \begin_layout Plain Layout
36151 Formula ! in section headings
36159 \begin_layout Standard
36160 When formulas are used in section headings, the following has to be taken
36164 \begin_layout Standard
36165 \begin_inset Note Greyedout
36168 \begin_layout Plain Layout
36174 \begin_inset Index idx
36177 \begin_layout Plain Layout
36178 Packages ! hyperref
36183 support is enabled in the document settings dialog under
36186 \begin_inset space ~
36191 , PDF-bookmarks are created for every section heading in the table of contents.
36192 If a section heading contains formulas, they are incorrectly displayed
36193 in the bookmark text, because formulas in bookmarks infringe the PDF convention
36202 \begin_layout Standard
36203 Both problems can be solved by inserting at the end of the section heading
36204 a short title with the menu
36206 Insert\SpecialChar \menuseparator
36208 \begin_inset space ~
36214 Short titles are used as alternative for multiline section headings to
36215 keep the table of contents clearly arranged.
36216 Only the short title appears in the table of contents and therefore also
36217 in the PDF-bookmark.
36220 \begin_layout Standard
36221 When formulas should be used in the table of contents but
36225 is used, one can use the following command in TeX-mode:
36228 \begin_layout Standard
36233 texorpdfstring{part}{alternative}
36234 \begin_inset Index idx
36237 \begin_layout Plain Layout
36248 \begin_layout Standard
36249 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
36250 This can be characters, formulas, footnotes, but also cross-references.
36251 The alternative is used instead of the part for the bookmark.
36254 \begin_layout Standard
36255 Here are two example headings:
36256 \begin_inset VSpace -3mm
36263 \begin_layout Plain Layout
36275 \begin_layout Subsubsection
36276 Heading without formula in table of contents
36277 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
36281 \begin_inset Argument
36284 \begin_layout Plain Layout
36285 Heading without formula in table of contents
36293 \begin_layout Subsubsection
36294 Heading with formula in table of contents
36298 \begin_layout Plain Layout
36308 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
36315 \begin_layout Plain Layout
36325 \begin_layout Standard
36329 \begin_layout Plain Layout
36338 In the first heading a short title was used, in the second one
36347 \begin_layout Standard
36348 To get the same formatting as for the other headings, the complete heading
36357 \begin_layout Plain Layout
36359 \begin_inset CommandInset ref
36361 reference "sub:Bold-Formulas"
36373 \begin_layout Subsection
36374 Formulas in multi-column Text
36375 \begin_inset Index idx
36378 \begin_layout Plain Layout
36379 Formula ! in multi-column text
36387 \begin_layout Standard
36388 Formulas in multi-column text are often too wide to fit into a column and
36389 thus need to be set over the whole page width.
36390 This is done by using the LaTeX-package
36398 \begin_layout Plain Layout
36403 is part of every LaTeX standard installation.
36409 \begin_inset Index idx
36412 \begin_layout Plain Layout
36413 Packages ! multicol
36418 , that is loaded with the LaTeX-preamble line
36421 \begin_layout Standard
36426 usepackage{multicol}
36429 \begin_layout Standard
36430 \begin_inset Note Greyedout
36433 \begin_layout Plain Layout
36434 Note that in this case the setting
36437 \begin_inset space ~
36444 Document\SpecialChar \menuseparator
36450 \begin_inset space ~
36470 \begin_layout Standard
36471 Before the multi-column text the command
36474 \begin_layout Standard
36479 begin{multicols}{column number}
36482 \begin_layout Standard
36483 is written in TeX-mode.
36484 The column number is a number in the range of 2
36485 \begin_inset space \thinspace{}
36489 \begin_inset space \thinspace{}
36493 Before the formula the multi-column text is ended by inserting the command
36496 \begin_layout Standard
36504 \begin_layout Standard
36508 \begin_layout Standard
36509 Due to the command some space is automatically added before the formula.
36511 \begin_inset space \thinspace{}
36514 mm vertical space is inserted before the formula.
36515 When the formula style
36521 \begin_layout Plain Layout
36523 \begin_inset CommandInset ref
36525 reference "sec:Formula-Styles"
36537 \begin_inset space \thinspace{}
36540 mm space is inserted instead.
36543 \begin_layout Standard
36544 As example a multi-column text with a displayed formula:
36547 \begin_layout Standard
36553 \begin_layout Plain Layout
36557 begin{multicols}{2}
36562 Das Spektrum wird fouriertransformiert.
36563 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
36564 , Lösungsmittel) zu trennen.
36565 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
36566 nun das Aussehen des Ausgangssignals.
36567 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
36568 über alle Phasen integrieren muss.
36570 \begin_inset Formula $S$
36573 unser normiertes Ausgangssignal und
36574 \begin_inset Formula $P$
36577 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
36581 \begin_layout Plain Layout
36591 \begin_inset VSpace -6mm
36595 \begin_inset Formula
36597 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
36606 \begin_layout Plain Layout
36610 begin{multicols}{2}
36616 \begin_inset Formula $S_{0}$
36619 das Signal ohne Gradient ist und die Normierungsbedingung
36620 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
36624 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
36626 \begin_inset Formula $\nicefrac{\pi}{2}$
36630 \begin_inset space \thinspace{}
36633 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
36634 das Signal zusätzlich abschwächt.
36635 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
36637 \begin_inset Formula $T_{2}$
36643 \begin_layout Standard
36649 \begin_layout Plain Layout
36661 \begin_layout Subsection
36662 Formulas with Description of Variables
36663 \begin_inset Index idx
36666 \begin_layout Plain Layout
36667 Formula ! with description of variables
36675 \begin_layout Standard
36676 To describe variables within a formula, like in formula
36677 \begin_inset CommandInset ref
36679 reference "eq:within"
36688 \begin_inset Formula $n$
36692 \begin_inset space ~
36695 matrix is used with left aligned columns for the
36696 \begin_inset Formula $n$
36703 \begin_layout Plain Layout
36705 \begin_inset CommandInset ref
36707 reference "sec:Matrices"
36716 To set the description in a smaller size, before the matrix e.
36717 \begin_inset space \thinspace{}
36721 \begin_inset space \space{}
36734 \begin_layout Plain Layout
36736 \begin_inset CommandInset ref
36738 reference "sub:Font-Sizes"
36750 \begin_layout Standard
36751 When the formula style
36757 \begin_layout Plain Layout
36759 \begin_inset CommandInset ref
36761 reference "sec:Formula-Styles"
36782 \begin_layout Plain Layout
36789 only works in formulas with the style
36794 \begin_inset CommandInset ref
36796 reference "sub:Variable-Space"
36805 is inserted before and after the matrix to have the same separation of
36806 the matrix from the equation and the side margin.
36809 \begin_layout Standard
36810 When the formula style
36814 is used, the method described in
36815 \begin_inset CommandInset ref
36817 reference "sub:Flalign-Environment"
36821 is used to indent formulas.
36823 \begin_inset CommandInset ref
36825 reference "eq:within"
36829 consists of five columns where in the first two columns contain the equation,
36830 the third the matrix and the last one an empty TeX-brace.
36831 \begin_inset Formula
36833 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
36834 \rho & \textrm{density}\\
36835 V & \textrm{volume}\\
36836 g & \textrm{gravitational acceleration}
36837 \end{array} & & {}\label{eq:within}
36845 \begin_layout Subsection
36846 Upright small Greek Letters
36847 \begin_inset CommandInset label
36849 name "sub:Upright-small-Greek"
36854 \begin_inset Index idx
36857 \begin_layout Plain Layout
36858 Greek letters ! upright
36866 \begin_layout Standard
36867 Most of the math fonts only provide italic small Greek letters.
36868 But for symbols of elementary particles like pions and neutrinos, upright
36869 Greek letters are needed.
36878 \begin_layout Plain Layout
36883 is part of the LaTeX-package
36888 \begin_inset Index idx
36891 \begin_layout Plain Layout
36896 \begin_layout Plain Layout
36916 \begin_inset Index idx
36919 \begin_layout Plain Layout
36925 that is loaded with the LaTeX-preamble line
36928 \begin_layout Standard
36933 usepackage{upgreek}
36936 \begin_layout Standard
36942 \begin_layout Plain Layout
36952 \begin_inset Note Note
36955 \begin_layout Plain Layout
36956 The following table will only be displayed when the LaTeX-package
36965 They are created when the command for a small Greek letter is started with
36971 For example the command
36978 \begin_inset Formula $\uptau$
36984 \begin_layout Standard
36985 With these commands reactions of elementary particles can be typeset:
36986 \begin_inset Formula
36988 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
36996 \begin_layout Standard
36997 The upright letters are more bold and wider than the italic ones.
36998 They should therefore not be used for units like
36999 \begin_inset Quotes eld
37003 \begin_inset Quotes erd
37009 \begin_layout Standard
37013 \begin_layout Plain Layout
37023 \begin_inset Note Note
37026 \begin_layout Plain Layout
37027 The following will be displayed when the LaTeX-package
37039 \begin_layout Standard
37040 You need to install the LaTeX-package
37044 to see the rest of this subsection in the output.
37047 \begin_layout Standard
37051 \begin_layout Plain Layout
37063 \begin_layout Standard
37064 \begin_inset Newpage newpage
37070 \begin_layout Subsection
37071 Text Characters in Formulas
37072 \begin_inset CommandInset label
37074 name "sub:Text-Characters-in"
37079 \begin_inset Index idx
37082 \begin_layout Plain Layout
37091 \begin_layout Standard
37092 In some cases you might want to insert text characters directly into formulas.
37093 When for example the centered dot · is often used in formulas like
37094 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
37097 , one would have to insert the command
37107 \begin_layout Plain Layout
37109 \begin_inset CommandInset ref
37111 reference "sub:Binary-Operators"
37120 all the time, because this character is defined in all encodings as text
37122 But the encoding can be changed by this LaTeX-preamble line:
37125 \begin_layout Standard
37130 Declare Inputtext{183}{
37140 f\SpecialChar \textcompwordmark{}
37144 \begin_layout Standard
37145 The character encoding (menu
37147 Document\SpecialChar \menuseparator
37148 Settings\SpecialChar \menuseparator
37151 ) specifies what character appears when a keyboard key is pressed.
37152 When the key for the character '·' is pressed, internally the command
37159 But this command is not available in a formula so that you would get LaTeX-erro
37161 With the changed encoding the right command is chosen automatically, depending
37162 on if the character was inserted into a formula or not.
37165 \begin_layout Standard
37166 The encoding of several characters is saved in definition files.
37167 For example the encoding
37171 is defined in the file
37175 which is in the installation folder of LaTeX.
37176 Encodings should only be changed via the LaTeX-preamble and not in the
37178 Otherwise documents could not be edited by other LyX users working on other
37182 \begin_layout Standard
37183 \begin_inset VSpace medskip
37186 Besides the centered dot, in this document the degree sign ° is defined
37187 with the following LaTeX-preamble line so that it can be directly inserted
37191 \begin_layout Standard
37196 DeclareInputtext{176}{
37206 f\SpecialChar \textcompwordmark{}
37210 \begin_layout Standard
37211 \begin_inset Newpage newpage
37217 \begin_layout Section
37220 \begin_inset Index idx
37223 \begin_layout Plain Layout
37232 \begin_layout Standard
37233 This section is a summary of the most important typographic rules, listed
37238 \begin_layout Plain Layout
37239 This collection was partly taken from the German semi-official dictionary
37241 \begin_inset Quotes eld
37245 \begin_inset Quotes erd
37249 \begin_inset CommandInset citation
37255 that lists some of the ISO rules.
37256 More rules are listed in
37257 \begin_inset CommandInset citation
37271 \begin_layout Itemize
37280 \begin_layout Plain Layout
37281 done with font styles, see
37282 \begin_inset CommandInset ref
37284 reference "sub:Font-Styles"
37293 , no matter if they appear in italic text: 30
37294 \begin_inset space \thinspace{}
37298 \begin_inset Newline newline
37301 Between the value and the unit is the smallest space, see
37302 \begin_inset CommandInset ref
37304 reference "sub:Predefined-Space"
37309 \begin_inset Newline newline
37312 This convention is automatically fulfilled when the command
37319 When it is entered to a formula, two boxes appear.
37320 In the first one the value is inserted, in the second one the unit, and
37322 \begin_inset Formula $\unit[30]{km/h}$
37326 \begin_inset space \thinspace{}
37336 is not a real LaTeX command but the command
37342 , therefore you cannot use it in TeX code.
37345 \begin_layout Itemize
37346 Percent and perthousand signs are set like physical units:
37347 \begin_inset Newline newline
37351 \begin_inset space \thinspace{}
37357 \begin_layout Itemize
37358 The degree sign follows directly on the value: 15°, but not when it is used
37360 \begin_inset space \thinspace{}
37366 \begin_layout Itemize
37367 In numbers with more than four digits the smallest space is inserted before
37368 every third digit to group them:
37378 \begin_inset space \thinspace{}
37382 \begin_inset space \thinspace{}
37388 \begin_layout Itemize
37389 For dimensions like 120×90×40
37390 \begin_inset space \thinspace{}
37393 cm the multiplication sign
37394 \begin_inset Quotes eld
37398 \begin_inset Quotes erd
37402 It is available either via the command
37410 Insert\SpecialChar \menuseparator
37411 Special Character\SpecialChar \menuseparator
37417 \begin_layout Itemize
37418 Functions with names consisting of several letters are set upright to avoid
37420 \begin_inset CommandInset ref
37422 reference "sub:Predefined-Functions"
37429 \begin_layout Itemize
37430 Indices consisting of several letters, are set upright:
37431 \begin_inset Formula $E_{\mathrm{kin}}$
37435 \begin_inset Newline newline
37438 Components of matrices are set italic:
37439 \begin_inset Formula $\hat{H}_{kl}$
37445 \begin_layout Itemize
37446 The differentiation/integration operator 'd', the Euler's number 'e' and
37447 the imaginary unit 'i' should be set upright, to avoid mixing them up with
37451 \begin_layout Itemize
37452 The character that denotes a
37456 transformation is inserted either by the command
37464 \begin_layout Plain Layout
37477 Insert\SpecialChar \menuseparator
37478 Special Character\SpecialChar \menuseparator
37479 Symbols\SpecialChar \menuseparator
37481 \begin_inset space ~
37487 \begin_inset Formula $\mathscr{F}$
37493 \begin_layout Standard
37494 \begin_inset Newpage newpage
37500 \begin_layout Section
37502 \begin_inset Index idx
37505 \begin_layout Plain Layout
37514 \begin_layout Standard
37515 Some characters and symbols can be created with several commands.
37516 Here is a list of the synonym commands:
37519 \begin_layout Standard
37520 \begin_inset VSpace bigskip
37524 \begin_inset space \hfill{}
37528 \begin_inset Tabular
37529 <lyxtabular version="3" rows="12" columns="2">
37530 <features tabularvalignment="middle">
37531 <column alignment="center" valignment="top" width="0pt">
37532 <column alignment="center" valignment="top" width="0pt">
37534 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37537 \begin_layout Plain Layout
37543 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37546 \begin_layout Plain Layout
37548 \begin_inset Note Note
37551 \begin_layout Plain Layout
37558 is only used as spacer.
37570 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37573 \begin_layout Plain Layout
37581 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37584 \begin_layout Plain Layout
37588 \begin_layout Plain Layout
37601 \begin_layout Plain Layout
37615 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37618 \begin_layout Plain Layout
37626 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37629 \begin_layout Plain Layout
37639 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37642 \begin_layout Plain Layout
37650 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37653 \begin_layout Plain Layout
37663 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37666 \begin_layout Plain Layout
37674 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37677 \begin_layout Plain Layout
37685 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37688 \begin_layout Plain Layout
37696 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37699 \begin_layout Plain Layout
37707 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37710 \begin_layout Plain Layout
37718 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37721 \begin_layout Plain Layout
37731 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37734 \begin_layout Plain Layout
37742 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37745 \begin_layout Plain Layout
37755 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37758 \begin_layout Plain Layout
37766 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37769 \begin_layout Plain Layout
37779 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37782 \begin_layout Plain Layout
37790 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37793 \begin_layout Plain Layout
37803 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37806 \begin_layout Plain Layout
37814 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37817 \begin_layout Plain Layout
37825 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37828 \begin_layout Plain Layout
37836 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37839 \begin_layout Plain Layout
37851 \begin_inset space \hfill{}
37855 \begin_inset Tabular
37856 <lyxtabular version="3" rows="12" columns="2">
37857 <features tabularvalignment="middle">
37858 <column alignment="center" valignment="top" width="0pt">
37859 <column alignment="center" valignment="top" width="0pt">
37861 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37864 \begin_layout Plain Layout
37870 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37873 \begin_layout Plain Layout
37881 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37884 \begin_layout Plain Layout
37892 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37895 \begin_layout Plain Layout
37907 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37910 \begin_layout Plain Layout
37918 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37921 \begin_layout Plain Layout
37931 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37934 \begin_layout Plain Layout
37942 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37945 \begin_layout Plain Layout
37955 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37958 \begin_layout Plain Layout
37966 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37969 \begin_layout Plain Layout
37977 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37980 \begin_layout Plain Layout
37988 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37991 \begin_layout Plain Layout
37999 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38002 \begin_layout Plain Layout
38010 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38013 \begin_layout Plain Layout
38023 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38026 \begin_layout Plain Layout
38034 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38037 \begin_layout Plain Layout
38047 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38050 \begin_layout Plain Layout
38058 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38061 \begin_layout Plain Layout
38071 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38074 \begin_layout Plain Layout
38082 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38085 \begin_layout Plain Layout
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38098 \begin_layout Plain Layout
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38147 \begin_inset space \hfill{}
38153 \begin_layout Standard
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38163 LatexCommand bibitem
38175 The LaTeX Companion
38178 Addison Wesley, 2004
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38184 LatexCommand bibitem
38190 \begin_inset CommandInset href
38193 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
38197 of LaTeX's math abilities
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38203 LatexCommand bibitem
38209 \begin_inset CommandInset href
38212 target "ftp://ftp.ams.org/pub/tex/doc/amsmath/amsldoc.pdf"
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38234 \begin_inset CommandInset bibitem
38235 LatexCommand bibitem
38241 \begin_inset CommandInset href
38244 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
38248 of all symbols available with LaTeX-packages
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38254 LatexCommand bibitem
38260 \begin_inset CommandInset href
38262 name "Documentation"
38263 target "http://mirrors.ctan.org/macros/latex/contrib/cancel/cancel.pdf"
38267 of the LaTeX-package
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38286 \begin_inset CommandInset bibitem
38287 LatexCommand bibitem
38293 \begin_inset CommandInset href
38295 name "Documentation"
38296 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
38300 of the LaTeX-package
38305 \begin_inset Index idx
38308 \begin_layout Plain Layout
38309 Packages ! hyperref
38317 \begin_layout Bibliography
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38319 \begin_inset CommandInset bibitem
38320 LatexCommand bibitem
38326 \begin_inset CommandInset href
38328 name "Documentation"
38329 target "http://www.ctan.org/tex-archive/macros/latex/contrib/mhchem/mhchem.pdf"
38333 of the LaTeX-package
38338 \begin_inset Index idx
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38353 LatexCommand bibitem
38359 \begin_inset CommandInset href
38362 target "http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf"
38373 \begin_inset CommandInset ref
38375 reference "sub:Operator-Limits"
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38397 LatexCommand bibitem
38408 Auflage, Duden 2001
38411 \begin_layout Bibliography
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38413 \begin_inset CommandInset bibitem
38414 LatexCommand bibitem
38420 \begin_inset CommandInset href
38423 target "http://physics.nist.gov/Document/checklist.pdf"
38427 for reviewing manuscripts
38430 \begin_layout Standard
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38432 LatexCommand printindex