1 #LyX 2.0.0svn created this file. For more info see http://www.lyx.org/
7 % DO NOT ALTER THIS PREAMBLE!!!
9 % This preamble is designed to ensure that the file prints
10 % out as advertised. If you mess with this preamble,
11 % parts of this document may not print out as expected. If you
12 % have problems LaTeXing this file, please contact
13 % the documentation team
14 % email: lyx-docs@lists.lyx.org
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}}}}
43 \settowidth{\abc}{\space}
45 \renewcommand{\equationautorefname}{\hspace{-\abc}}
46 \renewcommand{\sectionautorefname}{sec.\negthinspace}
47 \renewcommand{\subsectionautorefname}{sec.\negthinspace}
48 \renewcommand{\subsubsectionautorefname}{sec.\negthinspace}}
50 % don't load packages twice
51 % see first footnote in sec. 9.3
52 \@ifundefined{textcolor}{\usepackage{color}}{}
54 % the pages of the TOC are numbered roman
55 % and a PDF-bookmark for the TOC is added
57 \let\myTOC\tableofcontents
58 \renewcommand{\tableofcontents}{%
60 \pdfbookmark[1]{\contentsname}{}
63 \pagenumbering{arabic}}
65 % insert additional vertical space of 1.5 mm between footnotes,
67 \renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
69 % provides caption formatting
70 \setkomafont{captionlabel}{\bfseries}
73 \usepackage[samesize]{cancel}
75 % enables calculation of values
78 % for multiple columns used in sec. 23.7
84 % for the Fourier transformation symbol
87 % define a color, used in sec.9.3
88 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
90 % declare operators (see sec. 10.4 and sec. 15.2)
91 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
92 \DeclareMathOperator{\sgn}{sgn}
94 \newcommand{\spce}{\textvisiblespace}
96 % example definitions for sec. 20.1
97 \newcommand{\gr}{\Longrightarrow}
98 \newcommand{\us}[1]{\underline{#1}}
99 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
100 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
101 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
103 % example macro from sec. 19.4
104 %\def\tagform@#1{\maketag@@@{|#1|}}
106 % macro from sec. 10.2
107 \def\clap#1{\hbox to 0pt{\hss #1\hss}}
108 \def\mathclap {\mathpalette \mathclapinternal}
109 \def\mathclapinternal #1#2{\clap{$\mathsurround =0pt #1{#2}$}}
112 % ------------------------------------
113 % used to check for needed LaTeX packages
116 % check for package eurosym
117 % used for the Euro symbol
119 \IfFileExists{eurosym.sty}
120 {\usepackage[gennarrow]{eurosym}
121 \setboolean{eurosym}{true}}
122 {\setboolean{eurosym}{false}}
124 % check for package braket
125 % used for physical vectors
127 \IfFileExists{braket.sty}
129 \setboolean{braket}{true}}
130 {\setboolean{braket}{false}}
132 % check for package cancel
134 \IfFileExists{cancel.sty}
136 \setboolean{cancel}{true}}
137 {\setboolean{cancel}{false}}
139 % check for package upgreek
141 \IfFileExists{upgreek.sty}
142 {\usepackage{upgreek}
143 \setboolean{upgreek}{true}}
144 {\setboolean{upgreek}{false}}
146 \options bibliography=totoc,index=totoc,BCOR7.5mm,titlepage,captions=tableheading
147 \use_default_options false
148 \maintain_unincluded_children false
154 \font_typewriter default
155 \font_default_family default
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 false
213 \output_changes false
215 \html_be_strict false
221 LyX's detailed Math manual
229 \begin_layout Plain Layout
231 If you have comments or error corrections, please send them to the LyX Documenta
235 \begin_inset CommandInset href
237 name "lyx-docs@lists.lyx.org"
238 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
249 \begin_inset Note Note
252 \begin_layout Plain Layout
259 \begin_inset Newline newline
263 \begin_inset Newline newline
271 \begin_layout Standard
272 \begin_inset CommandInset toc
273 LatexCommand tableofcontents
280 \begin_layout Standard
281 \begin_inset Note Note
284 \begin_layout Plain Layout
285 To export this document to PDF, PS or DVI the LaTeX-packages
287 braket, cancel, eurosym,
298 If they are not installed the document can be export anyway but the sections
299 where the packages are required will not appear in the output.
304 ; if it is not installed, this file cannot be exported.
307 \begin_layout Plain Layout
308 The latest PDF-version of this document can be found here:
309 \begin_inset Newline newline
314 http://wiki.lyx.org/LyX/DocumentationDevelopment#Math
322 \begin_layout Standard
323 \begin_inset Newpage newpage
329 \begin_layout Section
333 \begin_layout Standard
334 This document explains LyX's math features and is furthermore a collection
335 of LaTeX-commands used for mathematical characters and constructs.
336 The explanations are designed for the usage of commands.
337 It is therefore required that you have read the section
348 \begin_layout Standard
349 Most of the characters and many constructs explained in this manual are
350 also accessible via the menu
354 \SpecialChar \menuseparator
370 But everybody who has to write lots of formulas will notice that it is
371 much faster to use commands instead of the math toolbar.
372 Therefore this manual is focused on commands but also mentions the correspondin
373 g toolbar buttons when available.
376 \begin_layout Standard
377 If not specially mentioned the commands are only available within formulas.
378 To be able to use all commands explained in this document, the option
382 must be used in the document settings (menu
384 Document\SpecialChar \menuseparator
385 Settings\SpecialChar \menuseparator
396 \begin_layout Plain Layout
399 Use AMS math package automatically
405 \begin_layout Plain Layout
414 -math when math constructs are found that are supported by LyX.
422 \begin_layout Standard
423 This document doesn't list all
427 \begin_layout Plain Layout
440 \begin_layout Plain Layout
445 \begin_layout Plain Layout
454 -math commands is in the file
457 \begin_inset CommandInset href
460 target "ftp://ctan.tug.org/tex-archive/macros/amstex/doc/amsguide.ps"
466 , which is part of every LaTeX standard installation.
471 for lucidity reasons.
474 \begin_layout Section
478 \begin_layout Standard
479 To create an inline formula
480 \begin_inset Index idx
483 \begin_layout Plain Layout
489 that is embedded into a text line, use one of the shortcuts
495 or the toolbar button
496 \begin_inset Graphics
497 filename ../images/math-mode.png
503 \begin_inset Newline newline
506 To create a display style formula
507 \begin_inset Index idx
510 \begin_layout Plain Layout
511 Formula ! display style
516 that will appear bigger and in an own paragraph, use one of these shortcuts:
526 \begin_layout Standard
527 To change a display style formula to an inline formula, set the cursor into
528 the formula and use one of the shortcuts
536 Edit\SpecialChar \menuseparator
537 Math\SpecialChar \menuseparator
541 The same way is used to change an inline formula to a display style formula.
544 \begin_layout Standard
545 To display parts of an inline formula in the size of a display style formula,
553 \begin_inset Index idx
556 \begin_layout Plain Layout
565 Then a new blue box appears in which the desired formula part is inserted.
568 \begin_layout Standard
569 Only inline formulas are allowed inside tables.
572 \begin_layout Standard
577 can be turned on in the menu
579 View\SpecialChar \menuseparator
583 When you click there on
584 \begin_inset Quotes eld
588 \begin_inset Quotes erd
591 the toolbar will be shown permanently at the bottom; this state is visualized
596 menu with a checkmark.
597 When you click in this state again on
598 \begin_inset Quotes eld
602 \begin_inset Quotes erd
613 is only shown when the cursor is within a formula; this state is visualized
614 by the renaming of the menu entry from
615 \begin_inset Quotes eld
619 \begin_inset Quotes erd
623 \begin_inset Quotes eld
631 \begin_inset Quotes erd
637 \begin_layout Standard
639 \begin_inset Index idx
642 \begin_layout Plain Layout
648 is invoked by pressing the toolbar button
649 \begin_inset Graphics
650 filename ../images/ert-insert.png
657 Insert\SpecialChar \menuseparator
662 \begin_layout Plain Layout
678 \begin_inset Note Note
681 \begin_layout Plain Layout
682 In LyX there are three
683 \begin_inset Quotes eld
687 \begin_inset Quotes erd
690 that appear in the output with sub- and superscript letters: TeX, LaTeX
694 \begin_layout Plain Layout
695 To avoid that these names are recognized as proper names, a TeX-brace pair
704 \begin_layout Standard
705 To change the LaTeX-preamble
706 \begin_inset Index idx
709 \begin_layout Plain Layout
717 Document\SpecialChar \menuseparator
718 Settings\SpecialChar \menuseparator
723 \begin_layout Plain Layout
739 \begin_layout Standard
740 To edit matrices, case differentiations and multiline formulas subsequently,
743 Edit\SpecialChar \menuseparator
748 Edit\SpecialChar \menuseparator
750 \begin_inset space \thinspace{}
754 \begin_inset space \thinspace{}
764 When lines and columns are swapped via the menu, the column or line where
765 the cursor is in is exchanged with the column to the right or the line
767 Is the cursor in the last column or row, the exchange is done with the
768 column to the left or the line above.
771 \begin_layout Standard
772 To write text in formulas
776 \begin_layout Plain Layout
777 For multiline formulas the command
784 \begin_inset CommandInset ref
786 reference "sub:Text-in-multiline"
800 \begin_inset Index idx
803 \begin_layout Plain Layout
810 \begin_inset Index idx
813 \begin_layout Plain Layout
820 This mode is invoked with the shortcut
826 or by the insertion of the command
833 \begin_inset Index idx
836 \begin_layout Plain Layout
845 The text appears black in LyX and can therefore be distinguished from the
846 other formula parts that appear blue.
847 In the output mathematical text is set upright, in contrary to other formula
851 \begin_layout Subsection*
855 \begin_layout Standard
856 Most of the LaTeX-commands for math constructs have the following scheme:
859 \begin_layout Standard
875 \begin_layout Standard
876 A command starts always with a backslash
877 \begin_inset Quotes gld
887 \begin_inset Quotes grd
891 To omit optional arguments, also omit the associated brackets.
892 The braces around the required arguments are named in this document as
894 \begin_inset Index idx
897 \begin_layout Plain Layout
904 If you add in a formula a left brace to a command name, LyX creates automatical
906 In all other cases TeX-braces are created in formulas with the command
914 TeX-braces appear red in LyX, in contrary to normal braces that appear
916 In TeX-mode no command is needed to get TeX-braces.
917 TeX-braces don't appear in the output.
920 \begin_layout Standard
921 When commands without arguments, like commands for symbols are entered in
922 TeX-mode, a space character must
926 be behind the command to end it.
927 This space doesn't appear in the output.
928 When the space should appear in the output, the space must be followed
929 by a protected space in normal text.
932 \begin_layout Standard
933 A protected space is inserted with
936 arg "space-insert protected"
942 \begin_layout Subsection*
943 \begin_inset Newpage newpage
949 \begin_layout Itemize
954 \begin_layout Plain Layout
955 This visible space character can be created with the command
962 \begin_inset Index idx
965 \begin_layout Plain Layout
973 , inserted in TeX-mode.
982 \begin_layout Plain Layout
995 denotes a space character to be input.
998 \begin_layout Itemize
1000 \begin_inset Formula $\to$
1003 denotes the usage of the corresponding arrow key on the keyboard.
1006 \begin_layout Subsection*
1010 \begin_layout Standard
1012 \begin_inset Float table
1018 \begin_layout Plain Layout
1020 \begin_inset Caption
1022 \begin_layout Plain Layout
1023 \begin_inset CommandInset label
1025 name "tab:Available-units"
1037 \begin_layout Plain Layout
1039 \begin_inset Tabular
1040 <lyxtabular version="3" rows="13" columns="2">
1041 <features tabularvalignment="middle">
1042 <column alignment="center" valignment="top" width="0">
1043 <column alignment="center" valignment="top" width="0">
1045 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1048 \begin_layout Plain Layout
1054 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1057 \begin_layout Plain Layout
1065 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1068 \begin_layout Plain Layout
1074 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1077 \begin_layout Plain Layout
1085 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1088 \begin_layout Plain Layout
1094 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1097 \begin_layout Plain Layout
1105 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1108 \begin_layout Plain Layout
1114 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1117 \begin_layout Plain Layout
1119 \begin_inset space \thinspace{}
1123 \begin_inset space \thinspace{}
1133 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1136 \begin_layout Plain Layout
1142 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1145 \begin_layout Plain Layout
1147 \begin_inset space \thinspace{}
1151 \begin_inset space \thinspace{}
1161 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1164 \begin_layout Plain Layout
1170 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1173 \begin_layout Plain Layout
1175 \begin_inset space \thinspace{}
1179 \begin_inset space \thinspace{}
1189 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1192 \begin_layout Plain Layout
1198 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1201 \begin_layout Plain Layout
1203 \begin_inset space \thinspace{}
1207 \begin_inset space \thinspace{}
1217 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1220 \begin_layout Plain Layout
1226 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1229 \begin_layout Plain Layout
1231 \begin_inset space \thinspace{}
1235 \begin_inset space \thinspace{}
1245 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1248 \begin_layout Plain Layout
1254 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1257 \begin_layout Plain Layout
1259 \begin_inset space \thinspace{}
1263 \begin_inset Formula $\approx$
1267 \begin_inset space \thinspace{}
1277 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1280 \begin_layout Plain Layout
1286 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1289 \begin_layout Plain Layout
1291 \begin_inset space \thinspace{}
1295 \begin_inset space \thinspace{}
1305 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1308 \begin_layout Plain Layout
1314 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1317 \begin_layout Plain Layout
1321 \begin_inset Quotes eld
1327 \begin_inset Quotes erd
1337 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1340 \begin_layout Plain Layout
1346 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1349 \begin_layout Plain Layout
1351 \begin_inset Quotes eld
1359 \begin_inset Quotes erd
1369 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1372 \begin_layout Plain Layout
1378 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1381 \begin_layout Plain Layout
1383 \begin_inset space \thinspace{}
1387 \begin_inset Formula $\nicefrac{1}{18}$
1391 \begin_inset space \thinspace{}
1412 \begin_layout Standard
1413 \begin_inset Newpage newpage
1419 \begin_layout Section
1423 \begin_layout Subsection
1425 \begin_inset Index idx
1428 \begin_layout Plain Layout
1435 \begin_inset Index idx
1438 \begin_layout Plain Layout
1445 \begin_inset Index idx
1448 \begin_layout Plain Layout
1453 \begin_layout Plain Layout
1464 \begin_layout Plain Layout
1477 \begin_inset Index idx
1480 \begin_layout Plain Layout
1485 \begin_layout Plain Layout
1496 \begin_layout Plain Layout
1511 \begin_layout Standard
1512 Indices are created with an underscore
1513 \begin_inset Quotes eld
1517 \begin_inset Quotes erd
1520 or via the math toolbar button
1521 \begin_inset Graphics
1522 filename ../images/math-subscript.png
1527 , exponents with a caret
1528 \begin_inset Quotes eld
1532 \begin_inset Quotes erd
1535 or via the math toolbar button
1536 \begin_inset Graphics
1537 filename ../images/math-superscript.png
1545 \begin_layout Standard
1547 \begin_inset Tabular
1548 <lyxtabular version="3" rows="4" columns="2">
1549 <features tabularvalignment="middle">
1550 <column alignment="center" valignment="top" width="0pt">
1551 <column alignment="center" valignment="top" width="0pt">
1553 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1556 \begin_layout Plain Layout
1562 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1565 \begin_layout Plain Layout
1567 \begin_inset Note Note
1570 \begin_layout Plain Layout
1577 is only used as spacer.
1589 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1592 \begin_layout Plain Layout
1598 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1601 \begin_layout Plain Layout
1602 \begin_inset Formula $B_{V}$
1612 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1615 \begin_layout Plain Layout
1621 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1624 \begin_layout Plain Layout
1625 \begin_inset Formula $\raisebox{5mm}{}B^{V}$
1635 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1638 \begin_layout Plain Layout
1643 \begin_layout Plain Layout
1657 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1660 \begin_layout Plain Layout
1661 \begin_inset Formula $\raisebox{5mm}{}B^{A}$
1677 \begin_layout Standard
1678 As the caret is in some languages an accent, vowels will be accentuated
1679 in this case and not set as exponents
1683 \begin_layout Plain Layout
1684 Depending on the used keyboard settings this can also happen for other character
1691 To get in this case exponents, press
1695 after the caret as in the last example.
1698 \begin_layout Subsection
1700 \begin_inset CommandInset label
1702 name "sub:Fractions"
1707 \begin_inset Index idx
1710 \begin_layout Plain Layout
1719 \begin_layout Standard
1720 Fractions are generated with the command
1727 \begin_inset Index idx
1730 \begin_layout Plain Layout
1738 or via the math toolbar button
1739 \begin_inset Graphics
1740 filename ../images/math/frac.png
1746 The font size is adjusted automatically, depending on whether the fraction
1747 is in an inline or display style formula.
1748 With the math toolbar button
1749 \begin_inset Graphics
1750 filename ../images/math/frac-square.png
1755 you can select different fraction types.
1758 \begin_layout Standard
1766 \begin_inset Index idx
1769 \begin_layout Plain Layout
1777 a fraction can be created that has in any case the size of a display style
1786 \begin_inset Index idx
1789 \begin_layout Plain Layout
1797 the fraction appears always with the size of an inline formula.
1801 \begin_layout Standard
1802 A line with the fraction
1803 \begin_inset Formula $\frac{1}{2}$
1806 that was created with the command
1815 \begin_layout Standard
1816 A line with the fraction
1817 \begin_inset Formula $\dfrac{1}{2}$
1820 that was created with the command
1829 \begin_layout Standard
1831 \begin_inset Tabular
1832 <lyxtabular version="3" rows="4" columns="2">
1833 <features tabularvalignment="middle">
1834 <column alignment="center" valignment="top" width="0pt">
1835 <column alignment="center" valignment="top" width="0pt">
1837 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1840 \begin_layout Plain Layout
1846 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1849 \begin_layout Plain Layout
1851 \begin_inset Note Note
1854 \begin_layout Plain Layout
1861 is only used as spacer.
1873 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1876 \begin_layout Plain Layout
1883 \begin_layout Plain Layout
1893 \begin_inset Formula $\downarrow$
1901 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1904 \begin_layout Plain Layout
1905 \begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$
1915 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1918 \begin_layout Plain Layout
1925 \begin_layout Plain Layout
1935 \begin_inset Formula $\downarrow$
1943 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1946 \begin_layout Plain Layout
1947 \begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$
1957 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1960 \begin_layout Plain Layout
1967 \begin_layout Plain Layout
1980 \begin_layout Plain Layout
1995 \begin_layout Plain Layout
2005 \begin_inset Formula $\downarrow$
2009 \begin_inset Formula $\downarrow\downarrow$
2017 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2020 \begin_layout Plain Layout
2021 \begin_inset Formula $\raisebox{8mm}{}\dfrac{e^{\frac{1}{2}}}{3}\raisebox{-4mm}{}$
2037 \begin_layout Standard
2038 \begin_inset VSpace bigskip
2042 \begin_inset Newpage newpage
2045 For nested fractions the command
2052 \begin_inset Index idx
2055 \begin_layout Plain Layout
2065 \begin_inset VSpace -3mm
2071 \begin_layout Standard
2072 \begin_inset Formula \begin{align*}
2073 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
2074 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}
2082 \begin_layout Standard
2083 The command for the example above is:
2086 \begin_layout Standard
2095 \begin_layout Plain Layout
2105 \begin_inset Formula $\downarrow$
2114 \begin_layout Plain Layout
2129 \begin_layout Plain Layout
2139 \begin_inset Formula $\downarrow$
2143 \begin_inset Formula $\downarrow$
2149 \begin_layout Standard
2150 \begin_inset VSpace medskip
2156 \begin_layout Standard
2163 sets the fraction always in the size of a displayed formula, also when
2164 it is part of another fraction.
2167 \begin_layout Standard
2168 It is possible to specify the alignment of the numerator.
2175 is used to left align it, the command
2188 centers the numerator.
2189 These fractions demonstrate the different alignments:
2192 \begin_layout Standard
2193 \begin_inset Formula $\cfrac[l]{A}{B+C}$
2197 \begin_inset Formula $\cfrac{A}{B+C}$
2201 \begin_inset Formula $\cfrac[r]{A}{B+C}$
2207 \begin_layout Standard
2208 \begin_inset Note Greyedout
2211 \begin_layout Plain Layout
2228 are no real LaTeX commands but represent the command
2232 cfrac[alignment]{numerator}{denominator}
2235 Therefore you cannot use them in TeX code.
2243 \begin_layout Standard
2244 \begin_inset VSpace medskip
2247 It is often advantageous to combine
2260 \begin_inset Formula \[
2261 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}\]
2268 \begin_layout Standard
2269 For inline fractions with a sloped fraction stroke you can use the command
2277 \begin_inset Index idx
2280 \begin_layout Plain Layout
2289 \begin_inset Formula $\nicefrac{5}{31}$
2299 \begin_inset Index idx
2302 \begin_layout Plain Layout
2311 \begin_inset Formula $\unitfrac{5}{31}$
2314 There is furthermore the command
2320 that offers to write a fraction in combination with a number:
2321 \begin_inset Formula $\unitfrac[2]{1}{3}$
2327 \begin_layout Standard
2328 \begin_inset Note Greyedout
2331 \begin_layout Plain Layout
2342 is not a real LaTeX command but the command
2343 \begin_inset Newline newline
2350 unitfrac[number]{numerator}{denominator}
2353 Therefore you cannot use it in TeX code.
2361 \begin_layout Standard
2362 How to define own fractions where the fraction stroke can be changed, is
2364 \begin_inset CommandInset ref
2366 reference "sub:Self-defined-Fractions"
2373 \begin_layout Subsection
2375 \begin_inset Index idx
2378 \begin_layout Plain Layout
2387 \begin_layout Standard
2388 Square roots are created with
2395 \begin_inset Index idx
2398 \begin_layout Plain Layout
2406 or the math toolbar button
2407 \begin_inset Graphics
2408 filename ../images/math/sqrt.png
2413 , all other roots with the command
2420 \begin_inset Index idx
2423 \begin_layout Plain Layout
2431 or with the math toolbar button
2432 \begin_inset Graphics
2433 filename ../images/math/root.png
2441 \begin_layout Standard
2443 \begin_inset Tabular
2444 <lyxtabular version="3" rows="3" columns="2">
2445 <features tabularvalignment="middle">
2446 <column alignment="center" valignment="top" width="0pt">
2447 <column alignment="center" valignment="top" width="0pt">
2449 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2452 \begin_layout Plain Layout
2458 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2461 \begin_layout Plain Layout
2463 \begin_inset Note Note
2466 \begin_layout Plain Layout
2473 is only used as spacer.
2485 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2488 \begin_layout Plain Layout
2495 \begin_layout Plain Layout
2509 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2512 \begin_layout Plain Layout
2513 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$
2523 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
2526 \begin_layout Plain Layout
2533 \begin_layout Plain Layout
2543 \begin_inset Formula $\downarrow$
2551 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
2554 \begin_layout Plain Layout
2555 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$
2571 \begin_layout Standard
2572 A square root can also be created with
2578 when the root index field is left empty.
2581 \begin_layout Standard
2582 With certain indices the distance to the root is too small, like in this
2584 \begin_inset Formula $\sqrt[\beta]{B}$
2588 \begin_inset Newline newline
2592 \begin_inset Formula $\beta$
2596 To avoid this, the commands
2603 \begin_inset Index idx
2606 \begin_layout Plain Layout
2621 \begin_inset Index idx
2624 \begin_layout Plain Layout
2632 are used with the following scheme:
2635 \begin_layout Standard
2649 \begin_layout Standard
2650 Distance is the number of Big Points (unit bp;
2651 \begin_inset Formula $\mathrm{72\, bp=1\, inch}$
2654 ), that the index should be moved to the left or top, resp..
2655 The commands are written to the index.
2656 This way the command
2657 \begin_inset Newline newline
2667 \begin_inset Formula $\to$
2673 \begin_inset Formula $\to$
2682 \begin_layout Plain Layout
2692 \begin_inset Formula $\to$
2696 \begin_inset Newline newline
2701 produces a correct typeset formula:
2702 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2708 \begin_layout Subsection
2709 Binomial Coefficients
2710 \begin_inset Index idx
2713 \begin_layout Plain Layout
2714 Binomial coefficients
2722 \begin_layout Standard
2723 Binomial coefficients are inserted with the command
2730 \begin_inset Index idx
2733 \begin_layout Plain Layout
2741 or with the submenu of the math toolbar button
2742 \begin_inset Graphics
2743 filename ../images/math/frac-square.png
2749 Analog to fractions (
2768 \begin_inset Index idx
2771 \begin_layout Plain Layout
2786 \begin_inset Index idx
2789 \begin_layout Plain Layout
2798 For other brackets around binomial coeficients there are the commands
2805 \begin_inset Index idx
2808 \begin_layout Plain Layout
2823 \begin_inset Index idx
2826 \begin_layout Plain Layout
2837 \begin_layout Standard
2839 \begin_inset Tabular
2840 <lyxtabular version="3" rows="6" columns="2">
2841 <features tabularvalignment="middle">
2842 <column alignment="center" valignment="top" width="0pt">
2843 <column alignment="center" valignment="top" width="0pt">
2845 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2848 \begin_layout Plain Layout
2854 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2857 \begin_layout Plain Layout
2859 \begin_inset Note Note
2862 \begin_layout Plain Layout
2869 is only used as spacer.
2881 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2884 \begin_layout Plain Layout
2891 \begin_layout Plain Layout
2901 \begin_inset Formula $\downarrow$
2909 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2912 \begin_layout Plain Layout
2913 \begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$
2923 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2926 \begin_layout Plain Layout
2933 \begin_layout Plain Layout
2943 \begin_inset Formula $\downarrow$
2951 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2954 \begin_layout Plain Layout
2955 \begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$
2965 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2968 \begin_layout Plain Layout
2975 \begin_layout Plain Layout
2985 \begin_inset Formula $\downarrow$
2993 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2996 \begin_layout Plain Layout
2997 \begin_inset Formula $\raisebox{5mm}{}\tbinom{A}{B}\raisebox{-2.5mm}{}$
3007 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3010 \begin_layout Plain Layout
3017 \begin_layout Plain Layout
3027 \begin_inset Formula $\downarrow$
3035 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3038 \begin_layout Plain Layout
3039 \begin_inset Formula $\raisebox{5mm}{}{A \brack B}\raisebox{-2.5mm}{}$
3049 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3052 \begin_layout Plain Layout
3059 \begin_layout Plain Layout
3069 \begin_inset Formula $\downarrow$
3077 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3080 \begin_layout Plain Layout
3081 \begin_inset Formula $\raisebox{5mm}{}{A \brace B}\raisebox{-2.5mm}{}$
3097 \begin_layout Subsection
3098 Case Differentiations
3099 \begin_inset Index idx
3102 \begin_layout Plain Layout
3103 Case differentiations
3111 \begin_layout Standard
3113 \begin_inset Tabular
3114 <lyxtabular version="3" rows="3" columns="2">
3115 <features tabularvalignment="middle">
3116 <column alignment="center" valignment="top" width="0pt">
3117 <column alignment="center" valignment="top" width="0pt">
3119 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3122 \begin_layout Plain Layout
3128 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3131 \begin_layout Plain Layout
3139 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3142 \begin_layout Plain Layout
3149 \begin_layout Plain Layout
3159 \begin_inset Formula $\to$
3163 \begin_inset Index idx
3166 \begin_layout Plain Layout
3179 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3182 \begin_layout Plain Layout
3183 \begin_inset Formula $\begin{cases}
3194 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3197 \begin_layout Plain Layout
3204 \begin_layout Plain Layout
3216 arg "newline-insert newline"
3224 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3227 \begin_layout Plain Layout
3228 \begin_inset Formula $\begin{cases}
3229 A & \textrm{for }x>0\\
3230 B & \textrm{for }x=0
3247 \begin_layout Standard
3254 or the usage of the math toolbar button
3255 \begin_inset Graphics
3256 filename ../images/math/cases.png
3261 you can create new lines with the shortcut
3264 arg "newline-insert newline"
3267 or the table toolbar button
3268 \begin_inset Graphics
3269 filename ../images/tabular-feature_append-row.png
3277 \begin_layout Standard
3284 is also available via the menu
3286 Insert\SpecialChar \menuseparator
3287 Math\SpecialChar \menuseparator
3293 \begin_layout Subsection
3295 \begin_inset Index idx
3298 \begin_layout Plain Layout
3307 \begin_layout Standard
3315 \begin_inset Index idx
3318 \begin_layout Plain Layout
3326 every character can be displayed canceled.
3327 The characters are quasi accentuated by a slash.
3330 \begin_layout Standard
3332 \begin_inset Tabular
3333 <lyxtabular version="3" rows="4" columns="2">
3334 <features tabularvalignment="middle">
3335 <column alignment="center" valignment="top" width="0pt">
3336 <column alignment="center" valignment="top" width="0pt">
3338 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3341 \begin_layout Plain Layout
3347 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3350 \begin_layout Plain Layout
3358 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3361 \begin_layout Plain Layout
3369 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3372 \begin_layout Plain Layout
3373 \begin_inset Formula $\not=$
3383 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3386 \begin_layout Plain Layout
3396 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3399 \begin_layout Plain Layout
3400 \begin_inset Formula $\not\le$
3410 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3413 \begin_layout Plain Layout
3423 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3426 \begin_layout Plain Layout
3427 \begin_inset Formula $\not\parallel$
3443 \begin_layout Standard
3444 The last example shows, that not all negations look good.
3445 Therefore there are for some negations special commands (see
3446 \begin_inset CommandInset ref
3448 reference "sub:Mathematical-Symbols"
3453 \begin_inset CommandInset ref
3455 reference "sec:Relations"
3462 \begin_layout Subsection
3464 \begin_inset CommandInset label
3466 name "sub:Placeholders"
3471 \begin_inset Index idx
3474 \begin_layout Plain Layout
3481 \begin_inset Index idx
3484 \begin_layout Plain Layout
3485 Chemical characters ! Isotopes
3491 \begin_inset Index idx
3494 \begin_layout Plain Layout
3499 \begin_layout Plain Layout
3510 \begin_layout Plain Layout
3525 \begin_layout Standard
3527 \begin_inset space \thinspace{}
3531 \begin_inset space \space{}
3538 \begin_layout Plain Layout
3539 Typesetting isotopes and chemical symbols is described in
3540 \begin_inset CommandInset ref
3542 reference "sub:Chemical-Symbols-and"
3551 the following problem occurs:
3554 \begin_layout Standard
3556 \begin_inset Tabular
3557 <lyxtabular version="3" rows="2" columns="2">
3558 <features tabularvalignment="middle">
3559 <column alignment="center" valignment="top" width="0pt">
3560 <column alignment="center" valignment="top" width="0pt">
3562 <cell alignment="center" valignment="top" usebox="none">
3565 \begin_layout Plain Layout
3566 Indices created with sub- and superscripts:
3571 <cell alignment="center" valignment="top" usebox="none">
3574 \begin_layout Plain Layout
3575 \begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
3585 <cell alignment="center" valignment="top" usebox="none">
3588 \begin_layout Plain Layout
3594 <cell alignment="center" valignment="top" usebox="none">
3597 \begin_layout Plain Layout
3598 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3612 \begin_inset Note Note
3615 \begin_layout Plain Layout
3622 is only used as spacer.
3630 \begin_layout Standard
3631 The shorter index is by default placed below or above the first character
3632 of the longer index.
3633 To avoid this there is the command
3640 \begin_inset Index idx
3643 \begin_layout Plain Layout
3651 or the math toolbar button
3652 \begin_inset space \thinspace{}
3659 \begin_layout Plain Layout
3660 can be found in the submenu of the toolbar button
3661 \begin_inset Graphics
3662 filename ../images/math/space.png
3673 \begin_inset Graphics
3674 filename ../images/math/phantom.png
3679 that creates one or more phantom characters.
3686 a small blue box appears that is superposed with two red arrows.
3687 The arrows indicate that the complete width and height of the box content
3688 will be created as placeholder.
3689 Phantom characters are accordingly placeholders with the size of the characters.
3692 \begin_layout Standard
3694 \begin_inset Tabular
3695 <lyxtabular version="3" rows="4" columns="2">
3696 <features tabularvalignment="middle">
3697 <column alignment="center" valignment="top" width="0">
3698 <column alignment="center" valignment="top" width="0">
3700 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3703 \begin_layout Plain Layout
3709 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3712 \begin_layout Plain Layout
3714 \begin_inset Note Note
3717 \begin_layout Plain Layout
3724 is only used as spacer.
3736 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3739 \begin_layout Plain Layout
3744 \begin_layout Plain Layout
3759 \begin_layout Plain Layout
3769 \begin_inset Formula $\to$
3776 \begin_layout Plain Layout
3790 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3793 \begin_layout Plain Layout
3794 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
3804 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3807 \begin_layout Plain Layout
3812 \begin_layout Plain Layout
3827 \begin_layout Plain Layout
3837 \begin_inset Formula $\to$
3844 \begin_layout Plain Layout
3858 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3861 \begin_layout Plain Layout
3862 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
3872 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3875 \begin_layout Plain Layout
3882 \begin_layout Plain Layout
3897 \begin_layout Plain Layout
3907 \begin_inset Formula $\to$
3914 \begin_layout Plain Layout
3928 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3931 \begin_layout Plain Layout
3932 \begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
3948 \begin_layout Standard
3949 Furthermore there are the commands
3956 \begin_inset Index idx
3959 \begin_layout Plain Layout
3968 \begin_inset space ~
3972 \begin_inset Graphics
3973 filename ../images/math/vphantom.png
3985 \begin_inset Index idx
3988 \begin_layout Plain Layout
3997 \begin_inset space ~
4001 \begin_inset Graphics
4002 filename ../images/math/hphantom.png
4014 creates only space for the maximal height of the characters in the box
4015 but not for its width.
4022 creates only space for the width of the box content.
4023 Therefore the boxes of both commands have only one red arrow.
4026 \begin_layout Standard
4037 \begin_layout Plain Layout
4052 space for the height of the integral sign,
4056 \begin_layout Plain Layout
4063 creates an integral sign, see
4064 \begin_inset CommandInset ref
4066 reference "sub:Big-Operators"
4075 because this is the larger character.
4076 An example application is in
4077 \begin_inset CommandInset ref
4079 reference "sub:Multiline-Brackets"
4086 \begin_layout Standard
4087 Placeholders can also be used for text when it is inserted via the menu
4090 Insert\SpecialChar \menuseparator
4091 Formatting\SpecialChar \menuseparator
4097 \begin_layout Standard
4099 \begin_inset Newline newline
4103 \begin_inset Phantom Phantom
4106 \begin_layout Plain Layout
4115 \begin_layout Subsection
4117 \begin_inset Index idx
4120 \begin_layout Plain Layout
4127 \begin_inset Index idx
4130 \begin_layout Plain Layout
4131 Formula ! underlined
4139 \begin_layout Standard
4141 \begin_inset Tabular
4142 <lyxtabular version="3" rows="4" columns="2">
4143 <features tabularvalignment="middle">
4144 <column alignment="center" valignment="top" width="0pt">
4145 <column alignment="center" valignment="top" width="0pt">
4147 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4150 \begin_layout Plain Layout
4156 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4159 \begin_layout Plain Layout
4161 \begin_inset Note Note
4164 \begin_layout Plain Layout
4171 is only used as spacer.
4183 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4186 \begin_layout Plain Layout
4193 \begin_layout Plain Layout
4203 \begin_inset Index idx
4206 \begin_layout Plain Layout
4219 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4222 \begin_layout Plain Layout
4223 \begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
4233 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
4236 \begin_layout Plain Layout
4243 \begin_layout Plain Layout
4253 \begin_inset Index idx
4256 \begin_layout Plain Layout
4269 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
4272 \begin_layout Plain Layout
4273 \begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
4283 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4286 \begin_layout Plain Layout
4293 \begin_layout Plain Layout
4308 \begin_layout Plain Layout
4322 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4325 \begin_layout Plain Layout
4326 \begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
4342 \begin_layout Standard
4343 In the last example it doesn't matter if first
4358 \begin_layout Standard
4359 To double underline e.
4360 \begin_inset space \thinspace{}
4364 \begin_inset space \space{}
4376 \begin_layout Standard
4377 It is possible to place up to 6 lines above or below characters.
4380 \begin_layout Standard
4381 \begin_inset VSpace bigskip
4384 Custom lines can be created using the command
4391 \begin_inset Index idx
4394 \begin_layout Plain Layout
4402 which has the following scheme:
4405 \begin_layout Standard
4410 rule[vertical offset]{length}{thickness}
4413 \begin_layout Standard
4414 The optional vertical offset shifts the line upwards (or downwards, when
4415 the value is negative).
4417 \begin_inset CommandInset ref
4419 reference "tab:Available-units"
4423 can be used for the values.
4424 Here are two example lines created with the commands
4425 \begin_inset Newline newline
4432 rule[-2ex]{3cm}{2pt}
4443 \begin_layout Standard
4445 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4451 \begin_layout Standard
4458 can also be used for text when a line is inserted via the menu
4460 Insert\SpecialChar \menuseparator
4461 Formatting\SpecialChar \menuseparator
4463 \begin_inset space ~
4471 \begin_layout Standard
4473 \begin_inset CommandInset line
4484 \begin_layout Subsection
4486 \begin_inset CommandInset label
4493 \begin_inset Index idx
4496 \begin_layout Plain Layout
4505 \begin_layout Standard
4506 There are different types of ellipses available.
4510 \begin_layout Plain Layout
4511 In the math toolbar in the submenu of the button
4512 \begin_inset Graphics
4513 filename ../images/math/ldots.png
4523 For listings dots at the baseline are used (
4530 \begin_inset Index idx
4533 \begin_layout Plain Layout
4541 ), while for operations dots are needed that are on the same height as the
4549 \begin_inset Index idx
4552 \begin_layout Plain Layout
4561 When using the command
4568 \begin_inset Index idx
4571 \begin_layout Plain Layout
4579 , LaTeX decides on the basis of the next character what type is used.
4582 \begin_layout Standard
4584 \begin_inset Tabular
4585 <lyxtabular version="3" rows="9" columns="2">
4586 <features tabularvalignment="middle">
4587 <column alignment="center" valignment="top" width="0pt">
4588 <column alignment="center" valignment="top" width="0pt">
4590 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4593 \begin_layout Plain Layout
4599 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4602 \begin_layout Plain Layout
4610 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4613 \begin_layout Plain Layout
4618 \begin_layout Plain Layout
4633 \begin_layout Plain Layout
4647 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4650 \begin_layout Plain Layout
4651 \begin_inset Formula $A_{1},\dots,A_{n}$
4661 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4664 \begin_layout Plain Layout
4669 \begin_layout Plain Layout
4684 \begin_layout Plain Layout
4698 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4701 \begin_layout Plain Layout
4702 \begin_inset Formula $A_{1}+\dots+A_{n}$
4712 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4715 \begin_layout Plain Layout
4720 \begin_layout Plain Layout
4735 \begin_layout Plain Layout
4749 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4752 \begin_layout Plain Layout
4753 \begin_inset Formula $A_{1},\ldots,A_{n}$
4763 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4766 \begin_layout Plain Layout
4771 \begin_layout Plain Layout
4786 \begin_layout Plain Layout
4800 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4803 \begin_layout Plain Layout
4804 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4814 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4817 \begin_layout Plain Layout
4825 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4828 \begin_layout Plain Layout
4829 \begin_inset Formula $\vdots$
4839 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4842 \begin_layout Plain Layout
4850 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4853 \begin_layout Plain Layout
4854 \begin_inset Formula $\ddots$
4864 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4867 \begin_layout Plain Layout
4875 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4878 \begin_layout Plain Layout
4879 \begin_inset Formula $\iddots$
4889 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4892 \begin_layout Plain Layout
4894 \begin_inset space \thinspace{}
4897 matrix with the different dots
4902 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4905 \begin_layout Plain Layout
4906 \begin_inset Formula $\begin{array}{ccc}
4907 A_{11} & \cdots & A_{1m}\\
4908 \vdots & \ddots & \vdots\\
4909 A_{n1} & \cdots & A_{nm}
4926 \begin_layout Standard
4927 The ellipses available in menu
4929 Insert\SpecialChar \menuseparator
4931 \begin_inset space ~
4945 \begin_layout Standard
4946 \begin_inset VSpace medskip
4955 , one of the options
4957 Use mathdots package (automatically)
4959 must be set in the document settings under
4962 \begin_inset space ~
4968 \begin_inset Newline newline
4973 Use mathdots package
4975 will improve the appearance of all dots in the documents if their font
4976 style or size is not the default.
4979 \begin_layout Standard
4980 \begin_inset VSpace medskip
4983 Specially for matrices there are ellipses that span over several columns.
4984 They are created with the command
4991 \begin_inset Index idx
4994 \begin_layout Plain Layout
5002 , that has the following scheme:
5005 \begin_layout Standard
5010 hdotsfor[distance]{number of columns}
5013 \begin_layout Standard
5014 The number of columns specifies how many columns should be spanned.
5015 Distance is a factor for the distance between the dots.
5018 \begin_layout Standard
5019 In the following matrix the command
5025 was inserted in the first box of the second line, to get an ellipsis with
5026 a dot distance twice as long as with the command
5033 \begin_inset Formula \[
5034 \left(\begin{array}{cccc}
5038 \end{array}\right)\]
5042 Note that the matrix fields that should be spanned must be empty, otherwise
5043 you get LaTeX-errors.
5046 \begin_layout Standard
5047 \begin_inset VSpace bigskip
5050 Furthermore you can fill with the command
5057 \begin_inset Index idx
5060 \begin_layout Plain Layout
5068 the rest of a line with dots.
5069 The effect of these commands is the same like with
5076 \begin_inset CommandInset ref
5078 reference "sub:Variable-Space"
5085 \begin_layout Standard
5086 For example the command
5094 \begin_layout Plain Layout
5108 \begin_layout Standard
5109 \begin_inset Formula $A\dotfill B$
5115 \begin_layout Standard
5122 there is for a line the command
5129 \begin_inset Index idx
5132 \begin_layout Plain Layout
5143 \begin_layout Standard
5144 \begin_inset Formula $A\hrulefill B$
5150 \begin_layout Standard
5151 To use the commands for text, they have to be inserted in TeX-mode.
5154 \begin_layout Section
5156 \begin_inset CommandInset label
5163 \begin_inset Index idx
5166 \begin_layout Plain Layout
5175 \begin_layout Standard
5176 Matrices can be inserted via the math toolbar button
5177 \begin_inset Graphics
5178 filename ../images/dialog-show_mathmatrix.png
5185 Insert\SpecialChar \menuseparator
5186 Math\SpecialChar \menuseparator
5190 In the matrix dialog you can specify the number of columns and rows, the
5191 alignment and the decoration.
5192 The vertical alignment is hereby only of importance for matrices in inline
5196 \begin_layout Standard
5197 The first matrix is top
5198 \begin_inset Formula $\begin{array}[t]{cccc}
5206 \begin_inset Formula $\begin{array}{cccc}
5213 and the third bottom
5214 \begin_inset Formula $\begin{array}[b]{cccc}
5224 \begin_layout Standard
5225 The horizontal alignment specifies how the column entries should be aligned.
5226 It is set by entering a letter for every column.
5231 denotes left aligned,
5240 To create for example a 4
5245 \begin_inset space ~
5248 matrix where the first column is left aligned, the second and third are
5249 centered and the last one is right aligned, one enters for the horizontal
5255 Normally are in a matrix all columns centered, therefore the default is
5256 for every column is a
5263 \begin_layout Standard
5264 Horizontal alignment:
5267 \begin_layout Standard
5273 \begin_inset Formula $\begin{array}{lll}
5285 \begin_inset Formula $\begin{array}{ccc}
5297 \begin_inset Formula $\begin{array}{rrr}
5307 \begin_layout Standard
5308 To add or delete rows and columns subsequently, the math toolbar buttons
5310 \begin_inset Graphics
5311 filename ../images/tabular-feature_append-row.png
5317 \begin_inset Graphics
5318 filename ../images/tabular-feature_delete-row.png
5324 \begin_inset space \thinspace{}
5329 Edit\SpecialChar \menuseparator
5333 New rows can also be created with
5336 arg "newline-insert newline"
5342 \begin_layout Standard
5343 \begin_inset VSpace bigskip
5350 adds parentheses in the selected style around the matrix.
5351 Alternatively, parentheses can can either be created with the commands
5359 \begin_inset Index idx
5362 \begin_layout Plain Layout
5377 \begin_inset Index idx
5380 \begin_layout Plain Layout
5391 \begin_inset space ~
5397 \begin_inset CommandInset ref
5399 reference "sub:Automatic-Bracket-Size"
5403 , or by using the following commands:
5404 \begin_inset VSpace medskip
5410 \begin_layout Standard
5411 \begin_inset space \hfill{}
5415 \begin_inset Tabular
5416 <lyxtabular version="3" rows="4" columns="2">
5417 <features tabularvalignment="middle">
5418 <column alignment="center" valignment="top" width="0">
5419 <column alignment="center" valignment="top" width="0">
5421 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5424 \begin_layout Plain Layout
5430 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5433 \begin_layout Plain Layout
5435 \begin_inset Note Note
5438 \begin_layout Plain Layout
5445 is only used as spacer.
5457 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5460 \begin_layout Plain Layout
5467 \begin_layout Plain Layout
5481 \begin_inset space \thinspace{}
5489 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5492 \begin_layout Plain Layout
5493 \begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
5494 0 & \textrm{-}\mathrm{i}\\
5496 \end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
5506 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5509 \begin_layout Plain Layout
5516 \begin_layout Plain Layout
5530 \begin_inset space \thinspace{}
5538 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5541 \begin_layout Plain Layout
5542 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
5543 0 & \textrm{-}\mathrm{i}\\
5545 \end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
5555 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5558 \begin_layout Plain Layout
5565 \begin_layout Plain Layout
5579 \begin_inset space \thinspace{}
5587 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5590 \begin_layout Plain Layout
5591 \begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
5592 0 & \textrm{-}\mathrm{i}\\
5594 \end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
5608 \begin_inset space \hfill{}
5612 \begin_inset Tabular
5613 <lyxtabular version="3" rows="4" columns="2">
5614 <features tabularvalignment="middle">
5615 <column alignment="center" valignment="top" width="0">
5616 <column alignment="center" valignment="top" width="0">
5618 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5621 \begin_layout Plain Layout
5627 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5630 \begin_layout Plain Layout
5638 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5641 \begin_layout Plain Layout
5648 \begin_layout Plain Layout
5662 \begin_inset space \thinspace{}
5670 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5673 \begin_layout Plain Layout
5674 \begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
5675 0 & \textrm{-}\mathrm{i}\\
5677 \end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
5687 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5690 \begin_layout Plain Layout
5697 \begin_layout Plain Layout
5711 \begin_inset space \thinspace{}
5719 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5722 \begin_layout Plain Layout
5723 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
5724 0 & \textrm{-}\mathrm{i}\\
5726 \end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
5736 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5739 \begin_layout Plain Layout
5746 \begin_layout Plain Layout
5760 \begin_inset space \thinspace{}
5768 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5771 \begin_layout Plain Layout
5772 \begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
5773 0 & \textrm{-}\mathrm{i}\\
5775 \end{array}\end{matrix}\raisebox{-5.3mm}{}$
5789 \begin_inset space \hfill{}
5795 \begin_layout Standard
5796 \begin_inset VSpace medskip
5800 \begin_inset space \thinspace{}
5804 \begin_inset space \space{}
5813 is inserted, a blue box appears between two vertical lines where the matrix
5815 \begin_inset Newline newline
5818 Note that decorated matrices ignore the vertical alignment.
5821 \begin_layout Standard
5822 \begin_inset VSpace bigskip
5825 As all multiline formulas are matrices, the length
5832 \begin_inset Index idx
5835 \begin_layout Plain Layout
5843 that is described in
5844 \begin_inset CommandInset ref
5846 reference "sub:Column-Separation"
5850 can also be used to change the column separation of matrices.
5853 \begin_layout Standard
5854 To change the row separation, the command
5861 \begin_inset Index idx
5864 \begin_layout Plain Layout
5873 It is used as follows:
5876 \begin_layout Standard
5883 arraystretch}{stretch factor}
5884 \begin_inset Index idx
5887 \begin_layout Plain Layout
5898 \begin_layout Standard
5905 assigns the stretch factor to the predefined command
5913 \begin_inset space \thinspace{}
5917 \begin_inset space \space{}
5920 the row separation, use the factor 2.
5921 This is then used for all following matrices.
5922 To go back to the original separation, assign the factor 1 to
5931 \begin_layout Standard
5932 To set matrices into a text line, the command
5939 \begin_inset Index idx
5942 \begin_layout Plain Layout
5951 When it is inserted a blue box with two dashed lines appears.
5952 In this box the matrix is inserted.
5955 \begin_layout Standard
5957 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5959 \end{smallmatrix}\right)$
5965 \begin_layout Section
5966 Brackets and Delimiters
5967 \begin_inset Index idx
5970 \begin_layout Plain Layout
5977 \begin_inset Index idx
5980 \begin_layout Plain Layout
5989 \begin_layout Subsection
5990 Vertical Brackets and Delimiters
5991 \begin_inset Index idx
5994 \begin_layout Plain Layout
6003 \begin_layout Standard
6004 \begin_inset space \hfill{}
6008 \begin_inset Tabular
6009 <lyxtabular version="3" rows="9" columns="2">
6010 <features tabularvalignment="middle">
6011 <column alignment="center" valignment="top" width="0pt">
6012 <column alignment="center" valignment="top" width="0pt">
6014 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6017 \begin_layout Plain Layout
6023 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6026 \begin_layout Plain Layout
6034 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6037 \begin_layout Plain Layout
6043 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6046 \begin_layout Plain Layout
6047 \begin_inset Formula $($
6057 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6060 \begin_layout Plain Layout
6066 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6069 \begin_layout Plain Layout
6070 \begin_inset Formula $\{$
6080 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6083 \begin_layout Plain Layout
6089 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6092 \begin_layout Plain Layout
6093 \begin_inset Formula $[$
6103 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6106 \begin_layout Plain Layout
6114 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6117 \begin_layout Plain Layout
6118 \begin_inset Formula $\langle$
6128 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6131 \begin_layout Plain Layout
6139 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6142 \begin_layout Plain Layout
6143 \begin_inset Formula $\lceil$
6153 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6156 \begin_layout Plain Layout
6164 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6167 \begin_layout Plain Layout
6168 \begin_inset Formula $\lfloor$
6178 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6181 \begin_layout Plain Layout
6187 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6190 \begin_layout Plain Layout
6191 \begin_inset Formula $/$
6201 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6204 \begin_layout Plain Layout
6210 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6213 \begin_layout Plain Layout
6214 \begin_inset Formula $|$
6228 \begin_inset space \hfill{}
6232 \begin_inset Tabular
6233 <lyxtabular version="3" rows="9" columns="2">
6234 <features tabularvalignment="middle">
6235 <column alignment="center" valignment="top" width="0pt">
6236 <column alignment="center" valignment="top" width="0pt">
6238 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6241 \begin_layout Plain Layout
6247 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6250 \begin_layout Plain Layout
6258 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6261 \begin_layout Plain Layout
6267 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6270 \begin_layout Plain Layout
6271 \begin_inset Formula $)$
6281 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6284 \begin_layout Plain Layout
6290 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6293 \begin_layout Plain Layout
6294 \begin_inset Formula $\}$
6304 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6307 \begin_layout Plain Layout
6313 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6316 \begin_layout Plain Layout
6317 \begin_inset Formula $]$
6327 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6330 \begin_layout Plain Layout
6338 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6341 \begin_layout Plain Layout
6342 \begin_inset Formula $\rangle$
6352 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6355 \begin_layout Plain Layout
6363 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6366 \begin_layout Plain Layout
6367 \begin_inset Formula $\rceil$
6377 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6380 \begin_layout Plain Layout
6388 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6391 \begin_layout Plain Layout
6392 \begin_inset Formula $\rfloor$
6402 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6405 \begin_layout Plain Layout
6415 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6418 \begin_layout Plain Layout
6419 \begin_inset Formula $\backslash$
6429 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6432 \begin_layout Plain Layout
6440 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6443 \begin_layout Plain Layout
6444 \begin_inset Formula $\|$
6458 \begin_inset space \hfill{}
6464 \begin_layout Standard
6467 \begin_inset Note Greyedout
6470 \begin_layout Plain Layout
6475 In TeX-mode the command
6482 \begin_inset Index idx
6485 \begin_layout Plain Layout
6493 must be used for the backslash, because the command
6501 produces there a line break.
6509 \begin_layout Standard
6510 For all characters listed above the size can be adjusted with the commands
6511 described in the following two subsections.
6512 When using these commands, the characters < and > can directly be used
6513 instead of the commands
6528 \begin_layout Subsubsection
6530 \begin_inset CommandInset label
6532 name "sub:Manual-Bracket-Size"
6537 \begin_inset Index idx
6540 \begin_layout Plain Layout
6541 Bracket size ! manual
6549 \begin_layout Standard
6550 The bracket size can be specified manually by the LaTeX-commands
6557 \begin_inset Index idx
6560 \begin_layout Plain Layout
6593 denotes the smallest and
6599 the largest bracket size.
6602 \begin_layout Standard
6603 These commands are used to emphasize levels of brackets:
6606 \begin_layout Standard
6608 \begin_inset Tabular
6609 <lyxtabular version="3" rows="2" columns="2">
6610 <features tabularvalignment="middle">
6611 <column alignment="center" valignment="top" width="0pt">
6612 <column alignment="center" valignment="top" width="0pt">
6614 <cell alignment="center" valignment="top" usebox="none">
6617 \begin_layout Plain Layout
6618 all brackets in the same size:
6623 <cell alignment="center" valignment="top" usebox="none">
6626 \begin_layout Plain Layout
6627 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
6637 <cell alignment="center" valignment="top" usebox="none">
6640 \begin_layout Plain Layout
6646 <cell alignment="center" valignment="top" usebox="none">
6649 \begin_layout Plain Layout
6650 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6664 \begin_inset Note Note
6667 \begin_layout Plain Layout
6674 is only used as spacer.
6682 \begin_layout Standard
6683 For the second formula the command
6693 \begin_layout Plain Layout
6707 \begin_layout Standard
6708 Here is an overview about all bracket sizes:
6711 \begin_layout Standard
6731 \begin_layout Plain Layout
6748 \begin_layout Plain Layout
6761 \begin_layout Plain Layout
6777 \begin_layout Standard
6779 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6785 \begin_layout Standard
6792 -commands there is the variant
6799 \begin_inset Index idx
6802 \begin_layout Plain Layout
6810 that adds a bit more space between the bracket and its content, and the
6824 \begin_inset Index idx
6827 \begin_layout Plain Layout
6837 , that don't add additional space.
6842 at the end of the command
6848 is for a left bracket; for a right bracket this will be replaced by an
6854 A left or right bracket can each be an opening or closing bracket.
6857 \begin_layout Standard
6858 In the following table is a comparison of the variants:
6861 \begin_layout Standard
6863 \begin_inset Tabular
6864 <lyxtabular version="3" rows="5" columns="2">
6865 <features tabularvalignment="middle">
6866 <column alignment="center" valignment="middle" width="0">
6867 <column alignment="center" valignment="middle" width="0">
6869 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6872 \begin_layout Plain Layout
6878 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6881 \begin_layout Plain Layout
6883 \begin_inset Note Note
6886 \begin_layout Plain Layout
6893 is only used as spacer.
6905 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6908 \begin_layout Plain Layout
6923 \begin_layout Plain Layout
6941 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6944 \begin_layout Plain Layout
6945 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
6955 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6958 \begin_layout Plain Layout
6973 \begin_layout Plain Layout
6991 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6994 \begin_layout Plain Layout
6995 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
7005 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7008 \begin_layout Plain Layout
7023 \begin_layout Plain Layout
7041 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7044 \begin_layout Plain Layout
7045 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
7055 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7058 \begin_layout Plain Layout
7070 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7073 \begin_layout Plain Layout
7074 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
7090 \begin_layout Subsubsection
7091 Automatic Bracket Size
7092 \begin_inset CommandInset label
7094 name "sub:Automatic-Bracket-Size"
7099 \begin_inset Index idx
7102 \begin_layout Plain Layout
7103 Bracket size ! automatic
7111 \begin_layout Standard
7112 Brackets with variable size can be inserted with the commands
7119 \begin_inset Index idx
7122 \begin_layout Plain Layout
7137 \begin_inset Index idx
7140 \begin_layout Plain Layout
7148 or via the math toolbar button
7149 \begin_inset Graphics
7150 filename ../images/dialog-show_mathdelimiter.png
7168 the wanted bracket must be inserted.
7169 The bracket size will then automatically be calculated for the output.
7172 \begin_layout Standard
7174 normal bracket: The command
7184 \begin_layout Plain Layout
7194 \begin_inset Formula $\downarrow$
7201 \begin_layout Plain Layout
7213 \begin_inset Formula \[
7221 \begin_layout Standard
7223 multiline bracket: The command
7235 \begin_layout Plain Layout
7245 \begin_inset Formula $\downarrow$
7252 \begin_layout Plain Layout
7266 \begin_inset Formula \[
7267 \ln\left(\frac{A}{C}\right)\]
7274 \begin_layout Standard
7290 \begin_inset space ~
7296 This has the advantage that you can see in LyX immediately the real bracket
7297 size and that the matching right bracket will be created too.
7298 \begin_inset Newline newline
7301 The command for the last example would then be:
7315 \begin_layout Plain Layout
7325 \begin_inset Formula $\downarrow$
7331 \begin_layout Standard
7332 To omit a left or right bracket, a dot is inserted for the omitted bracket.
7333 For example the command
7343 \begin_layout Plain Layout
7353 \begin_inset Formula $\downarrow$
7360 \begin_layout Plain Layout
7376 \begin_inset Formula \[
7377 \left.\frac{A}{B}\right\} \]
7395 will be converted by LyX to brackets in the right size when the document
7396 is reloaded and an omitted bracket will appear as dashed line.
7399 \begin_layout Standard
7400 \begin_inset VSpace bigskip
7403 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
7411 \begin_inset Index idx
7414 \begin_layout Plain Layout
7422 is additionally available for all brackets and limits.
7423 With this command the height of the following character is adapted to the
7424 one of the surrounding brackets, what is e.
7425 \begin_inset space \thinspace{}
7429 \begin_inset space \space{}
7432 needed for physical vectors:
7433 \begin_inset Formula \[
7434 \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle \]
7438 For physical vectors there is a special LaTeX-package, described in
7439 \begin_inset CommandInset ref
7441 reference "sub:Physical-Vectors"
7448 \begin_layout Subsection
7450 \begin_inset Index idx
7453 \begin_layout Plain Layout
7454 Brackets ! horizontal
7462 \begin_layout Standard
7464 \begin_inset Tabular
7465 <lyxtabular version="3" rows="4" columns="2">
7466 <features tabularvalignment="middle">
7467 <column alignment="center" valignment="top" width="0pt">
7468 <column alignment="center" valignment="top" width="0pt">
7470 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7473 \begin_layout Plain Layout
7475 \begin_inset Note Note
7478 \begin_layout Plain Layout
7485 is only used as spacer.
7495 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7498 \begin_layout Plain Layout
7506 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7509 \begin_layout Plain Layout
7513 \begin_layout Plain Layout
7528 \begin_layout Plain Layout
7541 \begin_layout Plain Layout
7554 \begin_layout Plain Layout
7567 \begin_layout Plain Layout
7575 \begin_inset Index idx
7578 \begin_layout Plain Layout
7591 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7594 \begin_layout Plain Layout
7595 \begin_inset Formula $\overbrace{A+B}^{3}$
7605 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7608 \begin_layout Plain Layout
7612 \begin_layout Plain Layout
7627 \begin_layout Plain Layout
7640 \begin_layout Plain Layout
7653 \begin_layout Plain Layout
7661 \begin_inset Index idx
7664 \begin_layout Plain Layout
7677 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7680 \begin_layout Plain Layout
7681 \begin_inset Formula $\underbrace{A+B}_{5}$
7691 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7694 \begin_layout Plain Layout
7701 \begin_layout Plain Layout
7716 \begin_layout Plain Layout
7729 \begin_layout Plain Layout
7742 \begin_layout Plain Layout
7755 \begin_layout Plain Layout
7768 \begin_layout Plain Layout
7781 \begin_layout Plain Layout
7795 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7798 \begin_layout Plain Layout
7799 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
7815 \begin_layout Standard
7816 In the last example it doesn't matter if
7828 is inserted at first.
7831 \begin_layout Standard
7832 \begin_inset VSpace bigskip
7835 When brackets are needed that overlap each other, multiline formulas, as
7837 \begin_inset CommandInset ref
7839 reference "sec:Multiline-Formulas"
7844 \begin_inset Formula \begin{eqnarray*}
7845 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
7846 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
7851 In the first row the formula is inserted together with the first brace.
7852 It is hereby important that the space command
7856 \begin_layout Plain Layout
7857 Space commands are explained in
7858 \begin_inset CommandInset ref
7860 reference "sub:Predefined-Space"
7875 is inserted before the first
7876 \begin_inset Formula $d$
7879 , because the brace that ends behind the
7880 \begin_inset Formula $q$
7883 prevents that the following
7884 \begin_inset Quotes eld
7888 \begin_inset Quotes erd
7891 is surrounded by space.
7895 \begin_layout Plain Layout
7896 because a bracket is not handled as character, see
7897 \begin_inset CommandInset ref
7899 reference "sub:Binary-Operators"
7908 In the second row the second brace is inserted.
7909 As it should begin before the
7910 \begin_inset Formula $b$
7925 \begin_layout Plain Layout
7933 \begin_inset CommandInset ref
7935 reference "sub:Placeholders"
7944 This space is needed because the
7945 \begin_inset Quotes eld
7949 \begin_inset Quotes erd
7952 is also surrounded by space in the formula.
7953 The brace is placed under the command
7962 \begin_layout Standard
7963 It gets more complicated when brackets overlap each other, like in the following
7968 \begin_layout Plain Layout
7980 \begin_inset Formula \begin{eqnarray*}
7981 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7982 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd
7991 \begin_layout Plain Layout
8002 The first formula row is the same as the second row of the previous example,
8003 with the difference that the brace is above.
8004 The second row contains the formula together with the second brace.
8005 To avoid that there is space between the upper brace in the first row and
8006 the formula, the row spacing need to be reduced.
8007 This is not easily possible due to a bug in LyX
8011 \begin_layout Plain Layout
8012 \begin_inset CommandInset href
8014 name "LyX-bug #1505"
8015 target "http://www.lyx.org/trac/ticket/1505"
8025 As solution for the problem, the global formula row separation
8032 \begin_inset Index idx
8035 \begin_layout Plain Layout
8043 must be changed to -6
8044 \begin_inset space \thinspace{}
8047 pt before the formula with the command
8062 is set back after the formula to the standard value of 3
8063 \begin_inset space \thinspace{}
8066 pt using the same command.
8067 More about the row separation in formulas is explained in
8068 \begin_inset CommandInset ref
8070 reference "sub:Line-Separation"
8077 \begin_layout Section
8079 \begin_inset Index idx
8082 \begin_layout Plain Layout
8091 \begin_layout Standard
8092 Arrows can be inserted via the math toolbar button
8093 \begin_inset Graphics
8094 filename ../images/math/leftarrow.png
8099 or the commands listed in the following subsections.
8102 \begin_layout Standard
8103 \begin_inset Newpage newpage
8109 \begin_layout Subsection
8111 \begin_inset Index idx
8114 \begin_layout Plain Layout
8123 \begin_layout Standard
8124 \begin_inset space \hfill{}
8128 \begin_inset Tabular
8129 <lyxtabular version="3" rows="8" columns="2">
8130 <features tabularvalignment="middle">
8131 <column alignment="center" valignment="top" width="0pt">
8132 <column alignment="center" valignment="top" width="0pt">
8134 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8137 \begin_layout Plain Layout
8143 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8146 \begin_layout Plain Layout
8154 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8157 \begin_layout Plain Layout
8165 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8168 \begin_layout Plain Layout
8169 \begin_inset Formula $\gets$
8179 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8182 \begin_layout Plain Layout
8190 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8193 \begin_layout Plain Layout
8194 \begin_inset Formula $\Leftarrow$
8204 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8207 \begin_layout Plain Layout
8215 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8218 \begin_layout Plain Layout
8219 \begin_inset Formula $\longleftarrow$
8229 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8232 \begin_layout Plain Layout
8240 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8243 \begin_layout Plain Layout
8244 \begin_inset Formula $\Longleftarrow$
8254 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8257 \begin_layout Plain Layout
8265 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8268 \begin_layout Plain Layout
8269 \begin_inset Formula $\leftharpoonup$
8279 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8282 \begin_layout Plain Layout
8290 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8293 \begin_layout Plain Layout
8294 \begin_inset Formula $\leftharpoondown$
8304 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8307 \begin_layout Plain Layout
8315 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8318 \begin_layout Plain Layout
8319 \begin_inset Formula $\hookleftarrow$
8333 \begin_inset space \hfill{}
8337 \begin_inset Tabular
8338 <lyxtabular version="3" rows="8" columns="2">
8339 <features tabularvalignment="middle">
8340 <column alignment="center" valignment="top" width="0pt">
8341 <column alignment="center" valignment="top" width="0pt">
8343 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8346 \begin_layout Plain Layout
8352 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8355 \begin_layout Plain Layout
8363 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8366 \begin_layout Plain Layout
8374 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8377 \begin_layout Plain Layout
8378 \begin_inset Formula $\to$
8388 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8391 \begin_layout Plain Layout
8399 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8402 \begin_layout Plain Layout
8403 \begin_inset Formula $\Rightarrow$
8413 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8416 \begin_layout Plain Layout
8424 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8427 \begin_layout Plain Layout
8428 \begin_inset Formula $\longrightarrow$
8438 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8441 \begin_layout Plain Layout
8449 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8452 \begin_layout Plain Layout
8453 \begin_inset Formula $\Longrightarrow$
8463 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8466 \begin_layout Plain Layout
8474 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8477 \begin_layout Plain Layout
8478 \begin_inset Formula $\rightharpoonup$
8488 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8491 \begin_layout Plain Layout
8499 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8502 \begin_layout Plain Layout
8503 \begin_inset Formula $\rightharpoondown$
8513 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8516 \begin_layout Plain Layout
8524 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8527 \begin_layout Plain Layout
8528 \begin_inset Formula $\hookrightarrow$
8542 \begin_inset space \hfill{}
8548 \begin_layout Standard
8549 \begin_inset space \hfill{}
8553 \begin_inset Tabular
8554 <lyxtabular version="3" rows="6" columns="2">
8555 <features tabularvalignment="middle">
8556 <column alignment="center" valignment="top" width="0pt">
8557 <column alignment="center" valignment="top" width="0pt">
8559 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8562 \begin_layout Plain Layout
8568 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8571 \begin_layout Plain Layout
8579 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8582 \begin_layout Plain Layout
8590 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8593 \begin_layout Plain Layout
8594 \begin_inset Formula $\leftrightarrow$
8604 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8607 \begin_layout Plain Layout
8615 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8618 \begin_layout Plain Layout
8619 \begin_inset Formula $\Leftrightarrow$
8629 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8632 \begin_layout Plain Layout
8640 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8643 \begin_layout Plain Layout
8644 \begin_inset Formula $\longleftrightarrow$
8654 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8657 \begin_layout Plain Layout
8665 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8668 \begin_layout Plain Layout
8669 \begin_inset Formula $\Longleftrightarrow$
8679 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8682 \begin_layout Plain Layout
8690 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8693 \begin_layout Plain Layout
8694 \begin_inset Formula $\rightleftharpoons$
8708 \begin_inset space \hspace{}
8713 \begin_inset space \hfill{}
8717 \begin_inset Tabular
8718 <lyxtabular version="3" rows="5" columns="2">
8719 <features tabularvalignment="middle">
8720 <column alignment="center" valignment="top" width="0pt">
8721 <column alignment="center" valignment="top" width="0pt">
8723 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8726 \begin_layout Plain Layout
8732 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8735 \begin_layout Plain Layout
8743 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8746 \begin_layout Plain Layout
8754 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8757 \begin_layout Plain Layout
8758 \begin_inset Formula $\mapsto$
8768 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8771 \begin_layout Plain Layout
8779 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8782 \begin_layout Plain Layout
8783 \begin_inset Formula $\longmapsto$
8793 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8796 \begin_layout Plain Layout
8804 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8807 \begin_layout Plain Layout
8808 \begin_inset Formula $\leadsto$
8818 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8821 \begin_layout Plain Layout
8829 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8832 \begin_layout Plain Layout
8833 \begin_inset Formula $\dasharrow$
8847 \begin_inset space \hfill{}
8853 \begin_layout Standard
8854 \begin_inset VSpace medskip
8857 Arrows used as accent like e.
8858 \begin_inset space \thinspace{}
8862 \begin_inset space \space{}
8865 vector arrows are listed in
8866 \begin_inset CommandInset ref
8868 reference "sec:Accents"
8875 \begin_layout Standard
8876 \begin_inset VSpace bigskip
8879 Furthermore there are the labeled arrows
8880 \begin_inset Index idx
8883 \begin_layout Plain Layout
8896 \begin_inset Index idx
8899 \begin_layout Plain Layout
8914 \begin_inset Index idx
8917 \begin_layout Plain Layout
8924 \begin_layout Plain Layout
8939 When inserting one of these commands in a formula, an arrow with two blue
8940 boxes appear where the label can be inserted.
8941 The length of the arrow adapts to the label width.
8944 \begin_layout Standard
8946 \begin_inset Tabular
8947 <lyxtabular version="3" rows="3" columns="2">
8948 <features tabularvalignment="middle">
8949 <column alignment="center" valignment="top" width="0pt">
8950 <column alignment="center" valignment="top" width="0pt">
8952 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8955 \begin_layout Plain Layout
8961 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8964 \begin_layout Plain Layout
8966 \begin_inset Note Note
8969 \begin_layout Plain Layout
8976 is only used as spacer.
8988 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8991 \begin_layout Plain Layout
8998 \begin_layout Plain Layout
9008 \begin_inset Formula $\downarrow$
9012 \begin_inset Formula $\to$
9020 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9023 \begin_layout Plain Layout
9024 \begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
9034 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9037 \begin_layout Plain Layout
9044 \begin_layout Plain Layout
9054 \begin_inset Formula $\downarrow$
9058 \begin_inset Formula $\to$
9066 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9069 \begin_layout Plain Layout
9070 \begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
9086 \begin_layout Subsection
9087 Vertical and diagonal Arrows
9088 \begin_inset Index idx
9091 \begin_layout Plain Layout
9098 \begin_inset Index idx
9101 \begin_layout Plain Layout
9110 \begin_layout Standard
9111 \begin_inset space \hfill{}
9115 \begin_inset Tabular
9116 <lyxtabular version="3" rows="7" columns="2">
9117 <features tabularvalignment="middle">
9118 <column alignment="center" valignment="top" width="0pt">
9119 <column alignment="center" valignment="top" width="0pt">
9121 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9124 \begin_layout Plain Layout
9130 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9133 \begin_layout Plain Layout
9141 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9144 \begin_layout Plain Layout
9152 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9155 \begin_layout Plain Layout
9156 \begin_inset Formula $\uparrow$
9166 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9169 \begin_layout Plain Layout
9177 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9180 \begin_layout Plain Layout
9181 \begin_inset Formula $\Uparrow$
9191 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9194 \begin_layout Plain Layout
9202 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9205 \begin_layout Plain Layout
9206 \begin_inset Formula $\updownarrow$
9216 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9219 \begin_layout Plain Layout
9227 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9230 \begin_layout Plain Layout
9231 \begin_inset Formula $\Updownarrow$
9241 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9244 \begin_layout Plain Layout
9252 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9255 \begin_layout Plain Layout
9256 \begin_inset Formula $\Downarrow$
9266 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9269 \begin_layout Plain Layout
9277 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9280 \begin_layout Plain Layout
9281 \begin_inset Formula $\downarrow$
9295 \begin_inset space \hfill{}
9299 \begin_inset Tabular
9300 <lyxtabular version="3" rows="5" columns="2">
9301 <features tabularvalignment="middle">
9302 <column alignment="center" valignment="top" width="0pt">
9303 <column alignment="center" valignment="top" width="0pt">
9305 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9308 \begin_layout Plain Layout
9314 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9317 \begin_layout Plain Layout
9325 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9328 \begin_layout Plain Layout
9336 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9339 \begin_layout Plain Layout
9340 \begin_inset Formula $\nearrow$
9350 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9353 \begin_layout Plain Layout
9361 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9364 \begin_layout Plain Layout
9365 \begin_inset Formula $\searrow$
9375 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9378 \begin_layout Plain Layout
9386 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9389 \begin_layout Plain Layout
9390 \begin_inset Formula $\swarrow$
9400 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9403 \begin_layout Plain Layout
9411 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9414 \begin_layout Plain Layout
9415 \begin_inset Formula $\nwarrow$
9429 \begin_inset space \hfill{}
9435 \begin_layout Standard
9436 \begin_inset VSpace medskip
9439 Vertical arrows can be used also as delimiter together with the commands
9441 \begin_inset CommandInset ref
9443 reference "sub:Manual-Bracket-Size"
9448 \begin_inset CommandInset ref
9450 reference "sub:Automatic-Bracket-Size"
9457 \begin_layout Standard
9458 \begin_inset Newpage newpage
9464 \begin_layout Section
9466 \begin_inset CommandInset label
9473 \begin_inset Index idx
9476 \begin_layout Plain Layout
9485 \begin_layout Standard
9486 Accents can be inserted via the math toolbar button
9487 \begin_inset Graphics
9488 filename ../images/math/hat.png
9493 or the commands listed in the following subsections.
9496 \begin_layout Subsection
9497 Accents for one Character
9501 \begin_layout Plain Layout
9514 \begin_layout Plain Layout
9516 \begin_inset CommandInset ref
9518 reference "sub:Accents-in-Text"
9531 \begin_layout Plain Layout
9539 \begin_inset Note Note
9542 \begin_layout Plain Layout
9549 is used to avoid that the footnote appears in the PDF-bookmark.
9552 \begin_layout Plain Layout
9560 \begin_inset CommandInset ref
9562 reference "sub:Formulas-in-Section"
9572 \begin_inset CommandInset label
9574 name "sub:Accents-for-one"
9579 \begin_inset Index idx
9582 \begin_layout Plain Layout
9583 Accents ! for one character
9591 \begin_layout Standard
9592 \begin_inset space \hfill{}
9596 \begin_inset Tabular
9597 <lyxtabular version="3" rows="8" columns="2">
9598 <features tabularvalignment="middle">
9599 <column alignment="center" valignment="top" width="0pt">
9600 <column alignment="center" valignment="top" width="0pt">
9602 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9605 \begin_layout Plain Layout
9611 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9614 \begin_layout Plain Layout
9616 \begin_inset Note Note
9619 \begin_layout Plain Layout
9626 is only used as spacer.
9638 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9641 \begin_layout Plain Layout
9648 \begin_layout Plain Layout
9662 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9665 \begin_layout Plain Layout
9666 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
9676 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9679 \begin_layout Plain Layout
9686 \begin_layout Plain Layout
9700 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9703 \begin_layout Plain Layout
9704 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
9714 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9717 \begin_layout Plain Layout
9724 \begin_layout Plain Layout
9738 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9741 \begin_layout Plain Layout
9742 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
9752 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9755 \begin_layout Plain Layout
9762 \begin_layout Plain Layout
9776 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9779 \begin_layout Plain Layout
9780 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
9790 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9793 \begin_layout Plain Layout
9800 \begin_layout Plain Layout
9810 \begin_inset Index idx
9813 \begin_layout Plain Layout
9824 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9827 \begin_layout Plain Layout
9828 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
9838 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9841 \begin_layout Plain Layout
9848 \begin_layout Plain Layout
9862 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9865 \begin_layout Plain Layout
9866 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
9876 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9879 \begin_layout Plain Layout
9886 \begin_layout Plain Layout
9900 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9903 \begin_layout Plain Layout
9904 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
9918 \begin_inset space \hfill{}
9922 \begin_inset Tabular
9923 <lyxtabular version="3" rows="7" columns="2">
9924 <features tabularvalignment="middle">
9925 <column alignment="center" valignment="top" width="0pt">
9926 <column alignment="center" valignment="top" width="0pt">
9928 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9931 \begin_layout Plain Layout
9937 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9940 \begin_layout Plain Layout
9948 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9951 \begin_layout Plain Layout
9958 \begin_layout Plain Layout
9972 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9975 \begin_layout Plain Layout
9976 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
9986 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9989 \begin_layout Plain Layout
9996 \begin_layout Plain Layout
10010 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10013 \begin_layout Plain Layout
10014 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
10024 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10027 \begin_layout Plain Layout
10034 \begin_layout Plain Layout
10048 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10051 \begin_layout Plain Layout
10052 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
10062 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10065 \begin_layout Plain Layout
10072 \begin_layout Plain Layout
10086 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10089 \begin_layout Plain Layout
10090 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
10100 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10103 \begin_layout Plain Layout
10110 \begin_layout Plain Layout
10124 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10127 \begin_layout Plain Layout
10128 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
10138 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10141 \begin_layout Plain Layout
10148 \begin_layout Plain Layout
10162 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10165 \begin_layout Plain Layout
10166 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
10180 \begin_inset space \hfill{}
10186 \begin_layout Standard
10187 \begin_inset VSpace bigskip
10193 \begin_layout Standard
10194 You can directly insert accents like é to formulas.
10195 LyX will transform them to the corresponding accent command.
10197 \begin_inset Index idx
10200 \begin_layout Plain Layout
10206 it is better to insert a quotation mark before the vowel.
10207 These two characters are then treated by LaTeX as
10211 character when the formula part with the umlaut is marked as German.
10219 \begin_inset Quotes eld
10223 \begin_inset Quotes erd
10226 umlauts are created as demonstrated in the following example:
10229 \begin_layout Standard
10230 \begin_inset VSpace -2mm
10236 \begin_layout Standard
10238 \begin_inset Tabular
10239 <lyxtabular version="3" rows="3" columns="2">
10240 <features tabularvalignment="middle">
10241 <column alignment="center" valignment="top" width="0">
10242 <column alignment="center" valignment="top" width="0">
10244 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10247 \begin_layout Plain Layout
10253 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10256 \begin_layout Plain Layout
10258 \begin_inset Note Note
10261 \begin_layout Plain Layout
10269 \begin_inset space \thinspace{}
10272 pt space are only used as spacer.
10284 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10287 \begin_layout Plain Layout
10290 \begin_inset Quotes grd
10298 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10301 \begin_layout Plain Layout
10302 \begin_inset space \hspace{}
10309 \begin_inset Formula $"i$
10319 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10322 \begin_layout Plain Layout
10329 \begin_layout Plain Layout
10343 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10346 \begin_layout Plain Layout
10347 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
10363 \begin_layout Standard
10364 Another advantage to
10370 is that umlauts can directly be converted to mathematical text because
10371 the accent commands above are
10377 in mathematical text
10380 To convert an accented character to mathematical text, only the character
10381 under the accent may be converted.
10382 This applies also for all other conversions, e.
10383 \begin_inset space \thinspace{}
10387 \begin_inset space \space{}
10393 \begin_layout Standard
10394 In mathematical text, umlauts and other accented characters can directly
10398 \begin_layout Subsection
10399 Accents for Operators
10400 \begin_inset Index idx
10403 \begin_layout Plain Layout
10404 Accents ! for operators
10412 \begin_layout Standard
10420 \begin_inset Index idx
10423 \begin_layout Plain Layout
10438 \begin_inset Index idx
10441 \begin_layout Plain Layout
10449 characters can be placed above or below an operator, respectively, to accent
10458 \begin_inset Index idx
10461 \begin_layout Plain Layout
10469 characters can be set before and behind an operator.
10470 The command scheme is:
10473 \begin_layout Standard
10489 \begin_layout Standard
10496 must always be before the operator that should be accented.
10497 You can accent with several characters and even with other operators and
10505 for example only characters behind an operator, write nothing between the
10506 first braces but don't omit the braces.
10509 \begin_layout Standard
10510 For example the command
10515 \begin_inset Formula $\to$
10525 \begin_inset Formula $\to$
10534 \begin_layout Plain Layout
10550 \begin_inset Formula \[
10551 \sideset{}{'}\sum_{k=1}^{n}\]
10558 \begin_layout Standard
10567 \begin_layout Plain Layout
10582 \begin_layout Plain Layout
10594 \begin_inset Formula $\uparrow$
10602 \begin_inset Formula \[
10603 \overset{a}{\maltese}\]
10607 As seen in the last example, with
10619 also symbols and characters can be accented; with
10625 this is not possible.
10628 \begin_layout Subsection
10629 Accents for several Characters
10630 \begin_inset Index idx
10633 \begin_layout Plain Layout
10634 Accents ! for several characters
10642 \begin_layout Standard
10643 \begin_inset space \hfill{}
10647 \begin_inset Tabular
10648 <lyxtabular version="3" rows="5" columns="2">
10649 <features tabularvalignment="middle">
10650 <column alignment="center" valignment="top" width="0pt">
10651 <column alignment="center" valignment="top" width="0pt">
10653 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10656 \begin_layout Plain Layout
10662 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10665 \begin_layout Plain Layout
10667 \begin_inset Note Note
10670 \begin_layout Plain Layout
10677 is only used as spacer.
10689 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10692 \begin_layout Plain Layout
10699 \begin_layout Plain Layout
10713 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10716 \begin_layout Plain Layout
10717 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
10727 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10730 \begin_layout Plain Layout
10737 \begin_layout Plain Layout
10751 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10754 \begin_layout Plain Layout
10755 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
10765 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10768 \begin_layout Plain Layout
10775 \begin_layout Plain Layout
10789 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10792 \begin_layout Plain Layout
10793 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
10803 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10806 \begin_layout Plain Layout
10809 underleftrightarrow
10813 \begin_layout Plain Layout
10827 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10830 \begin_layout Plain Layout
10831 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
10845 \begin_inset space \hfill{}
10849 \begin_inset Tabular
10850 <lyxtabular version="3" rows="5" columns="2">
10851 <features tabularvalignment="middle">
10852 <column alignment="center" valignment="top" width="0pt">
10853 <column alignment="center" valignment="top" width="0pt">
10855 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10858 \begin_layout Plain Layout
10864 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10867 \begin_layout Plain Layout
10875 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10878 \begin_layout Plain Layout
10885 \begin_layout Plain Layout
10899 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10902 \begin_layout Plain Layout
10903 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
10913 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10916 \begin_layout Plain Layout
10923 \begin_layout Plain Layout
10937 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10940 \begin_layout Plain Layout
10941 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
10951 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10954 \begin_layout Plain Layout
10961 \begin_layout Plain Layout
10975 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10978 \begin_layout Plain Layout
10979 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
10989 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10992 \begin_layout Plain Layout
10999 \begin_layout Plain Layout
11013 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11016 \begin_layout Plain Layout
11017 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
11031 \begin_inset space \hfill{}
11037 \begin_layout Standard
11038 \begin_inset VSpace medskip
11041 With these commands as many characters as you like can be accented.
11054 will only be set in the output with a length of three characters, as shown
11055 in the following example:
11056 \begin_inset Formula \[
11057 \widetilde{A+B=C-D}\]
11064 \begin_layout Standard
11072 \begin_inset Index idx
11075 \begin_layout Plain Layout
11090 \begin_inset Index idx
11093 \begin_layout Plain Layout
11101 described in the previous subsection it is also possible to accent several
11111 \begin_layout Plain Layout
11121 \begin_inset Formula $\downarrow$
11127 \begin_inset Formula \[
11128 \underset{***}{A=B}\]
11135 \begin_layout Section
11137 \begin_inset CommandInset label
11144 \begin_inset Index idx
11147 \begin_layout Plain Layout
11156 \begin_layout Subsection
11158 \begin_inset CommandInset label
11160 name "sub:Predefined-Space"
11165 \begin_inset Index idx
11168 \begin_layout Plain Layout
11169 Space ! horizontal ! predefined
11177 \begin_layout Standard
11178 Sometimes it is necessary to insert horizontal space to a formula.
11179 This is done by inserting a protected space (shortcut
11182 arg "space-insert protected"
11187 \begin_inset Quotes eld
11196 \begin_layout Plain Layout
11208 \begin_inset Quotes erd
11211 appears and by pressing
11215 several times one can select one of eight different space sizes.
11216 The spaces can also be inserted using the math toolbar button
11217 \begin_inset Graphics
11218 filename ../images/math/space.png
11223 or special commands.
11224 Independent from the inserted command, one can select the size again by
11232 \begin_layout Standard
11235 \begin_inset VSpace -5mm
11239 \begin_inset Tabular
11240 <lyxtabular version="3" rows="3" columns="7">
11241 <features tabularvalignment="middle">
11242 <column alignment="center" valignment="middle" width="6.8cm">
11243 <column alignment="center" valignment="top" width="0">
11244 <column alignment="center" valignment="top" width="0">
11245 <column alignment="center" valignment="top" width="0">
11246 <column alignment="center" valignment="top" width="0">
11247 <column alignment="center" valignment="top" width="0">
11248 <column alignment="center" valignment="top" width="0">
11250 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11253 \begin_layout Plain Layout
11259 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11262 \begin_layout Plain Layout
11270 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11273 \begin_layout Plain Layout
11281 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11284 \begin_layout Plain Layout
11292 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11295 \begin_layout Plain Layout
11303 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11306 \begin_layout Plain Layout
11314 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11317 \begin_layout Plain Layout
11327 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11330 \begin_layout Plain Layout
11335 keystrokes after inserting the protected space
11340 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11343 \begin_layout Plain Layout
11349 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11352 \begin_layout Plain Layout
11358 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11361 \begin_layout Plain Layout
11367 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11370 \begin_layout Plain Layout
11376 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11379 \begin_layout Plain Layout
11385 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11388 \begin_layout Plain Layout
11396 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11399 \begin_layout Plain Layout
11405 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11408 \begin_layout Plain Layout
11409 \begin_inset Formula $A\, B$
11417 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11420 \begin_layout Plain Layout
11421 \begin_inset Formula $A\: B$
11429 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11432 \begin_layout Plain Layout
11433 \begin_inset Formula $A\; B$
11441 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11444 \begin_layout Plain Layout
11445 \begin_inset Formula $A\quad B$
11453 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11456 \begin_layout Plain Layout
11457 \begin_inset Formula $A\qquad B$
11465 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11468 \begin_layout Plain Layout
11469 \begin_inset Formula $A\! B$
11485 \begin_layout Standard
11486 The last size seem to produce no space.
11487 It is displayed red in LyX contrary to the other sizes, because it is a
11489 There are two more negative spaces:
11492 \begin_layout Standard
11494 \begin_inset Tabular
11495 <lyxtabular version="3" rows="3" columns="3">
11496 <features tabularvalignment="middle">
11497 <column alignment="center" valignment="middle" width="6.8cm">
11498 <column alignment="center" valignment="top" width="0pt">
11499 <column alignment="center" valignment="top" width="0pt">
11501 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11504 \begin_layout Plain Layout
11510 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11513 \begin_layout Plain Layout
11521 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11524 \begin_layout Plain Layout
11534 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11537 \begin_layout Plain Layout
11542 keystrokes after inserting the protected space
11547 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11550 \begin_layout Plain Layout
11556 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11559 \begin_layout Plain Layout
11567 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11570 \begin_layout Plain Layout
11576 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11579 \begin_layout Plain Layout
11580 \begin_inset Formula $A\negmedspace B$
11588 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11591 \begin_layout Plain Layout
11592 \begin_inset Formula $A\negthickspace B$
11608 \begin_layout Standard
11609 Negative spaces can lead to characters overlapping each other.
11610 Thus they can be used to enforce ligatures, what is e.
11611 \begin_inset space \thinspace{}
11615 \begin_inset space \space{}
11618 useful for summation operators:
11621 \begin_layout Standard
11623 \begin_inset Tabular
11624 <lyxtabular version="3" rows="3" columns="2">
11625 <features tabularvalignment="middle">
11626 <column alignment="center" valignment="top" width="0">
11627 <column alignment="center" valignment="top" width="0">
11629 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11632 \begin_layout Plain Layout
11638 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11641 \begin_layout Plain Layout
11643 \begin_inset Note Note
11646 \begin_layout Plain Layout
11653 is only used as spacer.
11665 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11668 \begin_layout Plain Layout
11677 \begin_layout Plain Layout
11691 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11694 \begin_layout Plain Layout
11695 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
11705 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11708 \begin_layout Plain Layout
11719 \begin_layout Plain Layout
11733 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11736 \begin_layout Plain Layout
11737 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
11753 \begin_layout Standard
11754 Relations like for example equal signs, are always surrounded by space.
11755 To suppress this, the equal sign is placed into a TeX-brace.
11756 The following example demonstrates this:
11759 \begin_layout Standard
11761 \begin_inset Tabular
11762 <lyxtabular version="3" rows="2" columns="2">
11763 <features tabularvalignment="middle">
11764 <column alignment="center" valignment="top" width="0pt">
11765 <column alignment="center" valignment="top" width="0pt">
11767 <cell alignment="center" valignment="top" usebox="none">
11770 \begin_layout Plain Layout
11776 <cell alignment="center" valignment="top" usebox="none">
11779 \begin_layout Plain Layout
11780 \begin_inset Formula $A=B$
11790 <cell alignment="center" valignment="top" usebox="none">
11793 \begin_layout Plain Layout
11794 \begin_inset Note Note
11797 \begin_layout Plain Layout
11804 is only used as spacer.
11810 \begin_inset Formula $\raisebox{5mm}{}$
11813 equation without space
11818 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11821 \begin_layout Plain Layout
11822 \begin_inset Formula $A{=}B$
11838 \begin_layout Standard
11840 The command for the last formula is:
11845 \begin_inset Formula $\to$
11851 \begin_layout Standard
11852 \begin_inset VSpace bigskip
11855 Spaces are needed for physical units, because the space between the value
11856 and the unit is the smallest one and not a normal space.
11857 For units in text, the smallest space is inserted via the menu
11859 Insert\SpecialChar \menuseparator
11860 Formatting\SpecialChar \menuseparator
11862 \begin_inset space ~
11870 arg "space-insert thin"
11876 \begin_layout Standard
11877 An example to visualize the difference:
11880 \begin_layout Standard
11881 \begin_inset Tabular
11882 <lyxtabular version="3" rows="2" columns="2">
11883 <features tabularvalignment="middle">
11884 <column alignment="left" valignment="top" width="0">
11885 <column alignment="left" valignment="top" width="0">
11887 <cell alignment="center" valignment="top" usebox="none">
11890 \begin_layout Plain Layout
11892 \begin_inset Formula $\cdot$
11900 <cell alignment="center" valignment="top" usebox="none">
11903 \begin_layout Plain Layout
11904 space between value and unit
11911 <cell alignment="center" valignment="top" usebox="none">
11914 \begin_layout Plain Layout
11916 \begin_inset space \thinspace{}
11920 \begin_inset Formula $\cdot$
11928 <cell alignment="center" valignment="top" usebox="none">
11931 \begin_layout Plain Layout
11932 smallest space between value and unit
11945 \begin_layout Subsection
11950 \begin_layout Plain Layout
11963 \begin_layout Plain Layout
11964 for vertical space in formulas see
11965 \begin_inset CommandInset ref
11967 reference "sub:Line-Separation"
11980 \begin_layout Plain Layout
11988 \begin_inset Note Note
11991 \begin_layout Plain Layout
11994 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
11997 \begin_layout Plain Layout
12000 texorpdfstring is in section
12001 \begin_inset CommandInset ref
12003 reference "sub:Formulas-in-Section"
12013 \begin_inset CommandInset label
12015 name "sub:Variable-Space"
12020 \begin_inset Index idx
12023 \begin_layout Plain Layout
12024 Space ! horizontal ! variable
12032 \begin_layout Standard
12033 Space with a defined length can be inserted with the command
12040 \begin_inset Index idx
12043 \begin_layout Plain Layout
12053 \begin_inset Quotes eld
12062 \begin_layout Plain Layout
12074 \begin_inset Quotes erd
12078 The length can be specified by left-clicking on the
12079 \begin_inset Quotes eld
12088 \begin_layout Plain Layout
12100 \begin_inset Quotes erd
12104 The length may also be negative.
12105 To insert so many space that the formula uses all available space, the
12113 \begin_inset Index idx
12116 \begin_layout Plain Layout
12127 \begin_layout Standard
12128 \begin_inset VSpace -1mm
12134 \begin_layout Standard
12136 \begin_inset Tabular
12137 <lyxtabular version="3" rows="4" columns="2">
12138 <features tabularvalignment="middle">
12139 <column alignment="center" valignment="top" width="0">
12140 <column alignment="center" valignment="top" width="0">
12142 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12145 \begin_layout Plain Layout
12153 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12156 \begin_layout Plain Layout
12164 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12167 \begin_layout Plain Layout
12174 \begin_layout Plain Layout
12184 \begin_inset Formula $\to$
12190 \begin_inset space \thinspace{}
12198 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12201 \begin_layout Plain Layout
12202 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
12212 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12215 \begin_layout Plain Layout
12222 \begin_layout Plain Layout
12232 \begin_inset Formula $\to$
12238 \begin_inset space \thinspace{}
12246 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12249 \begin_layout Plain Layout
12250 \begin_inset Formula $A\hspace{-1mm}A\not=A$
12260 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12263 \begin_layout Plain Layout
12270 \begin_layout Plain Layout
12284 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12287 \begin_layout Plain Layout
12288 \begin_inset Formula $A=A\hfill B=B$
12304 \begin_layout Standard
12305 In the last example the available space is given by the longest column entry
12307 In an inline formula the space depends on the length of the line in which
12315 Thus, when the line uses the full width, no space will be created.
12322 only has an effect on displayed formulas when the formula style
12327 (Formula styles are explained in
12328 \begin_inset CommandInset ref
12330 reference "sec:Formula-Styles"
12337 \begin_layout Standard
12344 , there are the commands
12356 that fill the space with a pattern, see
12357 \begin_inset CommandInset ref
12359 reference "sub:Ellipses"
12366 \begin_layout Standard
12367 For text, variable space can be inserted via the menu
12369 Insert\SpecialChar \menuseparator
12370 Formatting\SpecialChar \menuseparator
12372 \begin_inset space ~
12380 \begin_layout Standard
12381 This is a line with
12382 \begin_inset space \hspace{}
12387 \begin_inset space \thinspace{}
12393 \begin_layout Standard
12394 This is a line with
12395 \begin_inset space \hfill{}
12401 \begin_layout Subsection
12402 Space besides inline Formulas
12403 \begin_inset Index idx
12406 \begin_layout Plain Layout
12407 Space ! besides inline formulas
12415 \begin_layout Standard
12416 The space that surrounds inline formulas can be adjusted with the length
12424 \begin_inset Index idx
12427 \begin_layout Plain Layout
12436 The value of a length is set with the command
12443 \begin_inset Index idx
12446 \begin_layout Plain Layout
12454 that has the following scheme:
12457 \begin_layout Standard
12462 setlength{length name}{value}
12465 \begin_layout Standard
12473 \begin_inset space \thinspace{}
12479 \begin_layout Standard
12489 \begin_layout Standard
12490 is inserted in TeX-mode.
12492 \begin_inset space \thinspace{}
12495 mm space will now be set around all inline formulas:
12499 \begin_layout Plain Layout
12513 \begin_layout Standard
12514 This is a line with an inline formula
12515 \begin_inset Formula $A=B$
12519 \begin_inset space \thinspace{}
12522 mm surrounding space.
12526 \begin_layout Plain Layout
12540 \begin_layout Standard
12541 To return to the predefined value,
12547 is set to the value 0
12548 \begin_inset space \thinspace{}
12554 \begin_layout Section
12556 \begin_inset Index idx
12559 \begin_layout Plain Layout
12566 \begin_inset Index idx
12569 \begin_layout Plain Layout
12574 \begin_layout Plain Layout
12585 \begin_layout Plain Layout
12600 \begin_layout Standard
12601 Boxes for text are described in chapter
12608 \begin_inset space ~
12616 \begin_layout Subsection
12618 \begin_inset CommandInset label
12620 name "sub:Boxes-with-Frame"
12625 \begin_inset Index idx
12628 \begin_layout Plain Layout
12637 \begin_layout Standard
12638 It is possible to frame formulas or parts of it with the commands
12645 \begin_inset Index idx
12648 \begin_layout Plain Layout
12663 \begin_inset Index idx
12666 \begin_layout Plain Layout
12677 \begin_layout Standard
12678 When one of these commands is inserted to a formula, a blue box appears
12679 within a frame to enter formula parts.
12686 an additional formula has to be created by
12690 within this box, because the box content will otherwise be treated as mathemati
12698 is used, a new formula is automatically created inside the frame.
12701 \begin_layout Standard
12708 is not suitable to frame displayed formulas because the formula will always
12709 be set in the size of the text.
12716 is in contrary not suitable to frame inline formulas, because the formula
12717 will always be set in the size of a displayed formula.
12720 \begin_layout Standard
12727 there is the command
12734 \begin_inset Index idx
12737 \begin_layout Plain Layout
12745 where additionally the frame width and the alignment can be specified.
12752 is used in the following scheme:
12755 \begin_layout Standard
12760 framebox[frame width][position]{box content}
12763 \begin_layout Standard
12764 The position can either be
12781 right aligns the formula in the box.
12782 When no position is given, the formula will be centered.
12783 \begin_inset Newline newline
12786 Is no width given, also no position can be given.
12787 In this case the frame width is adjusted to the box content like for
12796 \begin_layout Standard
12803 is inserted, a box appears containing three blue boxes.
12804 The first two boxes are surrounded by brackets and denote the two optional
12806 The third box is for formula parts like for
12815 \begin_layout Standard
12817 \begin_inset Tabular
12818 <lyxtabular version="3" rows="5" columns="2">
12819 <features tabularvalignment="middle">
12820 <column alignment="center" valignment="top" width="0">
12821 <column alignment="center" valignment="top" width="0">
12823 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12826 \begin_layout Plain Layout
12832 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12835 \begin_layout Plain Layout
12837 \begin_inset Note Note
12840 \begin_layout Plain Layout
12847 is only used as spacer.
12859 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12862 \begin_layout Plain Layout
12869 \begin_layout Plain Layout
12888 \begin_layout Plain Layout
12902 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12905 \begin_layout Plain Layout
12906 \begin_inset Formula $\raisebox{6mm}{}\fbox{\ensuremath{\int A=B}}\raisebox{-4mm}{}$
12916 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12919 \begin_layout Plain Layout
12926 \begin_layout Plain Layout
12941 \begin_layout Plain Layout
12955 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12958 \begin_layout Plain Layout
12959 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
12969 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12972 \begin_layout Plain Layout
12979 \begin_layout Plain Layout
12993 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12996 \begin_layout Plain Layout
12997 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
13007 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13010 \begin_layout Plain Layout
13017 \begin_layout Plain Layout
13027 \begin_inset Formula $\to$
13031 \begin_inset Formula $\to$
13044 \begin_layout Plain Layout
13054 \begin_inset Formula $\downarrow$
13062 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13065 \begin_layout Plain Layout
13066 \begin_inset Formula $\raisebox{6mm}{}$
13070 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
13074 \begin_inset Formula $\raisebox{-4mm}{}$
13090 \begin_layout Standard
13091 The frame thickness can also be adjusted.
13092 To do this the following commands have to be inserted in TeX-mode before
13096 \begin_layout Standard
13106 \begin_inset Quotes eld
13110 \begin_inset Quotes erd
13124 \begin_inset Quotes eld
13128 \begin_inset Quotes erd
13134 \begin_layout Standard
13135 \begin_inset Quotes eld
13139 \begin_inset Quotes erd
13142 specifies the minimal distance between the frame and the first character
13144 An example for this is the following framed formula:
13148 \begin_layout Plain Layout
13160 \begin_inset Formula \[
13165 Before this formula the commands
13168 \begin_layout Standard
13190 \begin_layout Standard
13191 were inserted in TeX-mode.
13192 The given values are used for all following boxes.
13195 \begin_layout Standard
13196 To return to the standard frame size, the command
13199 \begin_layout Standard
13224 \begin_layout Plain Layout
13238 \begin_layout Standard
13239 is inserted in TeX-mode before the next formula.
13242 \begin_layout Subsection
13243 Boxes without Frame
13244 \begin_inset CommandInset label
13246 name "sub:Boxes-without-Frame"
13251 \begin_inset Index idx
13254 \begin_layout Plain Layout
13255 Boxes ! without frame
13263 \begin_layout Standard
13264 For boxes without a frame there are the following box commands:
13271 \begin_inset Index idx
13274 \begin_layout Plain Layout
13289 \begin_inset Index idx
13292 \begin_layout Plain Layout
13307 \begin_inset Index idx
13310 \begin_layout Plain Layout
13321 \begin_layout Standard
13328 a box can be super- or subscripted.
13329 But in contrary to normal super- and subscripting, the characters in the
13330 box keep their font size.
13337 is used in the following scheme:
13340 \begin_layout Standard
13345 raisebox{height}{box content}
13348 \begin_layout Standard
13349 When the box should contain a formula, an extra formula is needed like for
13360 \begin_inset Note Greyedout
13363 \begin_layout Plain Layout
13374 this extra formula is created by pressing
13378 twice instead of once because LyX doesn't yet support
13392 \begin_layout Standard
13394 \begin_inset Tabular
13395 <lyxtabular version="3" rows="4" columns="2">
13396 <features tabularvalignment="middle">
13397 <column alignment="center" valignment="top" width="0">
13398 <column alignment="center" valignment="top" width="0">
13400 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13403 \begin_layout Plain Layout
13409 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13412 \begin_layout Plain Layout
13420 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13423 \begin_layout Plain Layout
13427 \begin_inset Formula $\to$
13433 \begin_inset Formula $\to$
13441 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13444 \begin_layout Plain Layout
13445 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13455 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13458 \begin_layout Plain Layout
13462 \begin_inset Formula $\to$
13468 \begin_inset Formula $\to$
13476 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13479 \begin_layout Plain Layout
13480 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13490 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13493 \begin_layout Plain Layout
13497 \begin_inset Formula $\to$
13516 \begin_layout Plain Layout
13530 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13533 \begin_layout Plain Layout
13534 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
13550 \begin_layout Standard
13575 , with the difference that there is no frame.
13578 \begin_layout Subsection
13580 \begin_inset CommandInset label
13582 name "sub:Colored-Boxes"
13587 \begin_inset Index idx
13590 \begin_layout Plain Layout
13599 \begin_layout Standard
13600 To be able to use all commands explained in this section, the LaTeX-package
13609 \begin_layout Plain Layout
13614 is part of every LaTeX standard installation.
13620 \begin_inset Index idx
13623 \begin_layout Plain Layout
13629 has to be loaded in the LaTeX-preamble with the line
13633 \begin_layout Plain Layout
13634 When text is colored somewhere in the document with a predefined color,
13635 LyX loads the LaTeX-package
13640 Thus it is possible that the package is loaded twice, but this doesn't
13647 \begin_inset Note Note
13650 \begin_layout Plain Layout
13651 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
13660 \begin_layout Standard
13668 \begin_layout Standard
13669 \begin_inset VSpace medskip
13672 To color boxes, the command
13679 \begin_inset Index idx
13682 \begin_layout Plain Layout
13690 is used in the following scheme:
13693 \begin_layout Standard
13698 colorbox{color}{box content}
13701 \begin_layout Standard
13702 The box content can also be a box and a
13708 can also be part of another box (see the 2nd and 3rd example).
13709 When the box should contain a formula, an extra formula has to be created,
13710 the same way as for
13720 \begin_layout Plain Layout
13721 This also applies for the command
13735 \begin_layout Standard
13736 One of the following predefined colors can be chosen:
13739 \begin_layout Standard
13773 \begin_layout Standard
13775 \begin_inset Tabular
13776 <lyxtabular version="3" rows="4" columns="2">
13777 <features tabularvalignment="middle">
13778 <column alignment="center" valignment="top" width="0">
13779 <column alignment="center" valignment="top" width="0">
13781 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13784 \begin_layout Plain Layout
13790 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13793 \begin_layout Plain Layout
13795 \begin_inset Note Note
13798 \begin_layout Plain Layout
13805 is only used as spacer.
13817 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13820 \begin_layout Plain Layout
13824 \begin_inset Formula $\to$
13834 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13837 \begin_layout Plain Layout
13838 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
13848 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13851 \begin_layout Plain Layout
13855 \begin_inset Formula $\to$
13866 \begin_layout Plain Layout
13880 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13883 \begin_layout Plain Layout
13884 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
13894 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13897 \begin_layout Plain Layout
13904 \begin_layout Plain Layout
13916 \begin_inset Formula $\to$
13935 \begin_layout Plain Layout
13949 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13952 \begin_layout Plain Layout
13953 \begin_inset Formula $\raisebox{7mm}{}\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}\raisebox{-5mm}{}$
13969 \begin_layout Standard
13976 only colors the box but not the characters in the box.
13977 To color all characters, the whole formula is highlighted and the wanted
13978 color is chosen in the
13981 \begin_inset space ~
13987 The dialog can be called with the toolbar button
13988 \begin_inset Graphics
13989 filename ../images/dialog-show_character.png
13996 Edit\SpecialChar \menuseparator
13998 \begin_inset space ~
14001 Style\SpecialChar \menuseparator
14005 The formula number has then the same color as the formula.
14006 When the formula number should get another color than the formula characters,
14007 the color must be changed within the formula.
14010 \begin_layout Standard
14014 \begin_layout Standard
14017 \begin_inset Formula \begin{equation}
14018 \int A=B\label{eq:red}\end{equation}
14025 \begin_inset Formula \begin{equation}
14026 \textcolor{red}{\int A=B}\label{eq:redgreen}\end{equation}
14033 \begin_layout Standard
14035 \begin_inset CommandInset ref
14041 is completely colored red.
14042 \begin_inset Newline newline
14046 \begin_inset CommandInset ref
14048 reference "eq:redgreen"
14052 was first completely colored green to set the color for the formula number.
14053 Subsequently the formula characters were colored red.
14056 \begin_layout Standard
14057 \begin_inset VSpace bigskip
14060 To color the frame different than the rest of the box, the command
14067 \begin_inset Index idx
14070 \begin_layout Plain Layout
14078 is used in the following scheme:
14081 \begin_layout Standard
14086 fcolorbox{frame color}{color}{box content}
14089 \begin_layout Standard
14096 is an extension of the command
14103 The frame width is set, like for
14126 \begin_layout Plain Layout
14138 \begin_inset Formula \[
14139 \fcolorbox{cyan}{magenta}{A=B}\]
14147 \begin_layout Plain Layout
14161 \begin_layout Standard
14162 This formula was created with the command
14163 \begin_inset Newline newline
14171 \begin_inset Formula $\to$
14177 \begin_inset Formula $\to$
14187 \begin_layout Standard
14188 \begin_inset VSpace bigskip
14191 To use other colors than the predefined ones, they have to be defined first.
14194 \begin_layout Standard
14195 One can for example define the color
14196 \begin_inset Quotes eld
14204 \begin_inset Quotes erd
14207 with the LaTeX-preamble line:
14210 \begin_layout Standard
14215 definecolor{darkgreen}{cmyk}{0.5,
14230 \begin_inset Index idx
14233 \begin_layout Plain Layout
14244 \begin_layout Standard
14249 is the color space that denotes the colors
14266 The four comma separated numbers are the portion factor for the corresponding
14267 colors of the color space.
14268 The factors can be in the range of 0
14269 \begin_inset space \thinspace{}
14273 \begin_inset space \thinspace{}
14281 also the color space
14285 can be used for definitions.
14302 , so that there are in this case three portion factors for the corresponding
14304 Furthermore there is the color space
14308 with one portion factor for the gray value.
14311 \begin_layout Standard
14312 As example a framed box with the new defined color
14316 where the characters have been colored
14321 \begin_inset Formula \begin{equation}
14322 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}\end{equation}
14329 \begin_layout Standard
14330 Self-defined colors can also be used for text with the help of the command
14338 \begin_inset Index idx
14341 \begin_layout Plain Layout
14350 \begin_layout Standard
14354 \begin_layout Plain Layout
14358 textcolor{darkgreen}{
14364 \begin_inset Quotes eld
14368 \begin_inset Quotes erd
14375 \begin_layout Plain Layout
14385 \begin_layout Standard
14393 \begin_inset Index idx
14396 \begin_layout Plain Layout
14404 is used in the scheme
14408 textcolor{color}{characters to color}
14413 \begin_layout Subsection
14415 \begin_inset CommandInset label
14417 name "sub:Paragraph-Boxes"
14422 \begin_inset Index idx
14425 \begin_layout Plain Layout
14426 Boxes ! as paragraph
14434 \begin_layout Standard
14435 A box that can contain several lines and paragraphs, a so called paragraph
14436 box (parbox), can be created with the menu
14438 Insert\SpecialChar \menuseparator
14441 or the toolbar button
14442 \begin_inset Graphics
14443 filename ../images/box-insert.png
14451 \begin_layout Standard
14452 The following example shows a framed parbox in a line:
14455 \begin_layout Standard
14456 \begin_inset VSpace medskip
14460 \begin_inset Box Boxed
14470 height_special "totalheight"
14473 \begin_layout Plain Layout
14474 This is a paragraph box.
14476 \begin_inset space \thinspace{}
14479 cm long and can also contain formulas:
14480 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14491 \begin_layout Standard
14492 \begin_inset VSpace medskip
14498 \begin_layout Standard
14499 Such a box is created by right-clicking on the gray box inset.
14500 A dialog pops up showing the box properties.
14514 \begin_inset space \thinspace{}
14519 Vertical Box Alignment
14524 \begin_layout Standard
14525 \begin_inset VSpace medskip
14528 In LaTeX a parbox is created with the command
14535 \begin_inset Index idx
14538 \begin_layout Plain Layout
14546 that has the following scheme:
14549 \begin_layout Standard
14554 parbox[position]{width}{box content}
14557 \begin_layout Standard
14571 for bottom means that the box is aligned within the surrounding text with
14577 for top this is done with the first line.
14578 When no position is given, the box will be vertically centered, see section
14586 \begin_inset space ~
14591 manual for examples.
14594 \begin_layout Standard
14595 \begin_inset VSpace bigskip
14598 To frame formulas completely, including the formula number, the formula
14599 must be set into a parbox.
14600 To do this, the command
14614 is inserted in TeX-mode before the formula.
14622 \begin_inset Index idx
14625 \begin_layout Plain Layout
14633 is hereby the line width set for the document.
14634 Because the frame is outside the parbox, 2
14635 \begin_inset space \thinspace{}
14638 times the frame separation and the frame thickness must be subtracted from
14640 As this is not automatically done by LyX due to a bug
14644 \begin_layout Plain Layout
14645 \begin_inset CommandInset href
14647 name "LyX-bug #4483"
14648 target "http://www.lyx.org/trac/ticket/4483"
14657 , TeX-mode has to be used.
14658 To be able to multiply and subtract in arguments, the LaTeX-package
14666 \begin_layout Plain Layout
14671 is part of every LaTeX standard installation.
14677 \begin_inset Index idx
14680 \begin_layout Plain Layout
14686 must be loaded in the LaTeX-preamble with the line
14689 \begin_layout Standard
14697 \begin_layout Standard
14698 Behind the formula both boxes are closed by entering
14703 Here is an example:
14707 \begin_layout Plain Layout
14721 \begin_layout Standard
14725 \begin_layout Plain Layout
14743 \begin_inset Formula \begin{equation}
14744 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}\end{equation}
14752 \begin_layout Plain Layout
14763 \begin_layout Plain Layout
14777 \begin_layout Standard
14778 \begin_inset VSpace medskip
14781 As a parbox is used as argument of
14787 , there is in this case no difference between
14802 \begin_layout Standard
14803 \begin_inset VSpace bigskip
14806 Paragraph boxes are very useful to comment formulas directly.
14813 is used in combination with the command
14827 \begin_inset CommandInset ref
14829 reference "sub:User-defined-Numbering"
14836 \begin_layout Standard
14837 An example of a formula commented with
14846 \begin_layout Standard
14850 \begin_layout Plain Layout
14863 This is a description.
14864 It is distinctly separated from the formula and multiline.
14868 \begin_layout Plain Layout
14880 \begin_layout Standard
14881 Such a formula must be inserted completely in TeX-mode because LyX does
14882 not yet support the command
14889 The formula is created with the following command sequence:
14892 \begin_layout Standard
14905 is inserted in TeX-mode.
14909 \begin_layout Plain Layout
14910 When the formula style
14922 can also be replaced by
14929 (formula styles see
14930 \begin_inset CommandInset ref
14932 reference "sec:Formula-Styles"
14941 Then the description follows as normal text and finally
14947 is inserted in TeX-mode.
14960 hereby create a displayed formula.
14963 \begin_layout Standard
14970 can be seen in this example that was
14971 \begin_inset Quotes eld
14975 \begin_inset Quotes erd
14978 using the mathematical textmode:
14979 \begin_inset Formula \[
14980 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}\]
14987 \begin_layout Section
14989 \begin_inset Index idx
14992 \begin_layout Plain Layout
15001 \begin_layout Subsection
15003 \begin_inset CommandInset label
15005 name "sub:Big-Operators"
15010 \begin_inset Index idx
15013 \begin_layout Plain Layout
15020 \begin_inset Index idx
15023 \begin_layout Plain Layout
15030 \begin_inset Index idx
15033 \begin_layout Plain Layout
15042 \begin_layout Standard
15043 To be able to use all integral operators listed here, the option
15045 Use esint package automatically
15047 must be set in the document settings under
15050 \begin_inset space ~
15058 \begin_layout Standard
15059 \begin_inset space \hfill{}
15063 \begin_inset Tabular
15064 <lyxtabular version="3" rows="11" columns="2">
15065 <features tabularvalignment="middle">
15066 <column alignment="center" valignment="top" width="0pt">
15067 <column alignment="center" valignment="top" width="0pt">
15069 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15072 \begin_layout Plain Layout
15078 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15081 \begin_layout Plain Layout
15089 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15092 \begin_layout Plain Layout
15096 \begin_inset Index idx
15099 \begin_layout Plain Layout
15112 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15115 \begin_layout Plain Layout
15116 \begin_inset Formula $\int$
15126 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15129 \begin_layout Plain Layout
15137 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15140 \begin_layout Plain Layout
15141 \begin_inset Formula $\oint$
15151 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15154 \begin_layout Plain Layout
15162 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15165 \begin_layout Plain Layout
15166 \begin_inset Formula $\ointctrclockwise$
15176 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15179 \begin_layout Plain Layout
15187 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15190 \begin_layout Plain Layout
15191 \begin_inset Formula $\ointclockwise$
15201 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15204 \begin_layout Plain Layout
15212 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15215 \begin_layout Plain Layout
15216 \begin_inset Formula $\sqint$
15226 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15229 \begin_layout Plain Layout
15237 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15240 \begin_layout Plain Layout
15242 \begin_inset Formula $\fint$
15252 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15255 \begin_layout Plain Layout
15263 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15266 \begin_layout Plain Layout
15268 \begin_inset Formula $\landupint$
15278 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15281 \begin_layout Plain Layout
15289 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15292 \begin_layout Plain Layout
15294 \begin_inset Formula $\landdownint$
15304 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15307 \begin_layout Plain Layout
15315 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15318 \begin_layout Plain Layout
15319 \begin_inset Formula $\bigcap$
15329 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15332 \begin_layout Plain Layout
15340 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15343 \begin_layout Plain Layout
15344 \begin_inset Formula $\bigcup$
15358 \begin_inset space \hfill{}
15362 \begin_inset Tabular
15363 <lyxtabular version="3" rows="11" columns="2">
15364 <features tabularvalignment="middle">
15365 <column alignment="center" valignment="top" width="0pt">
15366 <column alignment="center" valignment="top" width="0pt">
15368 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15371 \begin_layout Plain Layout
15377 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15380 \begin_layout Plain Layout
15388 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15391 \begin_layout Plain Layout
15395 \begin_inset Index idx
15398 \begin_layout Plain Layout
15411 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15414 \begin_layout Plain Layout
15415 \begin_inset Formula $\sum$
15425 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15428 \begin_layout Plain Layout
15432 \begin_inset Index idx
15435 \begin_layout Plain Layout
15448 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15451 \begin_layout Plain Layout
15452 \begin_inset Formula $\prod$
15462 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15465 \begin_layout Plain Layout
15473 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15476 \begin_layout Plain Layout
15477 \begin_inset Formula $\coprod$
15487 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15490 \begin_layout Plain Layout
15498 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15501 \begin_layout Plain Layout
15502 \begin_inset Formula $\bigodot$
15512 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15515 \begin_layout Plain Layout
15523 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15526 \begin_layout Plain Layout
15527 \begin_inset Formula $\bigotimes$
15537 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15540 \begin_layout Plain Layout
15548 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15551 \begin_layout Plain Layout
15552 \begin_inset Formula $\bigoplus$
15562 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15565 \begin_layout Plain Layout
15573 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15576 \begin_layout Plain Layout
15577 \begin_inset Formula $\bigwedge$
15587 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15590 \begin_layout Plain Layout
15598 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15601 \begin_layout Plain Layout
15602 \begin_inset Formula $\bigvee$
15612 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15615 \begin_layout Plain Layout
15623 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15626 \begin_layout Plain Layout
15627 \begin_inset Formula $\bigsqcup$
15637 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15640 \begin_layout Plain Layout
15648 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15651 \begin_layout Plain Layout
15652 \begin_inset Formula $\biguplus$
15666 \begin_inset space \hfill{}
15672 \begin_layout Standard
15673 All big operators can also be inserted via the math toolbar button
15674 \begin_inset Graphics
15675 filename ../images/math/intop.png
15683 \begin_layout Standard
15684 The operators are called big because they are bigger than the sometimes
15685 equal looking binary operators.
15686 All big operators can have limits as described in the next subsection.
15689 \begin_layout Standard
15690 For all integral operators there is a second version available, ending on
15708 These operators are different from
15715 \begin_inset space \space{}
15718 in the style the operator limits are displayed, see
15719 \begin_inset CommandInset ref
15721 reference "sub:Operator-Limits"
15729 \begin_layout Subsubsection*
15730 Advice for Integrals
15733 \begin_layout Standard
15738 in an integral is an operator, that therefore has to be set upright.
15739 This is done by highlighting the
15743 and using the keyboard shortcut
15753 \begin_layout Plain Layout
15759 \begin_inset CommandInset ref
15761 reference "sub:Font-Styles"
15771 Finally the smallest space is inserted before the
15775 , as this is usual for operators.
15779 \begin_layout Standard
15781 \begin_inset Formula $\int A(x)dx$
15785 \begin_inset Newline newline
15789 \begin_inset Phantom HPhantom
15792 \begin_layout Plain Layout
15799 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15805 \begin_layout Standard
15806 For multiple integrals there are the following commands:
15807 \begin_inset VSpace medskip
15813 \begin_layout Standard
15814 \begin_inset space \hfill{}
15818 \begin_inset Tabular
15819 <lyxtabular version="3" rows="4" columns="2">
15820 <features tabularvalignment="middle">
15821 <column alignment="center" valignment="top" width="0">
15822 <column alignment="center" valignment="top" width="0">
15824 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15827 \begin_layout Plain Layout
15833 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15836 \begin_layout Plain Layout
15838 \begin_inset Note Note
15841 \begin_layout Plain Layout
15848 is only used as spacer.
15860 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15863 \begin_layout Plain Layout
15871 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15874 \begin_layout Plain Layout
15875 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
15885 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15888 \begin_layout Plain Layout
15896 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15899 \begin_layout Plain Layout
15900 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
15910 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15913 \begin_layout Plain Layout
15921 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15924 \begin_layout Plain Layout
15925 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
15939 \begin_inset space \hfill{}
15943 \begin_inset Tabular
15944 <lyxtabular version="3" rows="4" columns="2">
15945 <features tabularvalignment="middle">
15946 <column alignment="center" valignment="top" width="0">
15947 <column alignment="center" valignment="top" width="0">
15949 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15952 \begin_layout Plain Layout
15958 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15961 \begin_layout Plain Layout
15969 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15972 \begin_layout Plain Layout
15980 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15983 \begin_layout Plain Layout
15984 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
15994 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15997 \begin_layout Plain Layout
16005 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16008 \begin_layout Plain Layout
16009 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
16019 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16022 \begin_layout Plain Layout
16030 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16033 \begin_layout Plain Layout
16034 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
16048 \begin_inset space \hfill{}
16054 \begin_layout Subsection
16056 \begin_inset CommandInset label
16058 name "sub:Operator-Limits"
16063 \begin_inset Index idx
16066 \begin_layout Plain Layout
16075 \begin_layout Standard
16076 Limits are created by super- and subscripts:
16079 \begin_layout Standard
16081 \begin_inset Tabular
16082 <lyxtabular version="3" rows="2" columns="2">
16083 <features tabularvalignment="middle">
16084 <column alignment="center" valignment="top" width="0pt">
16085 <column alignment="center" valignment="top" width="0pt">
16087 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16090 \begin_layout Plain Layout
16096 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16099 \begin_layout Plain Layout
16101 \begin_inset Note Note
16104 \begin_layout Plain Layout
16111 is only used as spacer.
16123 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16126 \begin_layout Plain Layout
16135 \begin_layout Plain Layout
16145 \begin_inset Formula $\to$
16149 \begin_inset Formula $\to$
16157 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16160 \begin_layout Plain Layout
16161 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
16177 \begin_layout Standard
16178 Limits of inline formulas are set right beside the operator.
16179 Limits in displayed formulas are set above or below the operator, except
16180 for integral limits.
16183 \begin_layout Standard
16184 To force that the limits are set beside the operator, the cursor is set
16185 directly behind the operator and the limits type is changed with the menu
16188 Edit\SpecialChar \menuseparator
16189 Math\SpecialChar \menuseparator
16208 \begin_layout Standard
16209 The default limits type is this:
16210 \begin_inset Formula \[
16211 \sum_{x=0}^{\infty}\frac{1}{x^{2}}\]
16215 This is how it looks when the limits type was changed to
16222 \begin_inset Formula \[
16223 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}\]
16227 For integrals, except those ending with
16243 etc., the limits are by default set beside the operator.
16244 But for multiple integrals the limits are often set below the operator.
16245 In the following example the limits type was therefore set to
16249 and so set below the integrals:
16250 \begin_inset Formula \begin{equation}
16251 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}\end{equation}
16258 \begin_layout Standard
16259 \begin_inset VSpace medskip
16262 To specify conditions for limits, the commands
16269 \begin_inset Index idx
16272 \begin_layout Plain Layout
16287 \begin_inset Index idx
16290 \begin_layout Plain Layout
16299 To create for example this expression
16300 \begin_inset Formula \begin{equation}
16301 \sum_{\begin{subarray}{c}
16305 \end{subarray}}^{n}k^{-2}\label{eq:substack}\end{equation}
16312 \begin_layout Standard
16313 the following has to be done:
16314 \begin_inset Newline newline
16329 \begin_layout Plain Layout
16341 One is now in a blue box under the summation operator and insert there
16350 \begin_layout Plain Layout
16362 The blue box is now within a purple box and now several lines can be written
16364 A new line is created by inserting a line break (
16367 arg "newline-insert newline"
16372 \begin_inset Newline newline
16377 0<k<1000 Ctrl+Return
16378 \begin_inset Newline newline
16383 is typed in, a new box appears below for the new line.
16386 \begin_layout Standard
16387 The alignment of the lines can be changed to left aligned with the
16397 Edit\SpecialChar \menuseparator
16401 To get right alignment,
16409 \begin_layout Plain Layout
16420 is inserted at the beginning of the line.
16423 \begin_layout Standard
16436 with the difference that the lines are always centered.
16439 \begin_layout Standard
16440 \begin_inset VSpace bigskip
16444 \begin_inset CommandInset ref
16446 reference "eq:substack"
16450 there can be too much space beside an operator, because the characters
16451 following the operator are set beside the limits.
16454 \begin_layout Standard
16455 To avoid this, the following macro can be used in the LaTeX-preamble:
16458 \begin_layout Standard
16472 \begin_inset Newline newline
16484 \begin_inset Newline newline
16491 mathclapinternal #1#2{
16495 mathsurround =0pt #1{#2}$}}
16498 \begin_layout Standard
16499 This defines the command
16506 \begin_inset Index idx
16509 \begin_layout Plain Layout
16517 that sets the width of the limit to 0
16518 \begin_inset space \thinspace{}
16522 The command scheme is
16525 \begin_layout Standard
16533 \begin_layout Standard
16534 where the limit can consist of several conditions.
16537 \begin_layout Standard
16539 \begin_inset CommandInset ref
16541 reference "eq:substack"
16545 , one uses the command
16548 \begin_layout Standard
16561 \begin_layout Plain Layout
16570 0<k<1000 Ctrl+Return
16573 \begin_layout Standard
16574 to create the lower limit.
16575 The summand is now directly behind the summation operator:
16576 \begin_inset Formula \[
16577 \sum_{\mathclap{\substack{0<k<1000\\
16588 \begin_layout Standard
16589 \begin_inset VSpace bigskip
16592 How to use one limit for several operators is described in
16593 \begin_inset CommandInset ref
16595 reference "sub:Self-defined-Operators"
16602 \begin_layout Subsection
16604 \begin_inset CommandInset label
16606 name "sub:Binary-Operators"
16611 \begin_inset Index idx
16614 \begin_layout Plain Layout
16623 \begin_layout Standard
16624 Binary operators are surrounded by space when there is a character before
16626 \begin_inset VSpace medskip
16632 \begin_layout Standard
16633 \begin_inset space \hfill{}
16637 \begin_inset Tabular
16638 <lyxtabular version="3" rows="13" columns="2">
16639 <features tabularvalignment="middle">
16640 <column alignment="center" valignment="top" width="0pt">
16641 <column alignment="center" valignment="top" width="0pt">
16643 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16646 \begin_layout Plain Layout
16648 \begin_inset Note Note
16651 \begin_layout Plain Layout
16658 is only used as spacer.
16668 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16671 \begin_layout Plain Layout
16679 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16682 \begin_layout Plain Layout
16688 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16691 \begin_layout Plain Layout
16692 \begin_inset Formula $+$
16702 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16705 \begin_layout Plain Layout
16711 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16714 \begin_layout Plain Layout
16715 \begin_inset Formula $-$
16725 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16728 \begin_layout Plain Layout
16736 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16739 \begin_layout Plain Layout
16740 \begin_inset Formula $\pm$
16750 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16753 \begin_layout Plain Layout
16761 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16764 \begin_layout Plain Layout
16765 \begin_inset Formula $\mp$
16775 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16778 \begin_layout Plain Layout
16786 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16789 \begin_layout Plain Layout
16790 \begin_inset Formula $\cdot$
16800 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16803 \begin_layout Plain Layout
16811 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16814 \begin_layout Plain Layout
16815 \begin_inset Formula $\times$
16825 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16828 \begin_layout Plain Layout
16836 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16839 \begin_layout Plain Layout
16840 \begin_inset Formula $\div$
16850 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16853 \begin_layout Plain Layout
16857 \begin_layout Plain Layout
16870 \begin_layout Plain Layout
16882 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16885 \begin_layout Plain Layout
16886 \begin_inset Formula $*$
16896 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16899 \begin_layout Plain Layout
16907 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16910 \begin_layout Plain Layout
16911 \begin_inset Formula $\star$
16921 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16924 \begin_layout Plain Layout
16932 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16935 \begin_layout Plain Layout
16936 \begin_inset Formula $\circ$
16946 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16949 \begin_layout Plain Layout
16957 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16960 \begin_layout Plain Layout
16961 \begin_inset Formula $\diamond$
16971 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16974 \begin_layout Plain Layout
16982 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16985 \begin_layout Plain Layout
16986 \begin_inset Formula $\bullet$
17000 \begin_inset space \hfill{}
17004 \begin_inset Tabular
17005 <lyxtabular version="3" rows="13" columns="2">
17006 <features tabularvalignment="middle">
17007 <column alignment="center" valignment="top" width="0pt">
17008 <column alignment="center" valignment="top" width="0pt">
17010 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17013 \begin_layout Plain Layout
17019 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17022 \begin_layout Plain Layout
17030 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17033 \begin_layout Plain Layout
17041 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17044 \begin_layout Plain Layout
17045 \begin_inset Formula $\nabla$
17055 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17058 \begin_layout Plain Layout
17066 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17069 \begin_layout Plain Layout
17070 \begin_inset Formula $\bigtriangledown$
17080 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17083 \begin_layout Plain Layout
17091 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17094 \begin_layout Plain Layout
17095 \begin_inset Formula $\bigtriangleup$
17105 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17108 \begin_layout Plain Layout
17116 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17119 \begin_layout Plain Layout
17120 \begin_inset Formula $\Box$
17130 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17133 \begin_layout Plain Layout
17141 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17144 \begin_layout Plain Layout
17145 \begin_inset Formula $\cap$
17155 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17158 \begin_layout Plain Layout
17166 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17169 \begin_layout Plain Layout
17170 \begin_inset Formula $\cup$
17180 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17183 \begin_layout Plain Layout
17191 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17194 \begin_layout Plain Layout
17195 \begin_inset Formula $\dagger$
17205 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17208 \begin_layout Plain Layout
17216 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17219 \begin_layout Plain Layout
17220 \begin_inset Formula $\ddagger$
17230 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17233 \begin_layout Plain Layout
17241 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17244 \begin_layout Plain Layout
17245 \begin_inset Formula $\wr$
17255 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17258 \begin_layout Plain Layout
17266 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17269 \begin_layout Plain Layout
17270 \begin_inset Formula $\bigcirc$
17280 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17283 \begin_layout Plain Layout
17291 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17294 \begin_layout Plain Layout
17295 \begin_inset Formula $\wedge$
17305 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17308 \begin_layout Plain Layout
17316 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17319 \begin_layout Plain Layout
17320 \begin_inset Formula $\vee$
17334 \begin_inset space \hfill{}
17338 \begin_inset Tabular
17339 <lyxtabular version="3" rows="13" columns="2">
17340 <features tabularvalignment="middle">
17341 <column alignment="center" valignment="top" width="0pt">
17342 <column alignment="center" valignment="top" width="0pt">
17344 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17347 \begin_layout Plain Layout
17353 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17356 \begin_layout Plain Layout
17364 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17367 \begin_layout Plain Layout
17375 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17378 \begin_layout Plain Layout
17379 \begin_inset Formula $\oplus$
17389 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17392 \begin_layout Plain Layout
17400 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17403 \begin_layout Plain Layout
17404 \begin_inset Formula $\ominus$
17414 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17417 \begin_layout Plain Layout
17425 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17428 \begin_layout Plain Layout
17429 \begin_inset Formula $\otimes$
17439 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17442 \begin_layout Plain Layout
17450 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17453 \begin_layout Plain Layout
17454 \begin_inset Formula $\oslash$
17464 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17467 \begin_layout Plain Layout
17475 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17478 \begin_layout Plain Layout
17479 \begin_inset Formula $\odot$
17489 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17492 \begin_layout Plain Layout
17500 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17503 \begin_layout Plain Layout
17504 \begin_inset Formula $\amalg$
17514 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17517 \begin_layout Plain Layout
17525 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17528 \begin_layout Plain Layout
17529 \begin_inset Formula $\uplus$
17539 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17542 \begin_layout Plain Layout
17550 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17553 \begin_layout Plain Layout
17554 \begin_inset Formula $\setminus$
17564 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17567 \begin_layout Plain Layout
17575 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17578 \begin_layout Plain Layout
17579 \begin_inset Formula $\sqcap$
17589 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17592 \begin_layout Plain Layout
17600 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17603 \begin_layout Plain Layout
17604 \begin_inset Formula $\sqcup$
17614 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17617 \begin_layout Plain Layout
17625 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17628 \begin_layout Plain Layout
17629 \begin_inset Formula $\triangleleft$
17639 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17642 \begin_layout Plain Layout
17650 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17653 \begin_layout Plain Layout
17654 \begin_inset Formula $\triangleright$
17668 \begin_inset space \hfill{}
17674 \begin_layout Standard
17675 All binary operators can also be inserted via the math toolbar button
17676 \begin_inset Graphics
17677 filename ../images/math/pm.png
17685 \begin_layout Standard
17686 To typeset the Laplace operator also
17703 \begin_inset Formula $\nabla^{2}$
17706 ) can be used instead of
17715 \begin_layout Standard
17722 Insert\SpecialChar \menuseparator
17734 \begin_layout Subsection
17735 Self-defined Operators
17736 \begin_inset CommandInset label
17738 name "sub:Self-defined-Operators"
17743 \begin_inset Index idx
17746 \begin_layout Plain Layout
17747 Operators ! self-defined
17755 \begin_layout Standard
17756 With the help of the command
17760 DeclareMathOperator
17763 \begin_inset Index idx
17766 \begin_layout Plain Layout
17771 DeclareMathOperator
17776 custom operators can be defined in the LaTeX-preamble.
17777 Its command scheme is:
17780 \begin_layout Standard
17785 DeclareMathOperator{new command}{display}
17788 \begin_layout Standard
17789 Display can be characters or symbols that define how the operator looks
17791 To define a big operator a * is set behind the command.
17792 All self-defined big operators can have limits as described in
17793 \begin_inset CommandInset ref
17795 reference "sub:Operator-Limits"
17802 \begin_layout Standard
17803 For example the LaTeX-preamble line
17806 \begin_layout Standard
17811 DeclareMathOperator*{
17818 \begin_layout Standard
17819 defines the command
17825 , that inserts a big operator consisting of the lozenge symbol from
17826 \begin_inset CommandInset ref
17828 reference "sub:Miscellaneous-Symbols"
17833 \begin_inset Formula \[
17834 \Lozenge_{n=1}^{\infty}\]
17838 The command for this formula is:
17849 \begin_inset Formula $\to$
17855 \begin_layout Standard
17856 \begin_inset VSpace bigskip
17859 When self-defined operators are not used several times in the document,
17860 they can also be defined with the commands
17867 \begin_inset Index idx
17870 \begin_layout Plain Layout
17885 \begin_inset Index idx
17888 \begin_layout Plain Layout
17896 , which have the following scheme:
17899 \begin_layout Standard
17913 \begin_layout Standard
17920 defines big operators,
17929 \begin_layout Standard
17937 \begin_inset space \thinspace{}
17941 \begin_inset space \space{}
17944 be used to use one limit for several operators:
17947 \begin_layout Standard
17948 \begin_inset Formula \[
17949 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}\]
17956 \begin_layout Standard
17957 The command for the formula above is:
17958 \begin_inset Newline newline
17977 \begin_layout Plain Layout
17989 \begin_inset Formula $\to$
17998 \begin_layout Plain Layout
18012 \begin_layout Section
18014 \begin_inset Index idx
18017 \begin_layout Plain Layout
18026 \begin_layout Subsection
18028 \begin_inset CommandInset label
18030 name "sub:Font-Styles"
18035 \begin_inset Index idx
18038 \begin_layout Plain Layout
18047 \begin_layout Standard
18048 Latin letters in formulas can be set in one of the following font styles:
18049 \begin_inset VSpace -2mm
18055 \begin_layout Standard
18057 \begin_inset Tabular
18058 <lyxtabular version="3" rows="7" columns="3">
18059 <features tabularvalignment="middle">
18060 <column alignment="center" valignment="top" width="0">
18061 <column alignment="center" valignment="top" width="0">
18062 <column alignment="center" valignment="top" width="0">
18064 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18067 \begin_layout Plain Layout
18073 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18076 \begin_layout Plain Layout
18082 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18085 \begin_layout Plain Layout
18093 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18096 \begin_layout Plain Layout
18105 \begin_layout Plain Layout
18121 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18124 \begin_layout Plain Layout
18125 \begin_inset Formula $\mathbb{ABC}$
18133 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18136 \begin_layout Plain Layout
18149 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18152 \begin_layout Plain Layout
18161 \begin_layout Plain Layout
18177 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18180 \begin_layout Plain Layout
18181 \begin_inset Formula $\mathbf{AbC}$
18189 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18192 \begin_layout Plain Layout
18205 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18208 \begin_layout Plain Layout
18217 \begin_layout Plain Layout
18233 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18236 \begin_layout Plain Layout
18237 \begin_inset Formula $\boldsymbol{AbC}$
18245 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18248 \begin_layout Plain Layout
18251 arg "font-boldsymbol"
18261 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18264 \begin_layout Plain Layout
18273 \begin_layout Plain Layout
18289 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18292 \begin_layout Plain Layout
18293 \begin_inset Formula $\mathcal{ABC}$
18301 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18304 \begin_layout Plain Layout
18317 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18320 \begin_layout Plain Layout
18329 \begin_layout Plain Layout
18345 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18348 \begin_layout Plain Layout
18349 \begin_inset Formula $\mathfrak{AbC}$
18357 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18360 \begin_layout Plain Layout
18368 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18371 \begin_layout Plain Layout
18380 \begin_layout Plain Layout
18396 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18399 \begin_layout Plain Layout
18400 \begin_inset Formula $\mathscr{AbC}$
18408 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18411 \begin_layout Plain Layout
18425 \begin_layout Standard
18427 \begin_inset Tabular
18428 <lyxtabular version="3" rows="5" columns="3">
18429 <features tabularvalignment="middle">
18430 <column alignment="center" valignment="top" width="0">
18431 <column alignment="center" valignment="top" width="0">
18432 <column alignment="center" valignment="top" width="0">
18434 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18437 \begin_layout Plain Layout
18443 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18446 \begin_layout Plain Layout
18452 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18455 \begin_layout Plain Layout
18463 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18466 \begin_layout Plain Layout
18475 \begin_layout Plain Layout
18491 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18494 \begin_layout Plain Layout
18495 \begin_inset Formula $\mathit{AbC}$
18503 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18506 \begin_layout Plain Layout
18514 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18517 \begin_layout Plain Layout
18526 \begin_layout Plain Layout
18542 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18545 \begin_layout Plain Layout
18546 \begin_inset Formula $\mathrm{AbC}$
18554 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18557 \begin_layout Plain Layout
18570 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18573 \begin_layout Plain Layout
18582 \begin_layout Plain Layout
18598 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18601 \begin_layout Plain Layout
18602 \begin_inset Formula $\mathsf{AbC}$
18610 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18613 \begin_layout Plain Layout
18626 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18629 \begin_layout Plain Layout
18638 \begin_layout Plain Layout
18654 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18657 \begin_layout Plain Layout
18658 \begin_inset Formula $\mathtt{AbC}$
18666 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18669 \begin_layout Plain Layout
18672 arg "font-typewriter"
18688 \begin_layout Standard
18689 \begin_inset Note Greyedout
18692 \begin_layout Plain Layout
18709 can only be used for big letters.
18717 \begin_layout Standard
18718 Predefined is the style
18727 \begin_layout Standard
18728 The style commands work also for letters in mathematical constructs:
18729 \begin_inset Formula \[
18730 \mathfrak{A=\frac{b}{C}}\]
18737 \begin_layout Standard
18738 Characters in mathematical text don't appear in a math font style but in
18739 the text font style
18746 That their style can't be set correctly via the text style dialog is a
18751 \begin_layout Plain Layout
18752 \begin_inset CommandInset href
18754 name "LyX-bug #4629"
18755 target "http://www.lyx.org/trac/ticket/4629"
18767 \begin_layout Standard
18768 Instead of the style commands the dialog
18770 Edit\SpecialChar \menuseparator
18771 Math\SpecialChar \menuseparator
18774 or the toolbar button
18775 \begin_inset Graphics
18776 filename ../images/math/font.png
18784 \begin_layout Subsection
18786 \begin_inset CommandInset label
18788 name "sub:Bold-Formulas"
18793 \begin_inset Index idx
18796 \begin_layout Plain Layout
18805 \begin_layout Standard
18806 To make a complete formula bold, the command
18812 from the previous subsection cannot be used, because it doesn't work for
18813 small Greek letters.
18814 Furthermore it prints Latin letters always upright, like in the following
18818 \begin_layout Standard
18819 \begin_inset Formula \[
18820 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}\]
18827 \begin_layout Standard
18828 To display the formula correctly, the command
18835 \begin_inset Formula \[
18836 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}\]
18840 It is also possible to set the formula in a
18842 boldmath environment
18845 This environment is created by inserting the command
18852 \begin_inset Index idx
18855 \begin_layout Plain Layout
18864 To end the environment, the command
18871 \begin_inset Index idx
18874 \begin_layout Plain Layout
18882 is inserted in TeX-mode.
18886 \begin_layout Plain Layout
18896 \begin_inset Formula \[
18897 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}\]
18905 \begin_layout Plain Layout
18917 \begin_layout Subsection
18919 \begin_inset Index idx
18922 \begin_layout Plain Layout
18931 \begin_layout Standard
18932 Formulas can be colored like normal text: Highlight a formula or a formula
18938 Here is a formula in magenta:
18939 \begin_inset Formula \[
18940 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}\]
18947 \begin_layout Standard
18948 You can also define your own colors as described in
18949 \begin_inset CommandInset ref
18951 reference "sub:Colored-Boxes"
18956 They can be used with the TeX code command
18963 \begin_inset Index idx
18966 \begin_layout Plain Layout
18977 \begin_layout Standard
18982 textcolor{color}{characters or formula}
18985 \begin_layout Standard
18986 The following example was colored completely dark green and partly red:
18989 \begin_layout Standard
18993 \begin_layout Plain Layout
18997 textcolor{darkgreen}{
19003 \begin_inset Formula \[
19004 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}\]
19012 \begin_layout Plain Layout
19022 \begin_layout Standard
19023 Due to a bug in LyX only complete formulas can be colored with self-defined
19028 \begin_layout Plain Layout
19029 \begin_inset CommandInset href
19031 name "LyX-bug #5269"
19032 target "http://www.lyx.org/trac/ticket/5269"
19044 \begin_layout Subsection
19046 \begin_inset CommandInset label
19048 name "sub:Font-Sizes"
19053 \begin_inset Index idx
19056 \begin_layout Plain Layout
19065 \begin_layout Standard
19066 For characters in formulas there are, analog to characters in text, the
19067 following size commands:
19070 \begin_layout Standard
19114 \begin_inset Newline newline
19136 \begin_layout Standard
19137 The size produced by the commands depends on the document font size, that
19138 corresponds with the command
19145 The other commands produce smaller or larger sizes than
19152 The font size can however not exceed a certain value.
19153 Is for example the document font size 12
19154 \begin_inset space \thinspace{}
19163 switches to the same size as
19173 \begin_layout Standard
19174 A size command is inserted in TeX-mode before the formula and sets the size
19175 for all following formula and text characters.
19176 To switch back to the initial size, the command
19182 is inserted behind the formula in TeX-mode.
19185 \begin_layout Standard
19186 \begin_inset Newpage newpage
19192 \begin_layout Standard
19193 Within a formula the size can be changed using the following size commands:
19196 \begin_layout Standard
19199 \begin_inset Tabular
19200 <lyxtabular version="3" rows="5" columns="2">
19201 <features tabularvalignment="middle">
19202 <column alignment="center" valignment="top" width="0">
19203 <column alignment="center" valignment="top" width="0">
19205 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19208 \begin_layout Plain Layout
19214 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19217 \begin_layout Plain Layout
19219 \begin_inset Note Note
19222 \begin_layout Plain Layout
19229 is only used as spacer.
19241 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19244 \begin_layout Plain Layout
19248 \begin_inset Index idx
19251 \begin_layout Plain Layout
19264 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19267 \begin_layout Plain Layout
19268 \begin_inset Formula $\raisebox{6.5mm}{}{\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-5.5mm}{}$
19278 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19281 \begin_layout Plain Layout
19289 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19292 \begin_layout Plain Layout
19293 \begin_inset Formula $\raisebox{4.5mm}{}{\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-4mm}{}$
19303 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19306 \begin_layout Plain Layout
19314 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19317 \begin_layout Plain Layout
19318 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
19328 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19331 \begin_layout Plain Layout
19339 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19342 \begin_layout Plain Layout
19343 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
19359 \begin_layout Standard
19360 After entering these commands, a blue box appears in which the formula parts
19364 \begin_layout Standard
19365 There is a further method to change the font size, that though only works
19366 for symbols or letters in mathematical text.
19367 To use it, one of the above text size commands is inserted in mathematical
19369 All following characters until the end of the mathematical text or until
19370 another size command will have the selected size.
19372 \begin_inset VSpace -2mm
19378 \begin_layout Standard
19382 \begin_layout Plain Layout
19392 \begin_inset Formula \[
19393 A=\frac{B}{c}\cdot\maltese\]
19398 \begin_inset Formula \[
19399 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}\]
19407 \begin_layout Plain Layout
19419 \begin_layout Standard
19420 \begin_inset VSpace medskip
19423 Before both formulas the command
19430 The command for the second formula is:
19431 \begin_inset Newline newline
19442 \begin_layout Plain Layout
19457 \begin_layout Plain Layout
19472 \begin_layout Plain Layout
19487 \begin_layout Plain Layout
19497 \begin_inset Formula $\to$
19501 \begin_inset Formula $\to$
19505 \begin_inset Newline newline
19509 \begin_inset space \hspace*{}
19523 \begin_layout Plain Layout
19538 \begin_layout Plain Layout
19553 \begin_layout Plain Layout
19565 \begin_layout Standard
19566 If a symbol cannot be displayed in different sizes, it will always be displayed
19567 in the default size.
19570 \begin_layout Standard
19571 \begin_inset Newpage newpage
19577 \begin_layout Section
19579 \begin_inset Index idx
19582 \begin_layout Plain Layout
19591 \begin_layout Standard
19592 All Greek letters can also be inserted via the toolbar button
19593 \begin_inset Graphics
19594 filename ../images/math/alpha.png
19602 \begin_layout Subsection
19604 \begin_inset Index idx
19607 \begin_layout Plain Layout
19608 Greek letters ! small
19616 \begin_layout Standard
19617 \begin_inset space \hfill{}
19621 \begin_inset Tabular
19622 <lyxtabular version="3" rows="11" columns="2">
19623 <features tabularvalignment="middle">
19624 <column alignment="center" valignment="top" width="0pt">
19625 <column alignment="center" valignment="top" width="0pt">
19627 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19630 \begin_layout Plain Layout
19636 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19639 \begin_layout Plain Layout
19647 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19650 \begin_layout Plain Layout
19658 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19661 \begin_layout Plain Layout
19662 \begin_inset Formula $\alpha$
19672 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19675 \begin_layout Plain Layout
19683 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19686 \begin_layout Plain Layout
19687 \begin_inset Formula $\beta$
19697 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19700 \begin_layout Plain Layout
19708 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19711 \begin_layout Plain Layout
19712 \begin_inset Formula $\gamma$
19722 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19725 \begin_layout Plain Layout
19733 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19736 \begin_layout Plain Layout
19737 \begin_inset Formula $\delta$
19747 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19750 \begin_layout Plain Layout
19758 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19761 \begin_layout Plain Layout
19762 \begin_inset Formula $\epsilon$
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 $\varepsilon$
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 $\zeta$
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 $\eta$
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 $\theta$
19872 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19875 \begin_layout Plain Layout
19883 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19886 \begin_layout Plain Layout
19887 \begin_inset Formula $\vartheta$
19901 \begin_inset space \hfill{}
19905 \begin_inset Tabular
19906 <lyxtabular version="3" rows="12" columns="2">
19907 <features tabularvalignment="middle">
19908 <column alignment="center" valignment="top" width="0pt">
19909 <column alignment="center" valignment="top" width="0pt">
19911 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19914 \begin_layout Plain Layout
19920 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19923 \begin_layout Plain Layout
19931 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19934 \begin_layout Plain Layout
19942 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19945 \begin_layout Plain Layout
19946 \begin_inset Formula $\iota$
19956 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19959 \begin_layout Plain Layout
19967 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19970 \begin_layout Plain Layout
19971 \begin_inset Formula $\kappa$
19981 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19984 \begin_layout Plain Layout
19992 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19995 \begin_layout Plain Layout
19996 \begin_inset Formula $\varkappa$
20006 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20009 \begin_layout Plain Layout
20017 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20020 \begin_layout Plain Layout
20021 \begin_inset Formula $\lambda$
20031 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20034 \begin_layout Plain Layout
20042 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20045 \begin_layout Plain Layout
20046 \begin_inset Formula $\mu$
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 $\nu$
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 $\xi$
20106 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20109 \begin_layout Plain Layout
20115 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20118 \begin_layout Plain Layout
20119 \begin_inset Formula $o$
20129 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20132 \begin_layout Plain Layout
20140 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20143 \begin_layout Plain Layout
20144 \begin_inset Formula $\pi$
20154 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20157 \begin_layout Plain Layout
20165 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20168 \begin_layout Plain Layout
20169 \begin_inset Formula $\varpi$
20179 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20182 \begin_layout Plain Layout
20190 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20193 \begin_layout Plain Layout
20194 \begin_inset Formula $\rho$
20208 \begin_inset space \hfill{}
20212 \begin_inset Tabular
20213 <lyxtabular version="3" rows="11" columns="2">
20214 <features tabularvalignment="middle">
20215 <column alignment="center" valignment="top" width="0pt">
20216 <column alignment="center" valignment="top" width="0pt">
20218 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20221 \begin_layout Plain Layout
20227 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20230 \begin_layout Plain Layout
20238 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20241 \begin_layout Plain Layout
20249 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20252 \begin_layout Plain Layout
20253 \begin_inset Formula $\varrho$
20263 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20266 \begin_layout Plain Layout
20274 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20277 \begin_layout Plain Layout
20278 \begin_inset Formula $\sigma$
20288 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20291 \begin_layout Plain Layout
20299 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20302 \begin_layout Plain Layout
20303 \begin_inset Formula $\varsigma$
20313 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20316 \begin_layout Plain Layout
20324 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20327 \begin_layout Plain Layout
20328 \begin_inset Formula $\tau$
20338 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20341 \begin_layout Plain Layout
20349 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20352 \begin_layout Plain Layout
20353 \begin_inset Formula $\upsilon$
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 $\phi$
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 $\varphi$
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 $\chi$
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 $\psi$
20463 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20466 \begin_layout Plain Layout
20474 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20477 \begin_layout Plain Layout
20478 \begin_inset Formula $\omega$
20492 \begin_inset space \hfill{}
20498 \begin_layout Standard
20499 \begin_inset VSpace medskip
20505 \begin_layout Standard
20506 How to create upright Greek letters is explained in
20507 \begin_inset CommandInset ref
20509 reference "sub:Upright-small-Greek"
20516 \begin_layout Subsection
20518 \begin_inset Index idx
20521 \begin_layout Plain Layout
20522 Greek letters ! big
20530 \begin_layout Standard
20531 \begin_inset space \hfill{}
20535 \begin_inset Tabular
20536 <lyxtabular version="3" rows="7" columns="2">
20537 <features tabularvalignment="middle">
20538 <column alignment="center" valignment="top" width="0pt">
20539 <column alignment="center" valignment="top" width="0pt">
20541 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20544 \begin_layout Plain Layout
20550 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20553 \begin_layout Plain Layout
20561 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20564 \begin_layout Plain Layout
20572 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20575 \begin_layout Plain Layout
20576 \begin_inset Formula $\Gamma$
20586 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20589 \begin_layout Plain Layout
20597 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20600 \begin_layout Plain Layout
20601 \begin_inset Formula $\Delta$
20611 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20614 \begin_layout Plain Layout
20622 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20625 \begin_layout Plain Layout
20626 \begin_inset Formula $\Theta$
20636 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20639 \begin_layout Plain Layout
20647 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20650 \begin_layout Plain Layout
20651 \begin_inset Formula $\Lambda$
20661 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20664 \begin_layout Plain Layout
20672 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20675 \begin_layout Plain Layout
20676 \begin_inset Formula $\Xi$
20686 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20689 \begin_layout Plain Layout
20697 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20700 \begin_layout Plain Layout
20701 \begin_inset Formula $\Pi$
20715 \begin_inset space \hfill{}
20719 \begin_inset Tabular
20720 <lyxtabular version="3" rows="6" columns="2">
20721 <features tabularvalignment="middle">
20722 <column alignment="center" valignment="top" width="0pt">
20723 <column alignment="center" valignment="top" width="0pt">
20725 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20728 \begin_layout Plain Layout
20734 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20737 \begin_layout Plain Layout
20745 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20748 \begin_layout Plain Layout
20756 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20759 \begin_layout Plain Layout
20760 \begin_inset Formula $\Sigma$
20770 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20773 \begin_layout Plain Layout
20781 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20784 \begin_layout Plain Layout
20785 \begin_inset Formula $\Upsilon$
20795 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20798 \begin_layout Plain Layout
20806 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20809 \begin_layout Plain Layout
20810 \begin_inset Formula $\Phi$
20820 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20823 \begin_layout Plain Layout
20831 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20834 \begin_layout Plain Layout
20835 \begin_inset Formula $\Psi$
20845 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20848 \begin_layout Plain Layout
20856 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20859 \begin_layout Plain Layout
20860 \begin_inset Formula $\Omega$
20874 \begin_inset space \hfill{}
20880 \begin_layout Standard
20881 \begin_inset VSpace medskip
20884 That the big Greek letters appear upright is caused by a design bug when
20886 To get correct italic big letters, begin every command with
20891 For example the command
20898 \begin_inset Formula $\varGamma$
20904 \begin_layout Subsection
20906 \begin_inset Index idx
20909 \begin_layout Plain Layout
20910 Greek letters ! bold
20918 \begin_layout Standard
20919 Greek letters cannot be set with different font styles like Latin letters.
20920 They can only be made bold with the command
20927 \begin_inset Index idx
20930 \begin_layout Plain Layout
20941 \begin_layout Standard
20943 \begin_inset Tabular
20944 <lyxtabular version="3" rows="3" columns="2">
20945 <features tabularvalignment="middle">
20946 <column alignment="center" valignment="top" width="0">
20947 <column alignment="center" valignment="top" width="0">
20949 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20952 \begin_layout Plain Layout
20958 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20961 \begin_layout Plain Layout
20969 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20972 \begin_layout Plain Layout
20984 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20987 \begin_layout Plain Layout
20988 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20998 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21001 \begin_layout Plain Layout
21013 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21016 \begin_layout Plain Layout
21017 \begin_inset Formula $\theta\boldsymbol{\theta}$
21033 \begin_layout Section
21038 \begin_layout Plain Layout
21051 \begin_layout Plain Layout
21052 A list with all symbols of most of the LaTeX-packages can be found in
21053 \begin_inset CommandInset citation
21068 \begin_layout Plain Layout
21076 \begin_inset Note Note
21079 \begin_layout Plain Layout
21082 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
21085 \begin_layout Plain Layout
21088 texorpdfstring is in section
21089 \begin_inset CommandInset ref
21091 reference "sub:Formulas-in-Section"
21101 \begin_inset Index idx
21104 \begin_layout Plain Layout
21113 \begin_layout Standard
21114 Many of the symbols listed in this section can also be inserted via the
21116 \begin_inset Graphics
21117 filename ../images/math/nabla.png
21123 \begin_inset Graphics
21124 filename ../images/math/digamma.png
21132 \begin_layout Subsection
21133 Mathematical Symbols
21134 \begin_inset CommandInset label
21136 name "sub:Mathematical-Symbols"
21141 \begin_inset Index idx
21144 \begin_layout Plain Layout
21145 Symbols ! mathematical
21153 \begin_layout Standard
21154 \begin_inset space \hfill{}
21158 \begin_inset Tabular
21159 <lyxtabular version="3" rows="10" columns="2">
21160 <features tabularvalignment="middle">
21161 <column alignment="center" valignment="top" width="0pt">
21162 <column alignment="center" valignment="top" width="0pt">
21164 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21167 \begin_layout Plain Layout
21173 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21176 \begin_layout Plain Layout
21184 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21187 \begin_layout Plain Layout
21195 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21198 \begin_layout Plain Layout
21199 \begin_inset Formula $\neg$
21209 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21212 \begin_layout Plain Layout
21220 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21223 \begin_layout Plain Layout
21224 \begin_inset Formula $\Im$
21234 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21237 \begin_layout Plain Layout
21245 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21248 \begin_layout Plain Layout
21249 \begin_inset Formula $\Re$
21259 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21262 \begin_layout Plain Layout
21270 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21273 \begin_layout Plain Layout
21274 \begin_inset Formula $\aleph$
21284 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21287 \begin_layout Plain Layout
21295 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21298 \begin_layout Plain Layout
21299 \begin_inset Formula $\partial$
21309 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21312 \begin_layout Plain Layout
21320 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21323 \begin_layout Plain Layout
21324 \begin_inset Formula $\infty$
21334 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21337 \begin_layout Plain Layout
21345 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21348 \begin_layout Plain Layout
21349 \begin_inset Formula $\wp$
21359 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21362 \begin_layout Plain Layout
21370 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21373 \begin_layout Plain Layout
21374 \begin_inset Formula $\imath$
21384 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21387 \begin_layout Plain Layout
21395 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21398 \begin_layout Plain Layout
21399 \begin_inset Formula $\jmath$
21413 \begin_inset space \hfill{}
21417 \begin_inset Tabular
21418 <lyxtabular version="3" rows="10" columns="2">
21419 <features tabularvalignment="middle">
21420 <column alignment="center" valignment="top" width="0pt">
21421 <column alignment="center" valignment="top" width="0pt">
21423 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21426 \begin_layout Plain Layout
21432 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21435 \begin_layout Plain Layout
21437 \begin_inset Note Note
21440 \begin_layout Plain Layout
21447 is only used as spacer.
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 $\forall$
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 $\exists$
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 $\nexists$
21534 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21537 \begin_layout Plain Layout
21545 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21548 \begin_layout Plain Layout
21549 \begin_inset Formula $\emptyset$
21559 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21562 \begin_layout Plain Layout
21570 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21573 \begin_layout Plain Layout
21574 \begin_inset Formula $\varnothing$
21584 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21587 \begin_layout Plain Layout
21595 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21598 \begin_layout Plain Layout
21599 \begin_inset Formula $\dag$
21609 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21612 \begin_layout Plain Layout
21620 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21623 \begin_layout Plain Layout
21624 \begin_inset Formula $\ddag$
21634 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21637 \begin_layout Plain Layout
21645 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21648 \begin_layout Plain Layout
21652 \begin_layout Plain Layout
21662 \begin_inset Formula $\complement$
21669 \begin_layout Plain Layout
21683 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21686 \begin_layout Plain Layout
21694 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21697 \begin_layout Plain Layout
21698 \begin_inset Formula $\Bbbk$
21712 \begin_inset space \hfill{}
21716 \begin_inset Tabular
21717 <lyxtabular version="3" rows="10" columns="2">
21718 <features tabularvalignment="middle">
21719 <column alignment="center" valignment="top" width="0pt">
21720 <column alignment="center" valignment="top" width="0pt">
21722 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21725 \begin_layout Plain Layout
21731 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21734 \begin_layout Plain Layout
21742 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21745 \begin_layout Plain Layout
21753 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21756 \begin_layout Plain Layout
21757 \begin_inset Formula $\prime$
21767 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21770 \begin_layout Plain Layout
21778 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21781 \begin_layout Plain Layout
21782 \begin_inset Formula $\backprime$
21792 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21795 \begin_layout Plain Layout
21803 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21806 \begin_layout Plain Layout
21807 \begin_inset Formula $\mho$
21817 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21820 \begin_layout Plain Layout
21828 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21831 \begin_layout Plain Layout
21832 \begin_inset Formula $\triangle$
21842 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21845 \begin_layout Plain Layout
21853 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21856 \begin_layout Plain Layout
21857 \begin_inset Formula $\angle$
21867 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21870 \begin_layout Plain Layout
21878 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21881 \begin_layout Plain Layout
21882 \begin_inset Formula $\measuredangle$
21892 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21895 \begin_layout Plain Layout
21903 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21906 \begin_layout Plain Layout
21907 \begin_inset Formula $\sphericalangle$
21917 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21920 \begin_layout Plain Layout
21928 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21931 \begin_layout Plain Layout
21932 \begin_inset Formula $\top$
21942 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21945 \begin_layout Plain Layout
21953 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21956 \begin_layout Plain Layout
21957 \begin_inset Formula $\bot$
21971 \begin_inset space \hfill{}
21977 \begin_layout Subsection
21978 Miscellaneous Symbols
21979 \begin_inset CommandInset label
21981 name "sub:Miscellaneous-Symbols"
21986 \begin_inset Index idx
21989 \begin_layout Plain Layout
21990 Symbols ! miscellaneous
21998 \begin_layout Standard
22001 \begin_inset Tabular
22002 <lyxtabular version="3" rows="10" columns="2">
22003 <features tabularvalignment="middle">
22004 <column alignment="center" valignment="top" width="0pt">
22005 <column alignment="center" valignment="top" width="0pt">
22007 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22010 \begin_layout Plain Layout
22016 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22019 \begin_layout Plain Layout
22027 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22030 \begin_layout Plain Layout
22038 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22041 \begin_layout Plain Layout
22042 \begin_inset Formula $\flat$
22052 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22055 \begin_layout Plain Layout
22063 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22066 \begin_layout Plain Layout
22067 \begin_inset Formula $\natural$
22077 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22080 \begin_layout Plain Layout
22088 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22091 \begin_layout Plain Layout
22092 \begin_inset Formula $\sharp$
22102 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22105 \begin_layout Plain Layout
22113 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22116 \begin_layout Plain Layout
22117 \begin_inset Formula $\surd$
22127 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22130 \begin_layout Plain Layout
22138 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22141 \begin_layout Plain Layout
22142 \begin_inset Formula $\checkmark$
22152 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22155 \begin_layout Plain Layout
22163 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22166 \begin_layout Plain Layout
22167 \begin_inset Formula $\yen$
22177 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22180 \begin_layout Plain Layout
22188 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22191 \begin_layout Plain Layout
22192 \begin_inset Formula $\pounds$
22202 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22205 \begin_layout Plain Layout
22211 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22214 \begin_layout Plain Layout
22215 \begin_inset Formula $\$$
22225 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22228 \begin_layout Plain Layout
22234 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22237 \begin_layout Plain Layout
22238 \begin_inset Formula $§$
22252 \begin_inset Tabular
22253 <lyxtabular version="3" rows="10" columns="2">
22254 <features tabularvalignment="middle">
22255 <column alignment="center" valignment="top" width="0">
22256 <column alignment="center" valignment="top" width="0">
22258 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22261 \begin_layout Plain Layout
22267 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22270 \begin_layout Plain Layout
22278 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22281 \begin_layout Plain Layout
22289 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22292 \begin_layout Plain Layout
22293 \begin_inset Formula $\hbar$
22303 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22306 \begin_layout Plain Layout
22314 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22317 \begin_layout Plain Layout
22318 \begin_inset Formula $\hslash$
22328 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22331 \begin_layout Plain Layout
22339 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22342 \begin_layout Plain Layout
22343 \begin_inset Formula $\clubsuit$
22353 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22356 \begin_layout Plain Layout
22364 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22367 \begin_layout Plain Layout
22368 \begin_inset Formula $\spadesuit$
22378 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22381 \begin_layout Plain Layout
22389 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22392 \begin_layout Plain Layout
22393 \begin_inset Formula $\bigstar$
22403 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22406 \begin_layout Plain Layout
22414 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22417 \begin_layout Plain Layout
22418 \begin_inset Formula $\blacklozenge$
22428 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22431 \begin_layout Plain Layout
22439 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22442 \begin_layout Plain Layout
22443 \begin_inset Formula $\blacktriangle$
22453 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22456 \begin_layout Plain Layout
22464 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22467 \begin_layout Plain Layout
22468 \begin_inset Formula $\blacktriangledown$
22478 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22481 \begin_layout Plain Layout
22489 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22492 \begin_layout Plain Layout
22493 \begin_inset Formula $\bullet$
22507 \begin_inset Tabular
22508 <lyxtabular version="3" rows="10" columns="2">
22509 <features tabularvalignment="middle">
22510 <column alignment="center" valignment="top" width="0pt">
22511 <column alignment="center" valignment="top" width="0pt">
22513 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22516 \begin_layout Plain Layout
22522 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22525 \begin_layout Plain Layout
22533 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22536 \begin_layout Plain Layout
22544 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22547 \begin_layout Plain Layout
22548 \begin_inset Formula $\diamondsuit$
22558 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22561 \begin_layout Plain Layout
22569 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22572 \begin_layout Plain Layout
22573 \begin_inset Formula $\Diamond$
22583 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22586 \begin_layout Plain Layout
22594 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22597 \begin_layout Plain Layout
22598 \begin_inset Formula $\heartsuit$
22608 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22611 \begin_layout Plain Layout
22619 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22622 \begin_layout Plain Layout
22623 \begin_inset Formula $\P$
22633 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22636 \begin_layout Plain Layout
22644 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22647 \begin_layout Plain Layout
22648 \begin_inset Formula $\copyright$
22658 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22661 \begin_layout Plain Layout
22669 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22672 \begin_layout Plain Layout
22673 \begin_inset Formula $\circledR$
22683 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22686 \begin_layout Plain Layout
22694 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22697 \begin_layout Plain Layout
22698 \begin_inset Formula $\maltese$
22708 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22711 \begin_layout Plain Layout
22719 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22722 \begin_layout Plain Layout
22723 \begin_inset Formula $\diagup$
22733 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22736 \begin_layout Plain Layout
22744 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22747 \begin_layout Plain Layout
22748 \begin_inset Formula $\diagdown$
22764 \begin_layout Standard
22765 \begin_inset VSpace medskip
22768 More symbols are listed in
22769 \begin_inset CommandInset ref
22771 reference "sub:Miscellaneous-special-Characters"
22778 \begin_layout Standard
22779 Some symbols can be displayed in different sizes, see
22780 \begin_inset CommandInset ref
22782 reference "sub:Font-Sizes"
22789 \begin_layout Subsection
22791 \begin_inset Index idx
22794 \begin_layout Plain Layout
22795 Symbols ! Euro-symbol
22801 \begin_inset Index idx
22804 \begin_layout Plain Layout
22811 \begin_layout Plain Layout
22828 \begin_layout Standard
22829 To use the Euro symbol in formulas, the LaTeX-package
22834 \begin_inset Index idx
22837 \begin_layout Plain Layout
22843 must be installed and loaded with the LaTeX-preamble line
22846 \begin_layout Standard
22851 usepackage[gennarrow]{eurosym}
22854 \begin_layout Standard
22855 The Euro symbol can now be inserted with the command
22862 \begin_inset Index idx
22865 \begin_layout Plain Layout
22876 \begin_layout Standard
22877 The Euro symbol can directly be inserted with the € key in mathematical
22878 text, without having
22893 can also be inserted in TeX-mode.
22894 The official currency symbol can then be inserted with the command
22901 \begin_inset Index idx
22904 \begin_layout Plain Layout
22912 , that is only available in TeX-mode.
22915 \begin_layout Standard
22919 \begin_layout Plain Layout
22929 \begin_inset Note Note
22932 \begin_layout Plain Layout
22933 The following table will only be displayed when the LaTeX-package
22945 \begin_layout Standard
22946 An overview about the different Euro symbols:
22949 \begin_layout Standard
22951 \begin_inset Tabular
22952 <lyxtabular version="3" rows="4" columns="3">
22953 <features tabularvalignment="middle">
22954 <column alignment="center" valignment="top" width="0pt">
22955 <column alignment="center" valignment="top" width="0pt">
22956 <column alignment="center" valignment="top" width="0pt">
22958 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
22961 \begin_layout Plain Layout
22967 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22970 \begin_layout Plain Layout
22976 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22979 \begin_layout Plain Layout
22987 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22990 \begin_layout Plain Layout
22996 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22999 \begin_layout Plain Layout
23007 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23010 \begin_layout Plain Layout
23011 \begin_inset Formula $\euro$
23021 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23024 \begin_layout Plain Layout
23030 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23033 \begin_layout Plain Layout
23039 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23042 \begin_layout Plain Layout
23043 \begin_inset Formula $\mbox{€}$
23053 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23056 \begin_layout Plain Layout
23062 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23065 \begin_layout Plain Layout
23073 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23076 \begin_layout Plain Layout
23080 \begin_layout Plain Layout
23102 \begin_layout Standard
23106 \begin_layout Plain Layout
23116 \begin_inset Note Note
23119 \begin_layout Plain Layout
23120 The following will be displayed when the LaTeX-package
23132 \begin_layout Standard
23133 You need to install the LaTeX-package
23137 to see the rest of this subsection in the output.
23140 \begin_layout Standard
23144 \begin_layout Plain Layout
23156 \begin_layout Section
23158 \begin_inset CommandInset label
23160 name "sec:Relations"
23165 \begin_inset Index idx
23168 \begin_layout Plain Layout
23175 \begin_inset Index idx
23178 \begin_layout Plain Layout
23183 \begin_layout Plain Layout
23194 \begin_layout Plain Layout
23209 \begin_layout Standard
23210 All relations can also be inserted via the toolbar button
23211 \begin_inset Graphics
23212 filename ../images/math/leq.png
23220 \begin_layout Standard
23221 \begin_inset space \hfill{}
23225 \begin_inset Tabular
23226 <lyxtabular version="3" rows="17" columns="2">
23227 <features tabularvalignment="middle">
23228 <column alignment="center" valignment="top" width="0pt">
23229 <column alignment="center" valignment="top" width="0pt">
23231 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23234 \begin_layout Plain Layout
23240 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23243 \begin_layout Plain Layout
23251 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23254 \begin_layout Plain Layout
23260 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23263 \begin_layout Plain Layout
23264 \begin_inset Formula $<$
23274 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23277 \begin_layout Plain Layout
23285 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23288 \begin_layout Plain Layout
23289 \begin_inset Formula $\le$
23299 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23302 \begin_layout Plain Layout
23310 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23313 \begin_layout Plain Layout
23314 \begin_inset Formula $\ll$
23324 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23327 \begin_layout Plain Layout
23335 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23338 \begin_layout Plain Layout
23339 \begin_inset Formula $\prec$
23349 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23352 \begin_layout Plain Layout
23360 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23363 \begin_layout Plain Layout
23364 \begin_inset Formula $\preceq$
23374 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23377 \begin_layout Plain Layout
23385 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23388 \begin_layout Plain Layout
23389 \begin_inset Formula $\subset$
23399 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23402 \begin_layout Plain Layout
23410 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23413 \begin_layout Plain Layout
23414 \begin_inset Formula $\subseteq$
23424 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23427 \begin_layout Plain Layout
23435 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23438 \begin_layout Plain Layout
23439 \begin_inset Formula $\sqsubseteq$
23449 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23452 \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 $\in$
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 $\vdash$
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 $\smile$
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 $\lhd$
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 $\unlhd$
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 $\gtrless$
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 $\mid$
23624 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23627 \begin_layout Plain Layout
23635 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23638 \begin_layout Plain Layout
23639 \begin_inset Formula $\nmid$
23653 \begin_inset space \hfill{}
23657 \begin_inset Tabular
23658 <lyxtabular version="3" rows="17" columns="2">
23659 <features tabularvalignment="middle">
23660 <column alignment="center" valignment="top" width="0pt">
23661 <column alignment="center" valignment="top" width="0pt">
23663 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23666 \begin_layout Plain Layout
23672 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23675 \begin_layout Plain Layout
23683 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23686 \begin_layout Plain Layout
23692 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23695 \begin_layout Plain Layout
23696 \begin_inset Formula $=$
23706 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23709 \begin_layout Plain Layout
23717 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23720 \begin_layout Plain Layout
23721 \begin_inset Formula $\not=$
23731 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23734 \begin_layout Plain Layout
23742 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23745 \begin_layout Plain Layout
23746 \begin_inset Formula $\equiv$
23756 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23759 \begin_layout Plain Layout
23767 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23770 \begin_layout Plain Layout
23771 \begin_inset Formula $\sim$
23781 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23784 \begin_layout Plain Layout
23792 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23795 \begin_layout Plain Layout
23796 \begin_inset Formula $\simeq$
23806 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23809 \begin_layout Plain Layout
23817 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23820 \begin_layout Plain Layout
23821 \begin_inset Formula $\approx$
23831 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23834 \begin_layout Plain Layout
23842 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23845 \begin_layout Plain Layout
23846 \begin_inset Formula $\cong$
23856 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23859 \begin_layout Plain Layout
23867 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23870 \begin_layout Plain Layout
23871 \begin_inset Formula $\bowtie$
23881 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23884 \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 $\notin$
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 $\perp$
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 $\propto$
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 $\asymp$
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 $\doteq$
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 $\circeq$
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 $\models$
24056 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24059 \begin_layout Plain Layout
24067 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24070 \begin_layout Plain Layout
24071 \begin_inset Formula $\widehat{=}$
24085 \begin_inset space \hfill{}
24089 \begin_inset Tabular
24090 <lyxtabular version="3" rows="17" columns="2">
24091 <features tabularvalignment="middle">
24092 <column alignment="center" valignment="top" width="0pt">
24093 <column alignment="center" valignment="top" width="0pt">
24095 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24098 \begin_layout Plain Layout
24104 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24107 \begin_layout Plain Layout
24115 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24118 \begin_layout Plain Layout
24124 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24127 \begin_layout Plain Layout
24128 \begin_inset Formula $>$
24138 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24141 \begin_layout Plain Layout
24149 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24152 \begin_layout Plain Layout
24153 \begin_inset Formula $\ge$
24163 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24166 \begin_layout Plain Layout
24174 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24177 \begin_layout Plain Layout
24178 \begin_inset Formula $\gg$
24188 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24191 \begin_layout Plain Layout
24199 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24202 \begin_layout Plain Layout
24203 \begin_inset Formula $\succ$
24213 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24216 \begin_layout Plain Layout
24224 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24227 \begin_layout Plain Layout
24228 \begin_inset Formula $\succeq$
24238 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24241 \begin_layout Plain Layout
24249 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24252 \begin_layout Plain Layout
24253 \begin_inset Formula $\supset$
24263 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24266 \begin_layout Plain Layout
24274 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24277 \begin_layout Plain Layout
24278 \begin_inset Formula $\supseteq$
24288 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24291 \begin_layout Plain Layout
24299 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24302 \begin_layout Plain Layout
24303 \begin_inset Formula $\sqsupseteq$
24313 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24316 \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 $\ni$
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 $\dashv$
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 $\frown$
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 $\rhd$
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 $\unrhd$
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 $\lessgtr$
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 $\parallel$
24488 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24491 \begin_layout Plain Layout
24499 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24502 \begin_layout Plain Layout
24503 \begin_inset Formula $\nparallel$
24517 \begin_inset space \hfill{}
24523 \begin_layout Standard
24524 \begin_inset VSpace medskip
24539 are bigger than the equal looking operators
24554 \begin_layout Standard
24555 Relations are, in contrary to symbols, always surrounded by space.
24558 \begin_layout Standard
24559 Relations with labels can be created with the command
24566 \begin_inset Index idx
24569 \begin_layout Plain Layout
24580 \begin_layout Standard
24582 \begin_inset Tabular
24583 <lyxtabular version="3" rows="2" columns="2">
24584 <features tabularvalignment="middle">
24585 <column alignment="center" valignment="top" width="0">
24586 <column alignment="center" valignment="top" width="0">
24588 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24591 \begin_layout Plain Layout
24597 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24600 \begin_layout Plain Layout
24602 \begin_inset Note Note
24605 \begin_layout Plain Layout
24612 is only used as spacer.
24624 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24627 \begin_layout Plain Layout
24634 \begin_layout Plain Layout
24651 \begin_layout Plain Layout
24661 \begin_inset Formula $\downarrow$
24670 \begin_layout Plain Layout
24683 \begin_layout Plain Layout
24697 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24700 \begin_layout Plain Layout
24701 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
24717 \begin_layout Section
24721 \begin_layout Subsection
24722 Predefined Functions
24723 \begin_inset CommandInset label
24725 name "sub:Predefined-Functions"
24730 \begin_inset Index idx
24733 \begin_layout Plain Layout
24734 Functions ! predefined
24742 \begin_layout Standard
24743 In general, variables are set
24747 in mathematical expressions, but not function names, because
24748 \begin_inset Formula $sin$
24751 could be misunderstood as
24752 \begin_inset Formula $s\cdot i\cdot n$
24756 Therefore there are predefined functions, that are additionally a bit separated
24758 They are inserted as commands starting with a backslash before their name.
24761 \begin_layout Standard
24763 \begin_inset Tabular
24764 <lyxtabular version="3" rows="2" columns="4">
24765 <features tabularvalignment="middle">
24766 <column alignment="center" valignment="top" width="0pt">
24767 <column alignment="center" valignment="top" width="0pt">
24768 <column alignment="center" valignment="top" width="0pt">
24769 <column alignment="center" valignment="top" width="0pt">
24771 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24774 \begin_layout Plain Layout
24780 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24783 \begin_layout Plain Layout
24789 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24792 \begin_layout Plain Layout
24798 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24801 \begin_layout Plain Layout
24809 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24812 \begin_layout Plain Layout
24818 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24821 \begin_layout Plain Layout
24822 \begin_inset Formula $Asin(x)+B$
24830 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24833 \begin_layout Plain Layout
24841 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24844 \begin_layout Plain Layout
24845 \begin_inset Formula $A\sin(x)+B$
24861 \begin_layout Standard
24862 The following functions are predefined:
24865 \begin_layout Standard
24866 \begin_inset VSpace -2mm
24872 \begin_layout Standard
24874 \begin_inset Tabular
24875 <lyxtabular version="3" rows="9" columns="4">
24876 <features tabularvalignment="middle">
24877 <column alignment="center" valignment="top" width="0pt">
24878 <column alignment="center" valignment="top" width="0pt">
24879 <column alignment="center" valignment="top" width="0pt">
24880 <column alignment="center" valignment="top" width="0pt">
24882 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24885 \begin_layout Plain Layout
24891 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24894 \begin_layout Plain Layout
24900 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24903 \begin_layout Plain Layout
24909 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24912 \begin_layout Plain Layout
24920 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24923 \begin_layout Plain Layout
24931 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24934 \begin_layout Plain Layout
24942 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24945 \begin_layout Plain Layout
24953 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24956 \begin_layout Plain Layout
24966 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24969 \begin_layout Plain Layout
24977 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24980 \begin_layout Plain Layout
24988 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24991 \begin_layout Plain Layout
24999 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25002 \begin_layout Plain Layout
25012 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25015 \begin_layout Plain Layout
25023 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25026 \begin_layout Plain Layout
25034 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25037 \begin_layout Plain Layout
25045 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25048 \begin_layout Plain Layout
25058 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25061 \begin_layout Plain Layout
25069 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25072 \begin_layout Plain Layout
25080 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25083 \begin_layout Plain Layout
25091 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25094 \begin_layout Plain Layout
25104 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25107 \begin_layout Plain Layout
25115 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25118 \begin_layout Plain Layout
25126 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25129 \begin_layout Plain Layout
25137 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25140 \begin_layout Plain Layout
25150 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25153 \begin_layout Plain Layout
25161 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25164 \begin_layout Plain Layout
25172 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25175 \begin_layout Plain Layout
25183 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25186 \begin_layout Plain Layout
25196 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25199 \begin_layout Plain Layout
25207 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25210 \begin_layout Plain Layout
25218 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25221 \begin_layout Plain Layout
25229 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25232 \begin_layout Plain Layout
25242 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25245 \begin_layout Plain Layout
25253 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25256 \begin_layout Plain Layout
25264 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25267 \begin_layout Plain Layout
25275 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25278 \begin_layout Plain Layout
25294 \begin_layout Standard
25295 They can also be inserted with the math toolbar button
25296 \begin_inset Graphics
25297 filename ../images/math/functions.png
25305 \begin_layout Subsection
25306 Self-defined Functions
25307 \begin_inset Index idx
25310 \begin_layout Plain Layout
25311 Functions ! self-defined
25319 \begin_layout Standard
25320 To use a function that is not predefined, like for example the sign function
25321 sgn(x), there are two possibilities:
25324 \begin_layout Itemize
25325 Define the function by inserting the following line to the LaTeX-preamble
25329 \begin_layout Plain Layout
25334 DeclareMathOperator
25337 \begin_inset CommandInset ref
25339 reference "sub:Self-defined-Operators"
25349 \begin_inset Newline newline
25353 \begin_inset VSpace -3mm
25357 \begin_inset Newline newline
25364 DeclareMathOperator{
25369 \begin_inset Index idx
25372 \begin_layout Plain Layout
25377 DeclareMathOperator
25383 \begin_inset Newline newline
25387 \begin_inset VSpace -2mm
25391 \begin_inset Newline newline
25394 Now the new defined function can be called with the command
25403 \begin_layout Itemize
25404 Write the formula as usual, mark the formula name, in our example the letters
25409 , and change it to mathematical text.
25410 At last a space is inserted between prefactor and function.
25413 \begin_layout Standard
25414 The result is the same with both methods as with a predefined function
25418 \begin_layout Plain Layout
25419 In LyX self-defined functions are displayed red, predefined ones black.
25427 \begin_layout Standard
25429 \begin_inset Tabular
25430 <lyxtabular version="3" rows="3" columns="2">
25431 <features tabularvalignment="middle">
25432 <column alignment="center" valignment="top" width="0pt">
25433 <column alignment="center" valignment="top" width="0pt">
25435 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25438 \begin_layout Plain Layout
25444 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25447 \begin_layout Plain Layout
25455 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25458 \begin_layout Plain Layout
25466 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25469 \begin_layout Plain Layout
25470 \begin_inset Formula $A\sgn(x)+B$
25480 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25483 \begin_layout Plain Layout
25487 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
25495 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25498 \begin_layout Plain Layout
25499 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
25515 \begin_layout Standard
25516 The first method is more suitable when the self-defined function should
25517 be used several times.
25520 \begin_layout Subsection
25522 \begin_inset Index idx
25525 \begin_layout Plain Layout
25534 \begin_layout Standard
25535 For limits there are defined besides
25542 \begin_inset Index idx
25545 \begin_layout Plain Layout
25565 furthermore the following functions:
25568 \begin_layout Standard
25570 \begin_inset Tabular
25571 <lyxtabular version="3" rows="5" columns="2">
25572 <features tabularvalignment="middle">
25573 <column alignment="center" valignment="top" width="0">
25574 <column alignment="center" valignment="top" width="0">
25576 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25579 \begin_layout Plain Layout
25585 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25588 \begin_layout Plain Layout
25590 \begin_inset Note Note
25593 \begin_layout Plain Layout
25600 is only used as spacer.
25612 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25615 \begin_layout Plain Layout
25623 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25626 \begin_layout Plain Layout
25627 \begin_inset Formula $\varliminf$
25637 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25640 \begin_layout Plain Layout
25648 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25651 \begin_layout Plain Layout
25652 \begin_inset Formula $\varlimsup$
25662 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25665 \begin_layout Plain Layout
25673 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25676 \begin_layout Plain Layout
25677 \begin_inset Formula $\varprojlim$
25687 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25690 \begin_layout Plain Layout
25698 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25701 \begin_layout Plain Layout
25702 \begin_inset Formula $\varinjlim$
25706 \begin_inset Formula $\raisebox{-2.5mm}{}$
25722 \begin_layout Standard
25723 \begin_inset VSpace medskip
25726 The limit is created by inserting a subscript.
25727 It is set right beside the function in an inline formula:
25730 \begin_layout Standard
25732 \begin_inset Tabular
25733 <lyxtabular version="3" rows="2" columns="2">
25734 <features tabularvalignment="middle">
25735 <column alignment="center" valignment="top" width="0pt">
25736 <column alignment="center" valignment="top" width="0pt">
25738 <cell alignment="center" valignment="top" usebox="none">
25741 \begin_layout Plain Layout
25747 <cell alignment="center" valignment="top" usebox="none">
25750 \begin_layout Plain Layout
25751 \begin_inset space \hspace{}
25756 \begin_inset Note Note
25759 \begin_layout Plain Layout
25766 are used here as spacer.
25778 <cell alignment="center" valignment="top" usebox="none">
25781 \begin_layout Plain Layout
25790 \begin_layout Plain Layout
25803 \begin_layout Plain Layout
25817 <cell alignment="center" valignment="top" usebox="none">
25820 \begin_layout Plain Layout
25821 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
25837 \begin_layout Standard
25838 In a displayed formula the limit is set below the formula, as usual:
25839 \begin_inset Formula \[
25847 \begin_layout Subsection
25849 \begin_inset Index idx
25852 \begin_layout Plain Layout
25853 Functions ! modulo-
25861 \begin_layout Standard
25862 The modulo-function is special, because it exists in four variants.
25865 \begin_layout Standard
25866 The variants in a displayed formula:
25867 \begin_inset Formula \begin{align*}
25868 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25869 \mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
25870 \mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
25871 \mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
25872 \mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b
25880 \begin_layout Standard
25881 In an inline formula less space is set before the function names for all
25885 \begin_layout Section
25887 \begin_inset Index idx
25890 \begin_layout Plain Layout
25899 \begin_layout Subsection
25900 Special Characters in Mathematical Text
25903 \begin_layout Standard
25904 The following commands can only be used in mathematical text or in TeX-mode:
25907 \begin_layout Standard
25908 \begin_inset space \hfill{}
25912 \begin_inset Tabular
25913 <lyxtabular version="3" rows="8" columns="2">
25914 <features tabularvalignment="middle">
25915 <column alignment="block" valignment="top" width="0">
25916 <column alignment="block" valignment="top" width="0">
25918 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25921 \begin_layout Plain Layout
25927 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25930 \begin_layout Plain Layout
25938 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25941 \begin_layout Plain Layout
25949 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25952 \begin_layout Plain Layout
25953 \begin_inset Formula $\textrm{œ}$
25963 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25966 \begin_layout Plain Layout
25974 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25977 \begin_layout Plain Layout
25978 \begin_inset Formula $\textrm{Œ}$
25988 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25991 \begin_layout Plain Layout
25999 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26002 \begin_layout Plain Layout
26003 \begin_inset Formula $\textrm{æ}$
26013 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26016 \begin_layout Plain Layout
26024 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26027 \begin_layout Plain Layout
26028 \begin_inset Formula $\textrm{Æ}$
26038 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26041 \begin_layout Plain Layout
26049 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26052 \begin_layout Plain Layout
26053 \begin_inset Formula $\textrm{\aa}$
26063 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26066 \begin_layout Plain Layout
26070 \begin_inset Index idx
26073 \begin_layout Plain Layout
26080 \begin_layout Plain Layout
26101 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26104 \begin_layout Plain Layout
26105 \begin_inset Formula $\textrm{Å}$
26115 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26118 \begin_layout Plain Layout
26126 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26129 \begin_layout Plain Layout
26130 \begin_inset Formula $\textrm{ı}$
26144 \begin_inset space \hfill{}
26148 \begin_inset Tabular
26149 <lyxtabular version="3" rows="8" columns="2">
26150 <features tabularvalignment="middle">
26151 <column alignment="block" valignment="top" width="0">
26152 <column alignment="center" valignment="top" width="0">
26154 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26157 \begin_layout Plain Layout
26159 \begin_inset Note Note
26162 \begin_layout Plain Layout
26164 \begin_inset space \thinspace{}
26167 mm is used for separation, because otherwise the output will be ¡ and ¿
26178 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26181 \begin_layout Plain Layout
26189 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26192 \begin_layout Plain Layout
26200 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26203 \begin_layout Plain Layout
26204 \begin_inset Formula $\textrm{ø}$
26214 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26217 \begin_layout Plain Layout
26225 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26228 \begin_layout Plain Layout
26229 \begin_inset Formula $\textrm{Ø}$
26239 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26242 \begin_layout Plain Layout
26250 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26253 \begin_layout Plain Layout
26254 \begin_inset Formula $\textrm{ł}$
26264 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26267 \begin_layout Plain Layout
26275 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26278 \begin_layout Plain Layout
26279 \begin_inset Formula $\textrm{Ł}$
26289 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26292 \begin_layout Plain Layout
26294 \begin_inset space \hspace{}
26302 \begin_layout Plain Layout
26316 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26319 \begin_layout Plain Layout
26320 \begin_inset Formula $\textrm{!`}$
26330 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26333 \begin_layout Plain Layout
26335 \begin_inset space \hspace{}
26343 \begin_layout Plain Layout
26357 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26360 \begin_layout Plain Layout
26361 \begin_inset Formula $\textrm{?`}$
26371 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26374 \begin_layout Plain Layout
26382 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26385 \begin_layout Plain Layout
26386 \begin_inset Formula $\textrm{ȷ}$
26400 \begin_inset space \hfill{}
26406 \begin_layout Standard
26408 \begin_inset Formula $\textrm{\textrm{Å}}$
26412 \begin_inset Formula $\textrm{\textrm{Ø}}$
26415 can also be inserted via the math toolbar button
26416 \begin_inset Graphics
26417 filename ../images/math/digamma.png
26425 \begin_layout Standard
26426 An exception are the commands
26429 \begin_inset space \hspace{}
26438 \begin_inset space \hspace{}
26444 , because they can be inserted in LyX directly to text.
26447 \begin_layout Subsection
26449 \begin_inset CommandInset label
26451 name "sub:Accents-in-Text"
26456 \begin_inset Index idx
26459 \begin_layout Plain Layout
26468 \begin_layout Standard
26469 With the following commands all letters can be accented.
26470 The commands must be inserted in TeX-mode.
26473 \begin_layout Standard
26474 \begin_inset space \hfill{}
26478 \begin_inset Tabular
26479 <lyxtabular version="3" rows="8" columns="2">
26480 <features tabularvalignment="middle">
26481 <column alignment="block" valignment="top" width="0">
26482 <column alignment="block" valignment="top" width="0">
26484 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26487 \begin_layout Plain Layout
26493 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26496 \begin_layout Plain Layout
26504 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26507 \begin_layout Plain Layout
26511 \begin_inset Quotes grd
26519 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26522 \begin_layout Plain Layout
26526 \begin_layout Plain Layout
26542 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26545 \begin_layout Plain Layout
26553 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26556 \begin_layout Plain Layout
26560 \begin_layout Plain Layout
26576 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26579 \begin_layout Plain Layout
26586 \begin_layout Plain Layout
26600 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26603 \begin_layout Plain Layout
26607 \begin_layout Plain Layout
26623 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26626 \begin_layout Plain Layout
26634 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26637 \begin_layout Plain Layout
26641 \begin_layout Plain Layout
26657 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26660 \begin_layout Plain Layout
26667 \begin_layout Plain Layout
26681 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26684 \begin_layout Plain Layout
26688 \begin_layout Plain Layout
26704 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26707 \begin_layout Plain Layout
26714 \begin_layout Plain Layout
26728 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26731 \begin_layout Plain Layout
26735 \begin_layout Plain Layout
26751 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26754 \begin_layout Plain Layout
26761 \begin_layout Plain Layout
26775 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26778 \begin_layout Plain Layout
26782 \begin_layout Plain Layout
26802 \begin_inset space \hfill{}
26806 \begin_inset Tabular
26807 <lyxtabular version="3" rows="8" columns="2">
26808 <features tabularvalignment="middle">
26809 <column alignment="block" valignment="top" width="0">
26810 <column alignment="center" valignment="top" width="0">
26812 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26815 \begin_layout Plain Layout
26821 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26824 \begin_layout Plain Layout
26832 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26835 \begin_layout Plain Layout
26842 \begin_layout Plain Layout
26856 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26859 \begin_layout Plain Layout
26863 \begin_layout Plain Layout
26879 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26882 \begin_layout Plain Layout
26890 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26893 \begin_layout Plain Layout
26897 \begin_layout Plain Layout
26913 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26916 \begin_layout Plain Layout
26920 \begin_inset Index idx
26923 \begin_layout Plain Layout
26934 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26937 \begin_layout Plain Layout
26941 \begin_layout Plain Layout
26957 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26960 \begin_layout Plain Layout
26968 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26971 \begin_layout Plain Layout
26975 \begin_layout Plain Layout
26991 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26994 \begin_layout Plain Layout
27001 \begin_layout Plain Layout
27015 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27018 \begin_layout Plain Layout
27022 \begin_layout Plain Layout
27038 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27041 \begin_layout Plain Layout
27048 \begin_layout Plain Layout
27062 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27065 \begin_layout Plain Layout
27069 \begin_layout Plain Layout
27085 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27088 \begin_layout Plain Layout
27095 \begin_layout Plain Layout
27109 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27112 \begin_layout Plain Layout
27116 \begin_layout Plain Layout
27136 \begin_inset space \hfill{}
27142 \begin_layout Standard
27143 \begin_inset VSpace medskip
27152 also two different characters can be accented.
27161 \begin_layout Plain Layout
27176 \begin_layout Plain Layout
27188 \begin_layout Standard
27201 can in combination with vowels directly be inserted with the keyboard without
27203 The same applies for the tilde
27207 \begin_layout Plain Layout
27208 This only applies for keyboards where the tilde is defined as accent.
27217 in combination with
27232 \begin_layout Standard
27275 and accents that are inserted directly with the keyboard are also available
27276 in mathematical text.
27277 For the other accents there are special math commands to be used in formulas,
27279 \begin_inset CommandInset ref
27281 reference "sub:Accents-for-one"
27288 \begin_layout Standard
27289 \begin_inset VSpace bigskip
27292 Furthermore, with the command
27299 \begin_inset Index idx
27302 \begin_layout Plain Layout
27310 all numbers and letters can be set into a circle, quasi accented with a
27311 circle, similar to the copyright symbol.
27314 \begin_layout Standard
27316 \begin_inset Tabular
27317 <lyxtabular version="3" rows="3" columns="2">
27318 <features tabularvalignment="middle">
27319 <column alignment="center" valignment="top" width="0">
27320 <column alignment="center" valignment="top" width="0">
27322 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27325 \begin_layout Plain Layout
27331 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27334 \begin_layout Plain Layout
27336 \begin_inset Note Note
27339 \begin_layout Plain Layout
27346 is only used as spacer.
27358 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27361 \begin_layout Plain Layout
27369 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27372 \begin_layout Plain Layout
27376 \begin_layout Plain Layout
27392 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27395 \begin_layout Plain Layout
27406 raisebox{-1.5pt}{W}}
27411 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27414 \begin_layout Plain Layout
27415 \begin_inset Formula $\raisebox{4.5mm}{}$
27422 \begin_layout Plain Layout
27440 \begin_inset Formula $\raisebox{-2mm}{}$
27456 \begin_layout Standard
27457 One has to take care that the character fits in the circle.
27468 \begin_layout Plain Layout
27470 \begin_inset CommandInset ref
27472 reference "sub:Font-Sizes"
27481 specifies thereby the size of the circle.
27492 \begin_layout Plain Layout
27494 \begin_inset CommandInset ref
27496 reference "sub:Boxes-without-Frame"
27505 the character can be centered.
27508 \begin_layout Subsection
27510 \begin_inset Index idx
27513 \begin_layout Plain Layout
27522 \begin_layout Standard
27523 Minuscule numbers are created with the command
27530 \begin_inset Index idx
27533 \begin_layout Plain Layout
27542 The command can be used in formulas and in TeX-mode.
27543 The command scheme is:
27546 \begin_layout Standard
27551 oldstylenums{number}
27554 \begin_layout Standard
27559 oldstylenums{0123456789
27562 \begin_inset Formula $\oldstylenums{0123456789}$
27568 \begin_layout Subsection
27569 Miscellaneous special Characters
27570 \begin_inset CommandInset label
27572 name "sub:Miscellaneous-special-Characters"
27577 \begin_inset Index idx
27580 \begin_layout Plain Layout
27581 Special characters ! miscellaneous
27589 \begin_layout Standard
27590 The following characters can only be inserted to formulas by using commands:
27593 \begin_layout Standard
27595 \begin_inset Tabular
27596 <lyxtabular version="3" rows="4" columns="2">
27597 <features tabularvalignment="middle">
27598 <column alignment="center" valignment="top" width="0">
27599 <column alignment="center" valignment="top" width="0">
27601 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27604 \begin_layout Plain Layout
27610 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27613 \begin_layout Plain Layout
27621 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27624 \begin_layout Plain Layout
27631 \begin_layout Plain Layout
27645 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27648 \begin_layout Plain Layout
27649 \begin_inset Formula $\mathcircumflex$
27659 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27662 \begin_layout Plain Layout
27670 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27673 \begin_layout Plain Layout
27674 \begin_inset Formula $\_$
27684 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27687 \begin_layout Plain Layout
27692 \begin_layout Plain Layout
27704 \begin_inset Index idx
27707 \begin_layout Plain Layout
27720 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27723 \begin_layout Plain Layout
27724 \begin_inset Formula $^{\circ}$
27740 \begin_layout Standard
27741 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
27742 contains the following line
27746 \begin_layout Plain Layout
27747 More about this is described in
27748 \begin_inset CommandInset ref
27750 reference "sub:Text-Characters-in"
27762 \begin_layout Standard
27767 DeclareInputtext{176}{
27780 \begin_layout Section
27782 \begin_inset CommandInset label
27784 name "sec:Formula-Styles"
27789 \begin_inset Index idx
27792 \begin_layout Plain Layout
27801 \begin_layout Itemize
27802 There are two different alignment styles:
27806 \begin_layout Description
27807 Centered is the predefined standard
27810 \begin_layout Description
27811 Indented for this the option
27815 must be inserted in the menu
27817 Document\SpecialChar \menuseparator
27823 \begin_inset space ~
27829 \begin_layout Standard
27834 is used, the indentation can be adjusted with the length
27841 \begin_inset Index idx
27844 \begin_layout Plain Layout
27853 Should the distance be 15
27854 \begin_inset space \thinspace{}
27857 mm, the following command line is inserted in the LaTeX-preamble
27860 \begin_layout Standard
27870 \begin_layout Standard
27871 When no length is specified, the predefined value of 30
27872 \begin_inset space \thinspace{}
27879 \begin_layout Itemize
27880 And two different numbering styles:
27884 \begin_layout Description
27885 Right is the predefined standard
27888 \begin_layout Description
27889 Left for this the option
27893 must be inserted in the menu
27895 Document\SpecialChar \menuseparator
27901 \begin_inset space ~
27908 \begin_layout Standard
27917 can also be used together.
27918 In this case both options are inserted, separated by a comma.
27921 \begin_layout Standard
27922 The chosen styles are used for all displayed formulas of the document.
27923 When both, centered and indented formulas should be created in a document,
27929 The indented formulas are then set in a flalign environment, see
27930 \begin_inset CommandInset ref
27932 reference "sub:Flalign-Environment"
27939 \begin_layout Section
27941 \begin_inset CommandInset label
27943 name "sec:Multiline-Formulas"
27948 \begin_inset Index idx
27951 \begin_layout Plain Layout
27952 Formula ! multiline
27960 \begin_layout Subsection
27964 \begin_layout Standard
27965 In LyX multiline formulas are created by pressing
27970 arg "newline-insert newline"
27976 This creates either an
27978 eqnarray environment
27980 that is described in
27981 \begin_inset CommandInset ref
27983 reference "sub:Eqnarray-Environment"
27987 or, when the option
27989 Use AMS math package
27991 in the document settings is selected, an
27995 that is described in
27996 \begin_inset CommandInset ref
27998 reference "sub:Standard-align-Environment"
28005 \begin_layout Standard
28006 There are other multiline formula environments that can be created via the
28009 Insert\SpecialChar \menuseparator
28013 These environments are described in the following sections.
28016 \begin_layout Standard
28017 In all multiline formula environments a new line is created by pressing
28021 arg "newline-insert newline"
28025 To add or delete lines, the math toolbar buttons
28026 \begin_inset Graphics
28027 filename ../images/tabular-feature_append-row.png
28033 \begin_inset Graphics
28034 filename ../images/tabular-feature_delete-row.png
28039 , respectively, or the menu
28041 Edit\SpecialChar \menuseparator
28047 \begin_layout Subsubsection
28049 \begin_inset CommandInset label
28051 name "sub:Line-Separation"
28056 \begin_inset Index idx
28059 \begin_layout Plain Layout
28060 Formula ! multiline ! Line separation
28068 \begin_layout Standard
28069 There is sometimes not enough space in multiline formulas between the lines:
28070 \begin_inset Formula \begin{eqnarray*}
28071 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}\\
28072 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
28080 \begin_layout Standard
28081 In LaTeX additional line space is specified as optional argument of the
28083 This is not yet possible in LyX
28087 \begin_layout Plain Layout
28089 \begin_inset CommandInset href
28091 name "LyX-bug #1505"
28092 target "http://www.lyx.org/trac/ticket/1505"
28101 , therefore the whole formula must be inserted in TeX-mode.
28102 To add in our example space, the command
28110 is inserted at the end of the first line.
28115 \begin_layout Plain Layout
28122 \begin_layout Plain Layout
28124 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
28127 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
28134 \begin_layout Plain Layout
28138 left(B^{2}+x_{0}^{2}
28146 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
28151 \begin_layout Plain Layout
28163 \begin_layout Standard
28164 \begin_inset VSpace bigskip
28167 To set the line separation for all lines in a formula, the length
28174 \begin_inset Index idx
28177 \begin_layout Plain Layout
28187 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
28198 \begin_inset space \thinspace{}
28203 \begin_inset space \thinspace{}
28206 mm additional line separation as in the previous example, the command
28209 \begin_layout Standard
28219 \begin_layout Standard
28220 is inserted in TeX-mode before the formula.
28221 This requires that the LaTeX-package
28229 \begin_layout Plain Layout
28234 is part of every LaTeX standard installation.
28240 \begin_inset Index idx
28243 \begin_layout Plain Layout
28249 was loaded in LaTeX-preamble with the line
28252 \begin_layout Standard
28260 \begin_layout Standard
28265 \begin_layout Plain Layout
28277 \begin_inset Formula \begin{eqnarray*}
28278 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}\\
28279 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
28287 \begin_layout Standard
28291 \begin_layout Plain Layout
28302 To get back to the predefined distance,
28308 is set to the value 3
28309 \begin_inset space \thinspace{}
28315 \begin_layout Subsubsection
28317 \begin_inset CommandInset label
28319 name "sub:Column-Separation"
28324 \begin_inset Index idx
28327 \begin_layout Plain Layout
28328 Formula ! multiline ! Column separation
28336 \begin_layout Standard
28337 Multiline formulas form a matrix.
28338 A formula in the eqnarray environment is for example a matrix with three
28340 By changing the column separation in this environment, the space beside
28341 the relation sign can be changed.
28344 \begin_layout Standard
28345 The column separation is specified with the length
28352 \begin_inset Index idx
28355 \begin_layout Plain Layout
28364 \begin_inset Newline newline
28367 column separation = 2
28368 \begin_inset space \thinspace{}
28378 \begin_inset Newline newline
28384 \begin_layout Standard
28394 \begin_layout Standard
28395 inserted in TeX-mode, sets for all following formulas a column separation
28397 \begin_inset space \thinspace{}
28401 To get back to the predefined distance,
28408 \begin_inset space \thinspace{}
28414 \begin_layout Standard
28416 \begin_inset space \thinspace{}
28419 cm column separation:
28423 \begin_layout Plain Layout
28435 \begin_inset Formula \begin{eqnarray*}
28442 A formula with the predefined column separation for matrices of 10
28443 \begin_inset space \thinspace{}
28450 \begin_layout Plain Layout
28462 \begin_inset Formula \begin{eqnarray*}
28472 \begin_layout Subsubsection
28474 \begin_inset Index idx
28477 \begin_layout Plain Layout
28486 \begin_layout Standard
28487 Long formulas can be typeset using these methods:
28490 \begin_layout Itemize
28491 When one side of the equation is much shorther than the line width, this
28492 one is chosen for the left side and the right side is typeset over two
28494 \begin_inset Formula \begin{eqnarray}
28495 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 \\
28496 & & -\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}
28501 The minus sign at the beginning of the second line does normally not appear
28502 as operator because it is the first character of the line.
28503 Thus it would not be surrounded by space and could not be distinguished
28504 from the fraction bar.
28506 \begin_inset space \thinspace{}
28509 pt space was inserted behind the minus sign with the command
28519 \begin_layout Plain Layout
28527 \begin_inset CommandInset ref
28529 reference "sub:Variable-Space"
28539 \begin_inset Index idx
28542 \begin_layout Plain Layout
28553 \begin_layout Itemize
28554 When both sides of the equation are too long, the command
28561 \begin_inset Index idx
28564 \begin_layout Plain Layout
28573 It is inserted to the first column of the first line and effects that all
28574 further insertions overwrite the following columns:
28575 \begin_inset Formula \begin{eqnarray}
28576 \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 \\
28577 & & -\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 \\
28578 & & =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}
28583 After the insertion of
28589 , the cursor is in a purple box that is a bit shifted to the left from the
28591 In this the formula is inserted.
28592 \begin_inset Newline newline
28595 The content of the further lines is inserted to the second or another formula
28597 The greater the column number where it was inserted, the larger the indentation.
28598 \begin_inset VSpace medskip
28602 \begin_inset Newline newline
28606 \begin_inset Note Greyedout
28609 \begin_layout Plain Layout
28610 Note the following when using
28619 \begin_layout Itemize
28620 The formula doesn't use the full page width.
28622 \begin_inset space \thinspace{}
28626 \begin_inset space \space{}
28630 \begin_inset Formula $-B^{2}$
28633 is added to the first line in the above example, it would have been outside
28635 To better use the width, negative space can be inserted at the beginning
28639 \begin_layout Itemize
28640 Due to a bug in LyX the cursor cannot be set with the mouse into the first
28645 \begin_layout Plain Layout
28646 \begin_inset CommandInset href
28648 name "LyX-bug #1429"
28649 target "http://www.lyx.org/trac/ticket/1429"
28658 One can only set the cursor at the beginning of the line and move it with
28667 \begin_layout Itemize
28668 Other methods to set long formulas are offered by the environments described
28670 \begin_inset CommandInset ref
28672 reference "sub:Multline-Environment"
28677 \begin_inset CommandInset ref
28679 reference "sub:Multiline-Formula-Parts"
28686 \begin_layout Subsubsection
28688 \begin_inset CommandInset label
28690 name "sub:Multiline-Brackets"
28695 \begin_inset Index idx
28698 \begin_layout Plain Layout
28699 Brackets ! for multiline expressions
28707 \begin_layout Standard
28708 For brackets spanning multiple lines the following problem occurs:
28709 \begin_inset Formula \begin{eqnarray*}
28710 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28711 & & \left.\cdots+B-D\right]
28719 \begin_layout Standard
28720 The closing bracket is smaller than the opening bracket because brackets
28721 with variable size may not span multiple lines.
28724 \begin_layout Standard
28725 To set the bracket size for the second line correctly, the first line is
28733 \begin_inset Index idx
28736 \begin_layout Plain Layout
28744 and the second line with
28752 \begin_layout Plain Layout
28766 \begin_inset CommandInset ref
28768 reference "sub:Automatic-Bracket-Size"
28780 \begin_inset Index idx
28783 \begin_layout Plain Layout
28809 \begin_layout Plain Layout
28828 \begin_layout Plain Layout
28847 \begin_layout Plain Layout
28859 \begin_inset Formula $\downarrow$
28865 \begin_inset Index idx
28868 \begin_layout Plain Layout
28876 is inserted, because the multiplication operator with its limits is the
28877 largest symbol in the first line and this should be the size for the bracket
28878 in the second line.
28881 \begin_layout Standard
28882 The result is this:
28883 \begin_inset Formula \begin{eqnarray*}
28884 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28885 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
28893 \begin_layout Subsection
28897 \begin_layout Standard
28898 Align environments can be used for every kind of multiline formulas.
28899 They are specially useful to set several formulas side by side.
28902 \begin_layout Standard
28903 Align environments consist of columns.
28904 The odd columns are right aligned, the even ones left aligned.
28905 Every line in an Align environment can be numbered.
28908 \begin_layout Standard
28909 Align environments are created via the menu
28911 Insert\SpecialChar \menuseparator
28917 Edit\SpecialChar \menuseparator
28918 Math\SpecialChar \menuseparator
28919 Change Formula Type
28921 already existing formulas can be converted to Align environments.
28924 \begin_layout Standard
28925 To add or delete columns, the math toolbar buttons
28926 \begin_inset Graphics
28927 filename ../images/tabular-feature_append-column.png
28933 \begin_inset Graphics
28934 filename ../images/tabular-feature_delete-column.png
28939 , respectively, or the menu
28941 Edit\SpecialChar \menuseparator
28947 \begin_layout Subsubsection
28948 Standard align Environment
28949 \begin_inset CommandInset label
28951 name "sub:Standard-align-Environment"
28956 \begin_inset Index idx
28959 \begin_layout Plain Layout
28960 Formula ! multiline ! align environment
28968 \begin_layout Standard
28969 This Align environment is created by presssing
28972 arg "newline-insert newline"
28975 in a formula or by the menu
28977 Insert\SpecialChar \menuseparator
28978 Math\SpecialChar \menuseparator
28979 AMS align Environment
28984 \begin_layout Standard
28985 An example for two formulas set side by side, that are created with a four
28986 column align environment:
28987 \begin_inset Formula \begin{align*}
28988 A & =\sin(B) & C & =D\\
28989 C & \ne A & B & \ne D
28994 As it can be seen, the formulas in this environment are placed so as if
29003 \begin_layout Plain Layout
29011 \begin_inset CommandInset ref
29013 reference "sub:Variable-Space"
29024 before the first and after every even column.
29025 When the formula style
29031 \begin_layout Plain Layout
29033 \begin_inset CommandInset ref
29035 reference "sec:Formula-Styles"
29046 is used, the formula is set without the
29052 before the first column.
29055 \begin_layout Subsubsection
29056 Alignat Environment
29057 \begin_inset Index idx
29060 \begin_layout Plain Layout
29061 Formula ! multiline ! alignat environment
29069 \begin_layout Standard
29070 The alignat environment has no predefined column separation.
29071 It can be inserted manually with the spaces that are described
29072 \begin_inset CommandInset ref
29074 reference "sub:Space"
29081 \begin_layout Standard
29082 The above example in the alignat environment where 1
29083 \begin_inset space \thinspace{}
29086 cm space was inserted at the beginning of the second formula:
29087 \begin_inset Formula \begin{alignat*}{2}
29088 A & =\sin(B) & \hspace{1cm}C & =D\\
29089 C & \ne A & B & \ne D
29094 Because the column separation can be set separately for every column, this
29095 environment is especially suitable to set three and more formulas side
29099 \begin_layout Subsubsection
29100 Flalign Environment
29101 \begin_inset CommandInset label
29103 name "sub:Flalign-Environment"
29108 \begin_inset Index idx
29111 \begin_layout Plain Layout
29112 Formula ! multiline ! flalign environment
29120 \begin_layout Standard
29121 In this environment the first two columns are always set as much as possible
29122 to the left and the last two ones to the right.
29124 \begin_inset Formula \begin{flalign*}
29125 A & =1 & B & =2 & C & =3\\
29126 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
29134 \begin_layout Standard
29135 By creating a flalign environment with an odd number of columns where an
29136 empty TeX-brace is inserted to the last column, several formulas in a document
29137 can be set to the left, although the formula style
29142 As example the indented formula
29143 \begin_inset CommandInset ref
29145 reference "eq:VolInt"
29150 \begin_inset Formula \begin{flalign}
29151 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}\end{flalign}
29155 The first two columns contain the formula.
29156 To indent it as with the formula style
29161 \begin_inset space \thinspace{}
29164 pt space was inserted at the beginning of the first column.
29167 \begin_layout Subsection
29168 Eqnarray Environment
29169 \begin_inset CommandInset label
29171 name "sub:Eqnarray-Environment"
29176 \begin_inset Index idx
29179 \begin_layout Plain Layout
29180 Formula ! multiline ! eqnarray environment
29188 \begin_layout Standard
29189 When this environment has been created, three blue boxes appear.
29190 The content of the first box is right aligned, the content of the last
29192 The content of the middle box appears centered and a bit smaller, because
29193 it is designed to insert there only relation characters.
29194 \begin_inset Formula \begin{eqnarray*}
29195 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
29205 \begin_layout Subsection
29207 \begin_inset Index idx
29210 \begin_layout Plain Layout
29211 Formula ! multiline ! gather environment
29219 \begin_layout Standard
29220 This environment consists of only one centered column.
29221 Every line can be numbered.
29222 \begin_inset Formula \begin{gather}
29232 \begin_layout Subsection
29233 Multline Environment
29234 \begin_inset CommandInset label
29236 name "sub:Multline-Environment"
29241 \begin_inset Index idx
29244 \begin_layout Plain Layout
29245 Formula ! multiline ! multline environment
29253 \begin_layout Standard
29254 The multline environment consists, like the gather environment, of only
29256 But the first line is left aligned, the last one right aligned.
29257 All other lines are centered.
29258 Therefore this environment is suitable for long formulas.
29260 \begin_inset CommandInset ref
29262 reference "eq:lefteqn"
29266 in the multline environment:
29267 \begin_inset Formula \begin{multline}
29268 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}\\
29269 -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}\\
29270 =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}}
29278 \begin_layout Standard
29279 In the output only the last (first) line of a multline environment appears
29280 numbered when the document numbering is right (left).
29284 \begin_layout Plain Layout
29285 numbering styles see
29286 \begin_inset CommandInset ref
29288 reference "sec:Formula-Styles"
29300 \begin_layout Standard
29308 \begin_inset Index idx
29311 \begin_layout Plain Layout
29326 \begin_inset Index idx
29329 \begin_layout Plain Layout
29337 a centered line can be right or left aligned, respectively.
29338 The commands are used as follows:
29341 \begin_layout Standard
29346 shoveright{line content}
29352 shoveleft{line content}
29355 \begin_layout Standard
29356 \begin_inset VSpace medskip
29366 \begin_inset Index idx
29369 \begin_layout Plain Layout
29377 specifies the distance of the first line from the left page margin.
29378 Predefined is the length 0
29379 \begin_inset space \thinspace{}
29385 \begin_layout Standard
29386 As example the above formula where the command
29389 \begin_layout Standard
29399 \begin_layout Standard
29400 was inserted in TeX-mode before:
29404 \begin_layout Plain Layout
29416 \begin_inset Formula \begin{multline}
29417 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}\\
29418 \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}}\\
29419 =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}}
29428 \begin_layout Plain Layout
29439 The second line was left aligned using
29448 \begin_layout Subsection
29449 Multiline Formula Parts
29450 \begin_inset CommandInset label
29452 name "sub:Multiline-Formula-Parts"
29457 \begin_inset Index idx
29460 \begin_layout Plain Layout
29461 Formula ! multiline ! formula parts
29469 \begin_layout Standard
29470 To display only parts of a formula with multiple lines, one of the following
29471 environments are used:
29488 They can be inserted via the menu
29490 Insert\SpecialChar \menuseparator
29493 or by using the commands described in this section.
29496 \begin_layout Standard
29497 The first three have the same properties as the corresponding multiline
29498 formula environments, but it is possible to set further formula parts beside
29501 \begin_inset Formula \[
29502 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29503 \Delta E\Delta t & \ge\frac{\hbar}{2}
29505 \right\} \textrm{Uncertainty relations}\]
29512 \begin_layout Standard
29513 To get this formula, a displayed formula is created where the command
29520 \begin_inset Index idx
29523 \begin_layout Plain Layout
29532 A purple box appears around the blue formula box where now columns and
29533 lines can be added.
29534 Outside the multiline environment other formula parts can be set, like
29538 \begin_layout Standard
29539 The aligned environment is also suitable for long formulas whose lines are
29540 horizontally aligned.
29541 Using aligned in a displayed formula has the advantage that the formula
29542 number is vertically centered behind the lines.
29544 \begin_inset CommandInset ref
29546 reference "eq:shortlong"
29550 in the aligned environment:
29551 \begin_inset Formula \begin{equation}
29552 \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}|}\\
29553 & -\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}|}
29562 \begin_layout Standard
29563 To use the environments
29582 \begin_inset Index idx
29585 \begin_layout Plain Layout
29600 \begin_inset Index idx
29603 \begin_layout Plain Layout
29618 \begin_inset Index idx
29621 \begin_layout Plain Layout
29629 are inserted, respectively.
29630 The split environment has the same properties as the aligned environment
29631 but it can only have two columns.
29634 \begin_layout Subsection
29635 Text in multiline Formulas
29636 \begin_inset CommandInset label
29638 name "sub:Text-in-multiline"
29643 \begin_inset Index idx
29646 \begin_layout Plain Layout
29653 \begin_inset Index idx
29656 \begin_layout Plain Layout
29657 Formula ! multiline ! text
29665 \begin_layout Standard
29666 In the Align environments, and the multline and gather environment, text
29667 can be inserted that will appear in a separate line and doesn't affect
29668 the column alignment.
29669 To do this, the command
29676 \begin_inset Index idx
29679 \begin_layout Plain Layout
29687 is used in the following scheme:
29690 \begin_layout Standard
29698 \begin_layout Standard
29699 The text should not be longer than a line because it cannot be hyphenated.
29700 As LyX doesn't yet support
29706 directly, the text is written as mathematical text.
29713 must hereby be at the beginning of a line and appears in the output above
29715 An example where the text was inserted at the beginning of the second line:
29716 \begin_inset Formula \begin{align}
29717 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29718 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29726 \begin_layout Section
29728 \begin_inset Index idx
29731 \begin_layout Plain Layout
29738 \begin_inset Index idx
29741 \begin_layout Plain Layout
29742 Formula ! numbering|see
29746 \begin_layout Plain Layout
29757 \begin_layout Plain Layout
29772 \begin_layout Subsection
29776 \begin_layout Standard
29777 Numbered formulas can be created with the menu
29779 Insert\SpecialChar \menuseparator
29780 Math\SpecialChar \menuseparator
29782 \begin_inset space ~
29790 \begin_inset space ~
29796 Existing formulas can be numbered with the menu
29798 Edit\SpecialChar \menuseparator
29799 Math\SpecialChar \menuseparator
29801 \begin_inset space ~
29809 arg "math-number-toggle"
29813 The formula number is displayed in LyX behind the formula as number sign
29815 The number sign is replaced in the output by the formula number.
29818 \begin_layout Standard
29819 When numbering is turned on in multiline formulas, all lines will be numbered.
29820 But the numbering can be controlled with the menu
29822 Edit\SpecialChar \menuseparator
29823 Math\SpecialChar \menuseparator
29825 \begin_inset space ~
29829 \begin_inset space ~
29833 \begin_inset space ~
29841 arg "math-number-line-toggle"
29847 \begin_layout Standard
29848 Except for inline formulas, all formulas can be numbered with two different
29850 \begin_inset CommandInset ref
29852 reference "sec:Formula-Styles"
29859 \begin_layout Subsection
29861 \begin_inset Index idx
29864 \begin_layout Plain Layout
29865 Cross-references ! to formulas
29873 \begin_layout Standard
29874 All labeled formulas can be cross-referenced.
29875 A label is added by the menu
29877 Insert\SpecialChar \menuseparator
29880 or the toolbar button
29881 \begin_inset Graphics
29882 filename ../images/label-insert.png
29888 The cursor must hereby be inside a displayed formula.
29889 A dialog pops up displaying the prefix
29894 The label is inserted there behind the prefix.
29895 The predefined prefix means
29896 \begin_inset Quotes eld
29900 \begin_inset Quotes erd
29903 and makes it easier to find labels in large documents because it marks
29904 it as formula label to divide it from e.
29905 \begin_inset space \thinspace{}
29909 \begin_inset space \space{}
29913 To change a label, the menu
29915 Insert\SpecialChar \menuseparator
29921 \begin_layout Standard
29922 The name of the label is displayed in LyX within two parentheses behind
29924 A formula with a label is always numbered.
29927 \begin_layout Standard
29928 Cross-references are inserted via the menu
29930 Insert\SpecialChar \menuseparator
29933 or with the toolbar button
29934 \begin_inset Graphics
29935 filename ../images/dialog-show-new-inset_ref.png
29941 A formula cross-reference appears in the output as formula number.
29942 When in the cross-reference dialog window the format
29946 is chosen, the cross-reference appears in the output as formula number
29948 \begin_inset Newline newline
29951 By right-clicking on a cross-reference in LyX, one jumps to the formula
29952 that is referenced.
29955 \begin_layout Standard
29956 Here are as examples cross-references to formulas of the following subsections:
29957 \begin_inset Note Note
29960 \begin_layout Plain Layout
29961 Note the different cross-reference types.
29969 \begin_layout Standard
29971 \begin_inset CommandInset ref
29978 \begin_inset CommandInset ref
29986 \begin_inset CommandInset ref
29992 ) big Latin letters are used for the numbering in contrary to (
29993 \begin_inset CommandInset ref
30002 \begin_layout Standard
30003 \begin_inset VSpace medskip
30006 When the argument of
30014 \begin_layout Plain Layout
30022 \begin_inset CommandInset ref
30024 reference "sub:User-defined-Numbering"
30035 contains a box like in
30036 \begin_inset CommandInset ref
30038 reference "sub:Paragraph-Boxes"
30042 , the formula cannot be referenced.
30045 \begin_layout Subsection
30047 \begin_inset Index idx
30050 \begin_layout Plain Layout
30051 Formula numbering ! subnumbering
30059 \begin_layout Standard
30060 With the help of the commands
30064 begin{subequations}
30072 formulas can be subnumbered.
30073 Both commands are inserted in TeX-mode.
30076 \begin_layout Standard
30078 \begin_inset Formula \begin{equation}
30079 A=C-B\label{eq:a}\end{equation}
30087 \begin_layout Plain Layout
30091 addtocounter{equation}{-1}
30100 \begin_layout Plain Layout
30104 begin{subequations}
30110 \begin_inset VSpace -5mm
30114 \begin_inset Formula \begin{equation}
30115 B=C-A\label{eq:b}\end{equation}
30120 \begin_inset Formula \begin{equation}
30121 C=A+B\label{eq:c}\end{equation}
30128 \begin_layout Standard
30132 \begin_layout Plain Layout
30144 \begin_layout Standard
30145 To create the example, the following is done:
30148 \begin_layout Enumerate
30149 first formula is inserted
30152 \begin_layout Enumerate
30157 addtocounter{equation}{-1}
30159 begin{subequations}
30160 \begin_inset Index idx
30163 \begin_layout Plain Layout
30172 \begin_inset Newline newline
30177 is inserted after the first formula
30180 \begin_layout Enumerate
30181 second formula is inserted
30184 \begin_layout Enumerate
30185 third formula is inserted
30188 \begin_layout Enumerate
30195 is inserted after the third formula
30198 \begin_layout Standard
30199 Every formula between the commands
30211 is subnumbered as a, b,
30212 \begin_inset Newline linebreak
30215 c, \SpecialChar \ldots{}
30216 For multiline formulas every line will be subnumbered.
30217 All subnumbered formulas are treated as
30222 But as every numbered formula increases the counter
30226 by one, the command
30232 is needed to decrease it.
30233 Otherwise the formulas
30234 \begin_inset CommandInset ref
30241 \begin_inset CommandInset ref
30248 \begin_inset CommandInset ref
30254 would be numbered as
30255 \begin_inset CommandInset ref
30262 \begin_inset CommandInset ref
30269 \begin_inset CommandInset ref
30278 \begin_layout Standard
30279 By inserting the commands in TeX-mode, a space is created between the first
30282 \begin_inset space \thinspace{}
30285 mm vertical space is inserted after the command
30289 begin{subequations}
30292 When the formula style
30298 \begin_layout Plain Layout
30300 \begin_inset CommandInset ref
30302 reference "sec:Formula-Styles"
30314 \begin_inset space \thinspace{}
30317 mm space is inserted instead.
30320 \begin_layout Standard
30321 Here is an example for a multiline formula where the numbering was turned
30322 off for the second line:
30326 \begin_layout Plain Layout
30330 begin{subequations}
30336 \begin_inset Formula \begin{eqnarray}
30337 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
30338 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
30339 & = & B^{2}-2BZ+Z^{2}\label{eq:f}
30348 \begin_layout Plain Layout
30360 \begin_layout Subsection
30361 User-defined Numbering
30362 \begin_inset CommandInset label
30364 name "sub:User-defined-Numbering"
30369 \begin_inset Index idx
30372 \begin_layout Plain Layout
30373 Formula numbering ! user-defined
30381 \begin_layout Standard
30382 \begin_inset Index idx
30385 \begin_layout Plain Layout
30386 Formula numbering ! self-defined delimiters
30391 With the standard numbering parentheses are set around the formula number.
30392 To replace the parentheses for example by vertical bars, the following
30393 line is added to the LaTeX-preamble:
30396 \begin_layout Standard
30408 \begin_inset Note Note
30411 \begin_layout Plain Layout
30412 This macro is already declared in the LaTeX-preamble for testing.
30413 To activate it, remove the percent sign at the beginning.
30421 \begin_layout Standard
30422 To use other characters, the vertical bars besides the
30426 are replaced by one ore more characters.
30427 To get only the formula number the vertical bars are omitted.
30430 \begin_layout Standard
30431 \begin_inset VSpace bigskip
30434 When there should be an expression of your choice instead of the consecutive
30435 formula number in parentheses behind the formula, the command
30442 \begin_inset Index idx
30445 \begin_layout Plain Layout
30454 \begin_inset Formula \begin{equation}
30455 A+B=C\tag{something}\label{eq:tag}\end{equation}
30459 In this example the command
30467 \begin_layout Plain Layout
30478 was inserted to the formula.
30481 \begin_layout Standard
30490 \begin_layout Plain Layout
30501 is inserted instead, the star prevents the parentheses around the expression:
30502 \begin_inset Formula \[
30503 A+B=C\tag*{something}\]
30510 \begin_layout Standard
30511 \begin_inset VSpace bigskip
30514 To restart the formula numbering with new document parts or sections, the
30515 following command is used:
30518 \begin_layout Standard
30523 @addtoreset{equation}{part}
30526 \begin_inset Index idx
30529 \begin_layout Plain Layout
30534 \begin_layout Plain Layout
30545 \begin_layout Plain Layout
30558 \begin_layout Plain Layout
30569 \begin_layout Plain Layout
30582 \begin_inset Newline newline
30586 \begin_inset Newline newline
30593 @addtoreset{equation}{section}
30596 \begin_layout Standard
30597 To be able to use these commands in TeX-mode, the
30598 \begin_inset Quotes eld
30602 \begin_inset Quotes erd
30605 character has to be made
30606 \begin_inset Quotes eld
30610 \begin_inset Quotes erd
30613 for LaTeX using the command
30627 So the command sequence in TeX-mode is:
30630 \begin_layout Standard
30636 \begin_inset Newline newline
30641 @addtoreset{equation}{section}
30642 \begin_inset Newline newline
30650 \begin_layout Standard
30651 In the LaTeX-preamble
30663 can be omitted as they are automatically internally inserted by LyX.
30666 \begin_layout Standard
30681 \begin_layout Plain Layout
30686 is part of the LaTeX-package
30691 \begin_inset Index idx
30694 \begin_layout Plain Layout
30695 Packages ! carlisle
30700 that is part of every LaTeX standard installation.
30706 \begin_inset Index idx
30709 \begin_layout Plain Layout
30710 Packages ! remreset
30715 has to be loaded in the LaTeX-preamble with the line
30718 \begin_layout Standard
30723 usepackage{remreset}
30726 \begin_layout Standard
30734 \begin_inset Index idx
30737 \begin_layout Plain Layout
30742 \begin_layout Plain Layout
30753 \begin_layout Plain Layout
30766 \begin_layout Plain Layout
30777 \begin_layout Plain Layout
30789 can be used with the same scheme as
30798 \begin_layout Standard
30799 \begin_inset VSpace bigskip
30802 Sometimes formulas should be numbered in the following form:
30805 \begin_layout Standard
30808 (section number.formula number)
30811 \begin_layout Standard
30812 The formula number should start with every section with
30813 \begin_inset Quotes eld
30817 \begin_inset Quotes erd
30823 \begin_layout Standard
30824 For this case there is the command
30831 \begin_inset Index idx
30834 \begin_layout Plain Layout
30842 , which is used with the following scheme:
30845 \begin_layout Standard
30850 numberwithin{counter}{sectioning}
30853 \begin_layout Standard
30854 Counter denotes what kind of numbering is affected, sectioning denotes what
30855 number is before the dot.
30858 \begin_layout Standard
30859 Thus in our case the following LaTeX-preamble or TeX-Code line is used:
30862 \begin_layout Standard
30867 numberwithin{equation}{section}
30870 \begin_layout Standard
30871 This is the result:
30875 \begin_layout Plain Layout
30879 numberwithin{equation}{section}
30885 \begin_inset Formula \begin{equation}
30886 A+B=C\end{equation}
30893 \begin_layout Standard
30895 \begin_inset space \thinspace{}
30899 \begin_inset space \space{}
30902 tables so that the number of the part is the sectioning,
30903 \begin_inset Newline newline
30910 numberwithin{table}{part}
30915 \begin_layout Standard
30916 To go back to the standard numbering or to prevent this kind of numbering
30917 when it is defined by the document class, the following command is inserted
30918 as TeX-Code or to the LaTeX-preamble:
30921 \begin_layout Standard
30931 \begin_inset Index idx
30934 \begin_layout Plain Layout
30948 \begin_layout Plain Layout
30964 \begin_inset Newline newline
30972 \begin_inset Newline newline
30984 \begin_layout Standard
30991 uses internally the command
30997 , described above, that also needs to be reverted.
31001 \begin_layout Plain Layout
31008 \begin_layout Plain Layout
31012 @removefromreset{equation}{section}
31015 \begin_layout Plain Layout
31027 \begin_layout Subsection
31028 Numbering with Roman Numbers and Letters
31029 \begin_inset Index idx
31032 \begin_layout Plain Layout
31033 Formula numbering ! with letters
31039 \begin_inset Index idx
31042 \begin_layout Plain Layout
31043 Formula numbering ! with Roman numbers
31051 \begin_layout Standard
31052 Formulas can also be numbered with Roman numbers and Latin letters.
31053 To number for example with small Roman numbers, the command
31056 \begin_layout Standard
31068 \begin_layout Standard
31069 is inserted before the formula in TeX-mode.
31077 \begin_inset Index idx
31080 \begin_layout Plain Layout
31088 redefines the predefined command
31104 \begin_layout Plain Layout
31111 has the same scheme like the command
31117 that is described in
31118 \begin_inset CommandInset ref
31120 reference "sub:The-Command-newcommand"
31133 is the formula counter.
31140 is used as prefix for a counter, the value of the counter is output as
31142 When a formula is numbered, LaTeX sets internally the command
31148 behind the formula.
31154 \begin_inset Index idx
31157 \begin_layout Plain Layout
31167 outputs the counter as small Roman number.
31170 \begin_layout Standard
31171 All formulas behind the command
31181 are now numbered Roman.
31182 To switch to numbering with big Roman numbers, the command is inserted
31196 \begin_inset Index idx
31199 \begin_layout Plain Layout
31211 \begin_inset Quotes eld
31215 \begin_inset Quotes erd
31218 with small Latin letters there is the command
31225 \begin_inset Index idx
31228 \begin_layout Plain Layout
31236 , for big ones there is the command
31243 \begin_inset Index idx
31246 \begin_layout Plain Layout
31259 \begin_layout Standard
31260 \begin_inset Note Greyedout
31263 \begin_layout Plain Layout
31268 Only maximal 26 formulas can be numbered with Latin letters in one document.
31276 \begin_layout Standard
31280 \begin_layout Plain Layout
31296 \begin_layout Standard
31297 \begin_inset Formula \begin{equation}
31298 A=\textrm{small roman}\end{equation}
31306 \begin_layout Plain Layout
31320 \begin_inset Formula \begin{equation}
31321 B=\textrm{big Roman}\label{eq:Rom}\end{equation}
31329 \begin_layout Plain Layout
31343 \begin_inset Formula \begin{equation}
31344 C=\textrm{small Latin}\end{equation}
31352 \begin_layout Plain Layout
31366 \begin_inset Formula \begin{equation}
31367 D=\textrm{big Latin}\label{eq:Lat}\end{equation}
31374 \begin_layout Standard
31375 To switch back to the default numbering, insert the command:
31378 \begin_layout Standard
31388 \begin_inset Index idx
31391 \begin_layout Plain Layout
31402 \begin_layout Standard
31406 \begin_layout Plain Layout
31420 \begin_inset Formula \begin{equation}
31421 E=\textrm{Arabic}\end{equation}
31428 \begin_layout Standard
31429 \begin_inset VSpace medskip
31432 As you see, formulas are numbered serially independent from the numbering
31434 When then numbering should start with
31435 \begin_inset Quotes eld
31439 \begin_inset Quotes erd
31442 when the style is changed, new equation counters have to be defined.
31443 A description about this can be found in the file
31444 \begin_inset CommandInset href
31446 name "Formula-numbering.lyx"
31447 target "run:Formula-numbering.lyx"
31454 \begin_layout Section
31455 Chemical Symbols and Equations
31456 \begin_inset CommandInset label
31458 name "sub:Chemical-Symbols-and"
31463 \begin_inset Index idx
31466 \begin_layout Plain Layout
31467 Chemical characters ! Symbols
31473 \begin_inset Index idx
31476 \begin_layout Plain Layout
31483 \begin_inset Index idx
31486 \begin_layout Plain Layout
31495 \begin_layout Standard
31496 An example text from chemistry:
31499 \begin_layout Quote
31501 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
31504 -ion reacts with two
31505 \begin_inset Formula $\mathrm{Na^{+}}$
31508 -ions to sodium sulfate
31509 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
31513 The chemical equation for this is:
31514 \begin_inset Formula \begin{equation}
31515 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}\end{equation}
31522 \begin_layout Standard
31523 This chemical equation can directly be created as formula.
31524 To avoid that the symbols appear italic, everything is highlighted and
31525 changed by the shortcut
31531 to the upright font style.
31535 \begin_layout Plain Layout
31541 \begin_inset CommandInset ref
31543 reference "sub:Font-Styles"
31555 \begin_layout Standard
31556 A more convenient way to typeset chemical formulas is to use the command
31564 \begin_inset Index idx
31567 \begin_layout Plain Layout
31575 that is available when the LaTeX-package
31580 \begin_inset Index idx
31583 \begin_layout Plain Layout
31596 to a formula a new blue box appears where chemical formulas can be inserted
31597 in an intuitive way.
31600 \begin_layout Standard
31602 \begin_inset Tabular
31603 <lyxtabular version="3" rows="9" columns="2">
31604 <features tabularvalignment="middle">
31605 <column alignment="center" valignment="top" width="0">
31606 <column alignment="center" valignment="top" width="0">
31608 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31611 \begin_layout Plain Layout
31617 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31620 \begin_layout Plain Layout
31622 \begin_inset Note Note
31625 \begin_layout Plain Layout
31632 is only used as spacer.
31644 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31647 \begin_layout Plain Layout
31654 \begin_layout Plain Layout
31668 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31671 \begin_layout Plain Layout
31672 \begin_inset Formula $\raisebox{4.5mm}{}\ce{H2CO3}\raisebox{-2mm}{}$
31682 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31685 \begin_layout Plain Layout
31692 \begin_layout Plain Layout
31706 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31709 \begin_layout Plain Layout
31710 \begin_inset Formula $\raisebox{5mm}{}\ce{SO4^{2-}}\raisebox{-2mm}{}$
31720 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31723 \begin_layout Plain Layout
31730 \begin_layout Plain Layout
31744 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31747 \begin_layout Plain Layout
31748 \begin_inset Formula $\raisebox{4.5mm}{}\ce{(NH4)2S}\raisebox{-2mm}{}$
31758 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31761 \begin_layout Plain Layout
31768 \begin_layout Plain Layout
31782 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31785 \begin_layout Plain Layout
31786 \begin_inset Formula $\raisebox{4.5mm}{}\ce{KCr(SO4)2.12H2O}\raisebox{-2mm}{}$
31796 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31799 \begin_layout Plain Layout
31806 \begin_layout Plain Layout
31821 \begin_layout Plain Layout
31836 \begin_layout Plain Layout
31850 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31853 \begin_layout Plain Layout
31854 \begin_inset Formula $\raisebox{4.5mm}{}\ce{A-B\dbond C\tbond D}\raisebox{-2mm}{}$
31864 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31867 \begin_layout Plain Layout
31874 \begin_layout Plain Layout
31884 \begin_inset Formula $\downarrow$
31888 \begin_inset Formula $\to$
31896 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31899 \begin_layout Plain Layout
31900 \begin_inset Formula $\raisebox{5mm}{}\ce{_{90}^{227}Th+}\raisebox{-2mm}{}$
31910 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31913 \begin_layout Plain Layout
31920 \begin_layout Plain Layout
31933 \begin_layout Plain Layout
31946 \begin_layout Plain Layout
31959 \begin_layout Plain Layout
31972 \begin_layout Plain Layout
31986 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31989 \begin_layout Plain Layout
31990 \begin_inset Formula $\raisebox{4.5mm}{}\ce{CO2 + C <=> 2CO}\raisebox{-2mm}{}$
32000 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32003 \begin_layout Plain Layout
32010 \begin_layout Plain Layout
32023 \begin_layout Plain Layout
32036 \begin_layout Plain Layout
32049 \begin_layout Plain Layout
32066 \begin_layout Plain Layout
32080 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32083 \begin_layout Plain Layout
32084 \begin_inset Formula $\raisebox{5mm}{}\ce{CO2 + C ->[\alpha][\beta] 2CO}\raisebox{-4mm}{}$
32100 \begin_layout Standard
32101 \begin_inset Note Greyedout
32104 \begin_layout Plain Layout
32109 Inserting a formula to a
32115 box will lead to LaTeX errors.
32116 In this case TeX code has to be used like for
32130 \begin_layout Plain Layout
32151 \begin_layout Standard
32158 the command for equation
32159 \begin_inset space ~
32163 \begin_inset CommandInset ref
32165 reference "eq:chem-reaction"
32170 \begin_inset Newline newline
32181 \begin_layout Plain Layout
32194 \begin_layout Plain Layout
32207 \begin_layout Plain Layout
32220 \begin_layout Plain Layout
32233 \begin_layout Plain Layout
32246 \begin_layout Plain Layout
32258 \begin_layout Standard
32259 To create multiline chemical equations first a multiline formula is created
32261 \begin_inset CommandInset ref
32263 reference "sec:Multiline-Formulas"
32268 Afterwards the command
32274 is used in every small blue box of the formula.
32276 \begin_inset CommandInset ref
32278 reference "eq:TEOS-reaction-1"
32283 \begin_inset CommandInset ref
32285 reference "eq:TEOS-reaction-2"
32289 are an example of a multi-stage chemical reaction where every equation
32290 has its own number.
32291 \begin_inset Formula \begin{eqnarray}
32292 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
32293 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
32301 \begin_layout Standard
32312 package provides the command
32319 \begin_inset Index idx
32322 \begin_layout Plain Layout
32330 that has to be used for special cases.
32331 For more information about
32337 and more examples have a look at the documentation of
32342 \begin_inset CommandInset citation
32351 \begin_layout Standard
32352 \begin_inset Newpage newpage
32358 \begin_layout Section
32362 \begin_layout Standard
32363 LyX supports two types of commutative diagrams:
32371 that are explained in the following.
32374 \begin_layout Subsection
32376 \begin_inset Index idx
32379 \begin_layout Plain Layout
32388 \begin_layout Standard
32389 Diagrams of this type visualize relations by vertical and horizontal lines
32391 \begin_inset Formula \[
32392 \begin{CD}A@>>>B@>>>C\\
32402 \begin_layout Standard
32403 To get them, the command
32408 \begin_inset Index idx
32411 \begin_layout Plain Layout
32421 is inserted to a formula.
32422 A blue box appears with two dashed lines where further commands can be
32427 arg "newline-insert newline"
32430 a new line is created.
32431 Horizontal relations are inserted in odd, vertical in even formula lines.
32434 \begin_layout Standard
32435 To create the relations there are the following commands:
32438 \begin_layout Itemize
32443 creates a left arrow,
32454 \begin_layout Itemize
32459 creates an up arrow,
32467 a vertical equal sign
32470 \begin_layout Itemize
32476 is a placeholder for non-existent relations
32479 \begin_layout Standard
32480 All arrows can be labeled as follows:
32483 \begin_layout Itemize
32484 Is text inserted between the first and second < or >, resp., it is placed
32486 When it is inserted between the second and third one, it appears under
32490 \begin_layout Itemize
32491 When text for vertical arrows is inserted between the first and second A
32492 or V, resp., it is placed left beside the arrow.
32493 When it is inserted between the second and third one, it appears right
32495 If the text contains an A or V, these letters must be set into a TeX-brace.
32498 \begin_layout Standard
32499 As example a diagram with all possible relations:
32502 \begin_layout Standard
32503 \begin_inset Formula \[
32504 \begin{CD}A@>j>>B@>>k>C@=F\\
32514 \begin_layout Standard
32515 The command for this is:
32516 \begin_inset Newline newline
32527 \begin_layout Plain Layout
32536 A@>j>>B@>>k>C@=F Ctrl+Return
32537 \begin_inset Newline newline
32541 \begin_inset Phantom HPhantom
32544 \begin_layout Plain Layout
32553 \begin_layout Plain Layout
32572 \begin_inset Formula $\to$
32578 \begin_inset Newline newline
32582 \begin_inset Phantom HPhantom
32585 \begin_layout Plain Layout
32594 \begin_layout Plain Layout
32611 \begin_layout Subsection
32613 \begin_inset Index idx
32616 \begin_layout Plain Layout
32617 Diagrams ! xymatrix
32625 \begin_layout Standard
32626 To be able to use xymatrices, the LaTeX-package
32631 A xymatrix is created by inserting the command
32638 Then you are able to add new matrix columns and rows like for normal matrices,
32640 \begin_inset CommandInset ref
32642 reference "sec:Matrices"
32649 \begin_layout Standard
32650 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
32652 All possibilities to create commutative diagrams and decorations are explained
32657 that you find in the menu
32659 Help\SpecialChar \menuseparator
32661 \begin_inset space ~
32669 \begin_layout Subsection
32675 \begin_inset Index idx
32678 \begin_layout Plain Layout
32687 \begin_layout Standard
32692 -diagrams, the LaTeX-package
32701 -diagram is created by inserting the command
32708 Then you are able to add new matrix columns and rows like for normal matrices,
32710 \begin_inset CommandInset ref
32712 reference "sec:Matrices"
32719 \begin_layout Standard
32720 Examples how to create
32724 diagrams in LyX is given in the
32726 Feynman-diagram manual
32728 that you find in the menu
32730 Help\SpecialChar \menuseparator
32732 \begin_inset space ~
32740 \begin_layout Section
32741 User-defined Commands
32742 \begin_inset Index idx
32745 \begin_layout Plain Layout
32746 User-defined commands
32754 \begin_layout Standard
32755 \begin_inset Note Greyedout
32758 \begin_layout Plain Layout
32763 The names of user-defined commands and macros may only consist of Latin
32772 \begin_layout Subsection
32776 \begin_inset CommandInset label
32778 name "sub:The-Command-newcommand"
32783 \begin_inset Index idx
32786 \begin_layout Plain Layout
32787 User-defined commands !
32795 \begin_inset Index idx
32798 \begin_layout Plain Layout
32809 \begin_layout Standard
32810 Many LaTeX-commands are too long to be used frequently.
32811 But it is possible to define with the command
32817 new shorter commands.
32820 \begin_layout Standard
32821 The command scheme of
32830 \begin_layout Standard
32835 newcommand{new command name}[number of arguments][optional
32840 \begin_inset Newline newline
32844 \begin_inset Phantom HPhantom
32847 \begin_layout Plain Layout
32857 {command definition}
32860 \begin_layout Standard
32861 \begin_inset Note Greyedout
32864 \begin_layout Plain Layout
32869 Assure that the name of the new command is not already used in your document
32870 or by LaTeX-packages that you use.
32871 When you for example define the command
32883 , you get an error message because
32889 is already defined as command for
32890 \begin_inset Quotes eld
32894 \begin_inset Formula $\le$
32898 \begin_inset Quotes erd
32909 \begin_layout Standard
32910 The number of arguments is an integer in the range 0
32911 \begin_inset space \thinspace{}
32915 \begin_inset space \thinspace{}
32918 9 and specifies how many arguments the new command should have.
32919 With the optional value a value for an optional argument can be predefined.
32920 When this is done, the
32928 rgument of the new command is automatically an optional one.
32931 \begin_layout Standard
32932 Here are some examples:
32935 \begin_layout Itemize
32936 To define the command
32948 , the LaTeX-preamble line is:
32949 \begin_inset VSpace medskip
32953 \begin_inset Newline newline
32967 \begin_layout Itemize
32968 To define the command
32980 , the argument (that should be underlined) must be taken into account.
32981 For this the preamble line is:
32982 \begin_inset VSpace medskip
32986 \begin_inset Newline newline
33000 \begin_inset VSpace medskip
33004 \begin_inset Newline newline
33011 acts as argument placeholder, the
33015 behind it denotes that it is the placeholder for the first argument.
33018 \begin_layout Itemize
33026 \begin_inset space \thinspace{}
33030 \begin_inset space \space{}
33040 \begin_inset VSpace medskip
33044 \begin_inset Newline newline
33055 framebox#1#2{$#3$}}
33058 \begin_inset VSpace medskip
33062 \begin_inset Newline newline
33065 The two Dollar signs creates the extra formula needed for
33072 \begin_inset CommandInset ref
33074 reference "sub:Boxes-with-Frame"
33081 \begin_layout Itemize
33082 To create a new command for
33088 where the color for the box needn't to be specified, the argument for the
33089 color is defined optional:
33090 \begin_inset VSpace medskip
33094 \begin_inset Newline newline
33105 fcolorbox{#2}{#1}{$#3$}}
33108 \begin_inset VSpace medskip
33112 \begin_inset Newline newline
33115 When the color is not specified when using
33121 , the predefined color
33128 \begin_layout Standard
33129 A test of the new defined commands:
33132 \begin_layout Standard
33134 \begin_inset Tabular
33135 <lyxtabular version="3" rows="6" columns="2">
33136 <features tabularvalignment="middle">
33137 <column alignment="center" valignment="top" width="0">
33138 <column alignment="center" valignment="top" width="0">
33140 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33143 \begin_layout Plain Layout
33149 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33152 \begin_layout Plain Layout
33154 \begin_inset Note Note
33157 \begin_layout Plain Layout
33164 is only used as spacer.
33176 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33179 \begin_layout Plain Layout
33186 \begin_layout Plain Layout
33200 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33203 \begin_layout Plain Layout
33204 \begin_inset Formula $A\gr B$
33214 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33217 \begin_layout Plain Layout
33225 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33228 \begin_layout Plain Layout
33229 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
33239 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33242 \begin_layout Plain Layout
33246 \begin_inset Formula $\to$
33252 \begin_inset Formula $\to$
33263 \begin_layout Plain Layout
33277 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33280 \begin_layout Plain Layout
33281 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
33291 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33294 \begin_layout Plain Layout
33298 \begin_inset Formula $\to$
33309 \begin_layout Plain Layout
33323 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33326 \begin_layout Plain Layout
33327 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
33337 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33340 \begin_layout Plain Layout
33346 \begin_inset Formula $\to$
33357 \begin_layout Plain Layout
33371 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33374 \begin_layout Plain Layout
33375 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
33391 \begin_layout Subsection
33393 \begin_inset Index idx
33396 \begin_layout Plain Layout
33397 User-defined commands! Math macros
33403 \begin_inset Index idx
33406 \begin_layout Plain Layout
33415 \begin_layout Standard
33416 User-defined commands are especially convenient for complex expressions.
33417 When you are for example dealing in a document with quadratic equations,
33418 the same solution type occurs several times.
33419 The general form of a quadratic equation is
33420 \begin_inset Formula \[
33421 0=\lambda^{2}+p\lambda+q\]
33425 The general form of the solution is
33426 \begin_inset Formula \[
33427 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}\]
33434 \begin_layout Standard
33435 To define a command for the solution formula where only the three parameters
33437 \begin_inset Formula $\lambda$
33441 \begin_inset Formula $p$
33445 \begin_inset Formula $q$
33448 need to be specified and the index of
33449 \begin_inset Formula $\lambda$
33452 can be given optionally, the LaTeX-preamble line is
33453 \begin_inset Newline newline
33469 \begin_inset Newline newline
33473 \begin_inset Phantom HPhantom
33476 \begin_layout Plain Layout
33490 frac{#3^{2}}{4}-#4}}
33493 \begin_layout Standard
33494 To create with this the solution formula, the command
33495 \begin_inset Newline newline
33505 \begin_inset Formula $\to$
33511 \begin_inset Formula $\to$
33518 is inserted to a formula
33523 \begin_layout Standard
33524 The definition of the new command is unintuitive because one has to know
33525 the schemes of all used LaTeX commands, e.
33526 \begin_inset space \thinspace{}
33530 \begin_inset space \space{}
33533 that a fraction is inserted in LaTeX as
33537 frac{numerator}{denominator}
33540 Furthermore one can easily forget a brace in the definition and cannot
33541 see in LyX what the new command is doing.
33542 To avoid these problems LyX offers the possibility to use math macros instead
33552 \begin_layout Standard
33553 A math macro is created by using the menu
33555 Insert\SpecialChar \menuseparator
33556 Math\SpecialChar \menuseparator
33559 or the toolbar button
33560 \begin_inset Graphics
33561 filename ../images/math-macro_newmacroname_newcommand.png
33567 The math macro toolbar appears together with the following box where the
33569 \begin_inset Newline newline
33573 \begin_inset space \hspace*{\fill}
33577 \begin_inset Graphics
33578 filename clipart/macrobox.png
33583 \begin_inset space \hspace*{\fill}
33587 \begin_inset Newline newline
33591 \begin_inset FormulaMacro
33592 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
33597 newmacroname is the default name of the macro that should be changed to
33598 something sensible.
33599 The wanted formula is inserted in the first blue box.
33600 An argument placeholder is inserted with the command
33607 \begin_inset space \thinspace{}
33611 \begin_inset space \space{}
33620 or by using the macro toolbar button
33621 \begin_inset Graphics
33622 filename ../images/math-macro-add-param.png
33628 Argument placeholders are displayed red.
33629 Maximum 9 arguments are possible.
33630 Optional arguments are created with the toolbar button
33631 \begin_inset Graphics
33632 filename ../images/math-macro-add-optional-param.png
33638 The first non-optional argument can be transformed to an optional one with
33640 \begin_inset Graphics
33641 filename ../images/math-macro-make-optional.png
33647 In the second blue box the appearance of the macro in LyX can be defined.
33648 Normally you want to see it as it is defined, so the box is kept empty.
33649 But when you have created a macro that needs lot of space on the screen,
33650 you can insert in the box for example
33651 \begin_inset Newline newline
33681 \begin_inset Newline newline
33686 For the macro only the arguments with the macro name in front of them will
33687 then be displayed in LyX, leading to a better overview.
33688 The formula appears in the output as defined in the first box.
33689 \begin_inset Newline newline
33692 The appearance of macros in formulas can furthermore be changed for single
33693 macros by setting the cursor in the macro and using the menu
33695 View\SpecialChar \menuseparator
33697 \begin_inset space ~
33701 \begin_inset space ~
33709 \begin_layout Standard
33710 To use a macro, the macro name is inserted as command to a formula, in our
33718 Our macro looks in LyX like this:
33719 \begin_inset Newline newline
33723 \begin_inset space \hspace*{\fill}
33727 \begin_inset Graphics
33728 filename clipart/macrouse.png
33733 \begin_inset space \hspace*{\fill}
33737 \begin_inset Newline newline
33740 Here is our macro example with the arguments
33741 \begin_inset Formula $x$
33745 \begin_inset Formula $\ln(x)$
33749 \begin_inset Formula $B$
33755 \begin_layout Standard
33756 \begin_inset Formula \[
33764 \begin_layout Standard
33765 LyX offers in the menu
33767 Tools\SpecialChar \menuseparator
33768 Preferences\SpecialChar \menuseparator
33769 Editing\SpecialChar \menuseparator
33772 different styles to edit macros.
33773 To find the style that suits you the most, choose a style and set the cursor
33774 in a macro formula to see the difference.
33777 \begin_layout Standard
33778 A math macro is transformed internally to a
33784 command when exporting the document.
33791 command is not placed in the LaTeX-preamble, therefore macros can only
33792 be used in formulas that are in the document below the macro definition
33796 \begin_layout Standard
33797 Math macros can also be directly be created from a
33804 When writing for example the command
33807 \begin_inset Newline newline
33816 xleftarrow[#2]{#1}}
33817 \begin_inset Newline newline
33822 in LyX as normal text, highlighting it completely and using then the shortcut
33827 , the command will be transformed to a math macro.
33828 Using this method you need to be careful that the
33834 command is typed correctly, otherwise you get a faulty macro leading to
33838 \begin_layout Standard
33839 Math macros currently yet have the problem that further formulas in macro
33840 definitions are handled wrongly.
33841 Therefore the example
33848 \begin_inset CommandInset ref
33850 reference "sub:The-Command-newcommand"
33854 cannot be created as macro.
33857 \begin_layout Standard
33858 When the cursor is in a macro definition box, you will see the macro toolbar
33862 \begin_layout Standard
33863 \begin_inset VSpace defskip
33869 \begin_layout Standard
33870 \begin_inset Graphics
33871 filename clipart/MacroToolbar.png
33876 \begin_inset Index idx
33879 \begin_layout Plain Layout
33888 \begin_layout Standard
33889 \begin_inset VSpace defskip
33895 \begin_layout Standard
33896 The macro toolbar contains from left to right the following buttons:
33899 \begin_layout Standard
33900 \begin_inset VSpace defskip
33906 \begin_layout Standard
33907 \begin_inset Tabular
33908 <lyxtabular version="3" rows="9" columns="2">
33909 <features islongtable="true" longtabularalignment="center">
33910 <column alignment="left" valignment="top" width="0">
33911 <column alignment="left" valignment="top" width="85col%">
33912 <row interlinespace="2.5mm">
33913 <cell alignment="center" valignment="top" usebox="none">
33916 \begin_layout Plain Layout
33917 \begin_inset Graphics
33918 filename ../images/math-macro-remove-param.png
33919 rotateOrigin center
33928 <cell alignment="center" valignment="top" usebox="none">
33931 \begin_layout Plain Layout
33934 Edit\SpecialChar \menuseparator
33935 Math\SpecialChar \menuseparator
33937 \begin_inset space ~
33940 Definition\SpecialChar \menuseparator
33941 Remove Last Argument
33947 <row interlinespace="2.5mm">
33948 <cell alignment="center" valignment="top" usebox="none">
33951 \begin_layout Plain Layout
33952 \begin_inset Graphics
33953 filename ../images/math-macro-add-param.png
33954 rotateOrigin center
33963 <cell alignment="center" valignment="top" usebox="none">
33966 \begin_layout Plain Layout
33969 Edit\SpecialChar \menuseparator
33970 Math\SpecialChar \menuseparator
33972 \begin_inset space ~
33975 Definition\SpecialChar \menuseparator
33982 <row interlinespace="2.5mm">
33983 <cell alignment="center" valignment="top" usebox="none">
33986 \begin_layout Plain Layout
33987 \begin_inset Graphics
33988 filename ../images/math-macro-make-optional.png
33989 rotateOrigin center
33998 <cell alignment="center" valignment="top" usebox="none">
34001 \begin_layout Plain Layout
34004 Edit\SpecialChar \menuseparator
34005 Math\SpecialChar \menuseparator
34007 \begin_inset space ~
34010 Definition\SpecialChar \menuseparator
34011 Make First Non-Optional into
34012 \begin_inset Newline newline
34016 \begin_inset Phantom HPhantom
34019 \begin_layout Plain Layout
34022 Edit\SpecialChar \menuseparator
34023 Math\SpecialChar \menuseparator
34025 \begin_inset space ~
34028 Definition\SpecialChar \menuseparator
34040 <row interlinespace="2.5mm">
34041 <cell alignment="center" valignment="top" usebox="none">
34044 \begin_layout Plain Layout
34045 \begin_inset Graphics
34046 filename ../images/math-macro-make-nonoptional.png
34047 rotateOrigin center
34056 <cell alignment="center" valignment="top" usebox="none">
34059 \begin_layout Plain Layout
34062 Edit\SpecialChar \menuseparator
34063 Math\SpecialChar \menuseparator
34065 \begin_inset space ~
34068 Definition\SpecialChar \menuseparator
34069 Make Last Optional into
34070 \begin_inset Newline newline
34074 \begin_inset Phantom HPhantom
34077 \begin_layout Plain Layout
34080 Edit\SpecialChar \menuseparator
34081 Math\SpecialChar \menuseparator
34083 \begin_inset space ~
34086 Definition\SpecialChar \menuseparator
34092 Non-Optional Argument
34098 <row interlinespace="2.5mm">
34099 <cell alignment="center" valignment="top" usebox="none">
34102 \begin_layout Plain Layout
34103 \begin_inset Graphics
34104 filename ../images/math-macro-remove-optional-param.png
34105 rotateOrigin center
34114 <cell alignment="center" valignment="top" usebox="none">
34117 \begin_layout Plain Layout
34120 Edit\SpecialChar \menuseparator
34121 Math\SpecialChar \menuseparator
34123 \begin_inset space ~
34126 Definition\SpecialChar \menuseparator
34127 Remove Optional Argument
34133 <row interlinespace="2.5mm">
34134 <cell alignment="center" valignment="top" usebox="none">
34137 \begin_layout Plain Layout
34138 \begin_inset Graphics
34139 filename ../images/math-macro-add-optional-param.png
34140 rotateOrigin center
34149 <cell alignment="center" valignment="top" usebox="none">
34152 \begin_layout Plain Layout
34155 Edit\SpecialChar \menuseparator
34156 Math\SpecialChar \menuseparator
34158 \begin_inset space ~
34161 Definition\SpecialChar \menuseparator
34162 Insert Optional Argument
34168 <row interlinespace="2.5mm">
34169 <cell alignment="center" valignment="top" usebox="none">
34172 \begin_layout Plain Layout
34173 \begin_inset Graphics
34174 filename ../images/math-macro-remove-greedy-param.png
34175 rotateOrigin center
34184 <cell alignment="center" valignment="top" usebox="none">
34187 \begin_layout Plain Layout
34190 Edit\SpecialChar \menuseparator
34191 Math\SpecialChar \menuseparator
34193 \begin_inset space ~
34196 Definition\SpecialChar \menuseparator
34197 Remove Last Argument
34198 \begin_inset Newline newline
34202 \begin_inset Phantom HPhantom
34205 \begin_layout Plain Layout
34208 Edit\SpecialChar \menuseparator
34209 Math\SpecialChar \menuseparator
34211 \begin_inset space ~
34214 Definition\SpecialChar \menuseparator
34220 Spitting Out To The Right
34226 <row interlinespace="2.5mm">
34227 <cell alignment="center" valignment="top" usebox="none">
34230 \begin_layout Plain Layout
34231 \begin_inset Graphics
34232 filename ../images/math-macro-append-greedy-param.png
34233 rotateOrigin center
34242 <cell alignment="center" valignment="top" usebox="none">
34245 \begin_layout Plain Layout
34248 Edit\SpecialChar \menuseparator
34249 Math\SpecialChar \menuseparator
34251 \begin_inset space ~
34254 Definition\SpecialChar \menuseparator
34256 \begin_inset Newline newline
34260 \begin_inset Phantom HPhantom
34263 \begin_layout Plain Layout
34266 Edit\SpecialChar \menuseparator
34267 Math\SpecialChar \menuseparator
34269 \begin_inset space ~
34272 Definition\SpecialChar \menuseparator
34278 Eating From The Right
34284 <row interlinespace="2.5mm">
34285 <cell alignment="center" valignment="top" usebox="none">
34288 \begin_layout Plain Layout
34289 \begin_inset Graphics
34290 filename ../images/math-macro-add-greedy-optional-param.png
34291 rotateOrigin center
34300 <cell alignment="center" valignment="top" usebox="none">
34303 \begin_layout Plain Layout
34306 Edit\SpecialChar \menuseparator
34307 Math\SpecialChar \menuseparator
34309 \begin_inset space ~
34312 Definition\SpecialChar \menuseparator
34313 Append Optional Argument
34314 \begin_inset Newline newline
34318 \begin_inset Phantom HPhantom
34321 \begin_layout Plain Layout
34324 Edit\SpecialChar \menuseparator
34325 Math\SpecialChar \menuseparator
34327 \begin_inset space ~
34330 Definition\SpecialChar \menuseparator
34336 Eating From The Right
34349 \begin_layout Standard
34350 \begin_inset Newpage newpage
34356 \begin_layout Section
34358 \begin_inset Index idx
34361 \begin_layout Plain Layout
34370 \begin_layout Subsection
34372 \begin_inset Index idx
34375 \begin_layout Plain Layout
34384 \begin_layout Standard
34385 Negative numbers often look ugly in formulas because the minus sign before
34386 the number is set with the same length as the minus operator sign.
34387 When writing the negative number in normal text, the minus sign appears
34391 \begin_layout Standard
34392 Thus, the problem disappears when converting the minus sign to mathematical
34396 \begin_layout Standard
34397 An example to visualize the problem:
34400 \begin_layout Standard
34402 \begin_inset Tabular
34403 <lyxtabular version="3" rows="3" columns="2">
34404 <features tabularvalignment="middle">
34405 <column alignment="right" valignment="top" width="0">
34406 <column alignment="left" valignment="top" width="0">
34408 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34411 \begin_layout Plain Layout
34417 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
34420 \begin_layout Plain Layout
34428 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34431 \begin_layout Plain Layout
34437 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34440 \begin_layout Plain Layout
34441 \begin_inset Formula $x=-2$
34451 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34454 \begin_layout Plain Layout
34460 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34463 \begin_layout Plain Layout
34464 \begin_inset Formula $x=\textrm{-}2$
34480 \begin_layout Subsection
34481 Comma as decimal Separator
34482 \begin_inset Index idx
34485 \begin_layout Plain Layout
34494 \begin_layout Standard
34495 In LaTeX a comma inside a formula is used, according to the English convention,
34496 as number group separator.
34497 So there will be space added behind all commas in formulas.
34500 \begin_layout Standard
34501 To avoid this, the comma is highlighted and changed to mathematical text
34511 \begin_layout Standard
34512 To use all formula commas in the document as decimal separator, the file
34521 \begin_layout Plain Layout
34526 is part of the LaTeX-package
34531 \begin_inset Index idx
34534 \begin_layout Plain Layout
34539 \begin_layout Plain Layout
34559 \begin_inset Index idx
34562 \begin_layout Plain Layout
34568 is loaded with the LaTeX-preamble line
34571 \begin_layout Standard
34579 \begin_layout Subsection
34581 \begin_inset CommandInset label
34583 name "sub:Physical-Vectors"
34588 \begin_inset Index idx
34591 \begin_layout Plain Layout
34600 \begin_layout Standard
34601 Predefined vectors are offered by the LaTeX-package
34606 \begin_inset Index idx
34609 \begin_layout Plain Layout
34615 that is loaded with the LaTeX-preamble line
34618 \begin_layout Standard
34626 \begin_layout Standard
34630 \begin_layout Plain Layout
34640 \begin_inset Note Note
34643 \begin_layout Plain Layout
34644 The following table will only be displayed when the LaTeX-package
34656 \begin_layout Standard
34657 The following commands are defined:
34660 \begin_layout Standard
34662 \begin_inset Tabular
34663 <lyxtabular version="3" rows="4" columns="2">
34664 <features tabularvalignment="middle">
34665 <column alignment="center" valignment="top" width="0">
34666 <column alignment="center" valignment="top" width="0">
34668 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34671 \begin_layout Plain Layout
34677 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34680 \begin_layout Plain Layout
34688 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34691 \begin_layout Plain Layout
34701 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34704 \begin_layout Plain Layout
34705 \begin_inset Formula $\Bra{\psi}$
34715 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34718 \begin_layout Plain Layout
34728 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34731 \begin_layout Plain Layout
34732 \begin_inset Formula $\Ket{\psi}$
34742 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34745 \begin_layout Plain Layout
34757 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34760 \begin_layout Plain Layout
34761 \begin_inset Formula $\Braket{\psi|\phi}$
34777 \begin_layout Standard
34784 assures that all vertical bars are set in the size of the surrounding brackets:
34785 \begin_inset Formula \[
34786 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}\]
34794 \begin_layout Plain Layout
34804 \begin_inset Note Note
34807 \begin_layout Plain Layout
34808 The following will be displayed when the LaTeX-package
34820 \begin_layout Standard
34821 You need to install the LaTeX-package
34825 to see the rest of this subsection in the output.
34828 \begin_layout Standard
34832 \begin_layout Plain Layout
34844 \begin_layout Standard
34851 can also be achieved using the command
34857 , that is described in
34858 \begin_inset CommandInset ref
34860 reference "sub:Automatic-Bracket-Size"
34867 \begin_layout Subsection
34868 Self-defined Fractions
34869 \begin_inset CommandInset label
34871 name "sub:Self-defined-Fractions"
34876 \begin_inset Index idx
34879 \begin_layout Plain Layout
34880 Fractions ! self-defined
34888 \begin_layout Standard
34889 To define custom commands for fractions, the command
34896 \begin_inset Index idx
34899 \begin_layout Plain Layout
34907 is used in the following scheme:
34910 \begin_layout Standard
34923 bracket}{fraction bar thickness}{style}
34924 \begin_inset Newline newline
34928 \begin_inset Phantom HPhantom
34931 \begin_layout Plain Layout
34941 {numerator}{denominator}
34944 \begin_layout Standard
34945 The style is a number in the range of 0
34946 \begin_inset space \thinspace{}
34950 \begin_inset space \thinspace{}
34956 \begin_layout Standard
34958 \begin_inset Tabular
34959 <lyxtabular version="3" rows="5" columns="2">
34960 <features tabularvalignment="middle">
34961 <column alignment="center" valignment="top" width="0">
34962 <column alignment="center" valignment="top" width="0">
34964 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34967 \begin_layout Plain Layout
34973 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34976 \begin_layout Plain Layout
34984 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34987 \begin_layout Plain Layout
34993 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34996 \begin_layout Plain Layout
34997 display style formula
35004 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35007 \begin_layout Plain Layout
35013 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35016 \begin_layout Plain Layout
35024 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35027 \begin_layout Plain Layout
35033 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35036 \begin_layout Plain Layout
35044 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35047 \begin_layout Plain Layout
35053 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35056 \begin_layout Plain Layout
35070 \begin_layout Standard
35071 When no style is given, the size is adjusted to the surrounding environment
35072 like for the command
35081 \begin_layout Standard
35082 When no fraction bar thickness is given, the predefined value of 0.4
35083 \begin_inset space \thinspace{}
35089 \begin_layout Standard
35090 \begin_inset VSpace medskip
35093 For example, the commands
35106 \begin_inset CommandInset ref
35108 reference "sub:Fractions"
35112 are defined with the commands
35115 \begin_layout Standard
35124 genfrac{}{}{}{0}{#1}{#2}}
35127 \begin_layout Standard
35131 \begin_layout Standard
35140 genfrac{(}{)}{0pt}{1}{#1}{#2}}
35143 \begin_layout Standard
35144 \begin_inset VSpace medskip
35147 To define a fraction where the fraction bar thickness can be given as optional
35148 argument, the following line is inserted to the LaTeX-preamble:
35151 \begin_layout Standard
35160 genfrac{}{}{#1}{}{#2}{#3}}
35163 \begin_layout Standard
35165 \begin_inset Formula \begin{align*}
35166 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
35167 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
35172 As one can see, the distance of the numerator and the denominator to the
35173 fraction bar is round about three times the bar thickness.
35176 \begin_layout Subsection
35178 \begin_inset Index idx
35181 \begin_layout Plain Layout
35190 \begin_layout Standard
35191 To cancel formulas or formula parts, the LaTeX-package
35196 \begin_inset Index idx
35199 \begin_layout Plain Layout
35205 has to be loaded with the LaTeX-preamble line
35208 \begin_layout Standard
35213 usepackage[samesize]{cancel}
35216 \begin_layout Standard
35220 \begin_layout Plain Layout
35230 \begin_inset Note Note
35233 \begin_layout Plain Layout
35234 The following table will only be displayed when the LaTeX-package
35246 \begin_layout Standard
35247 There are four ways to cancel formulas:
35250 \begin_layout Standard
35252 \begin_inset Tabular
35253 <lyxtabular version="3" rows="5" columns="2">
35254 <features tabularvalignment="middle">
35255 <column alignment="center" valignment="top" width="0">
35256 <column alignment="center" valignment="top" width="0">
35258 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35261 \begin_layout Plain Layout
35267 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35270 \begin_layout Plain Layout
35272 \begin_inset Note Note
35275 \begin_layout Plain Layout
35282 are used here as spacer.
35294 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35297 \begin_layout Plain Layout
35306 \begin_layout Plain Layout
35320 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35323 \begin_layout Plain Layout
35324 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
35334 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35337 \begin_layout Plain Layout
35346 \begin_layout Plain Layout
35360 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35363 \begin_layout Plain Layout
35364 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
35374 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35377 \begin_layout Plain Layout
35386 \begin_layout Plain Layout
35400 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35403 \begin_layout Plain Layout
35404 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
35414 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35417 \begin_layout Plain Layout
35421 \begin_inset Formula $\to$
35432 \begin_layout Plain Layout
35446 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35449 \begin_layout Plain Layout
35450 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
35466 \begin_layout Standard
35473 is especially suitable to visualize the reduction of fractions within formulas:
35474 \begin_inset Formula \[
35475 \frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}}\]
35482 \begin_layout Standard
35486 \begin_layout Plain Layout
35496 \begin_inset Note Note
35499 \begin_layout Plain Layout
35500 The following will be displayed when the LaTeX-package
35512 \begin_layout Standard
35513 You need to install the LaTeX-package
35517 to see the rest of this subsection in the output.
35520 \begin_layout Standard
35524 \begin_layout Plain Layout
35536 \begin_layout Subsection
35537 Formulas in Section Headings
35538 \begin_inset CommandInset label
35540 name "sub:Formulas-in-Section"
35545 \begin_inset Index idx
35548 \begin_layout Plain Layout
35549 Formula ! in section headings
35557 \begin_layout Standard
35558 When formulas are used in section headings, the following has to be taken
35562 \begin_layout Standard
35563 \begin_inset Note Greyedout
35566 \begin_layout Plain Layout
35572 \begin_inset Index idx
35575 \begin_layout Plain Layout
35576 Packages ! hyperref
35581 support is enabled in the document settings dialog under
35584 \begin_inset space ~
35589 , PDF-bookmarks are created for every section heading in the table of contents.
35590 If a section heading contains formulas, they are incorrectly displayed
35591 in the bookmark text, because formulas in bookmarks infringe the PDF convention
35600 \begin_layout Standard
35601 Both problems can be solved by inserting at the end of the section heading
35602 a short title with the menu
35604 Insert\SpecialChar \menuseparator
35606 \begin_inset space ~
35612 Short titles are used as alternative for multiline section headings to
35613 keep the table of contents clearly arranged.
35614 Only the short title appears in the table of contents and therefore also
35615 in the PDF-bookmark.
35618 \begin_layout Standard
35619 When formulas should be used in the table of contents but
35623 is used, one can use the following command in TeX-mode:
35626 \begin_layout Standard
35631 texorpdfstring{part}{alternative}
35632 \begin_inset Index idx
35635 \begin_layout Plain Layout
35646 \begin_layout Standard
35647 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
35648 This can be characters, formulas, footnotes, but also cross-references.
35649 The alternative is used instead of the part for the bookmark.
35652 \begin_layout Standard
35653 Here are two example headings:
35654 \begin_inset VSpace -3mm
35661 \begin_layout Plain Layout
35673 \begin_layout Subsubsection
35674 Heading without formula in table of contents
35675 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35679 \begin_inset Argument
35682 \begin_layout Plain Layout
35683 Heading without formula in table of contents
35691 \begin_layout Subsubsection
35692 Heading with formula in table of contents
35696 \begin_layout Plain Layout
35706 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35713 \begin_layout Plain Layout
35723 \begin_layout Standard
35727 \begin_layout Plain Layout
35736 In the first heading a short title was used, in the second one
35745 \begin_layout Standard
35746 To get the same formatting as for the other headings, the complete heading
35755 \begin_layout Plain Layout
35757 \begin_inset CommandInset ref
35759 reference "sub:Bold-Formulas"
35771 \begin_layout Subsection
35772 Formulas in multi-column Text
35773 \begin_inset Index idx
35776 \begin_layout Plain Layout
35777 Formula ! in multi-column text
35785 \begin_layout Standard
35786 Formulas in multi-column text are often too wide to fit into a column and
35787 thus need to be set over the whole page width.
35788 This is done by using the LaTeX-package
35796 \begin_layout Plain Layout
35801 is part of every LaTeX standard installation.
35807 \begin_inset Index idx
35810 \begin_layout Plain Layout
35811 Packages ! multicol
35816 , that is loaded with the LaTeX-preamble line
35819 \begin_layout Standard
35824 usepackage{multicol}
35827 \begin_layout Standard
35828 \begin_inset Note Greyedout
35831 \begin_layout Plain Layout
35832 Note herby that the setting
35835 \begin_inset space ~
35842 Document\SpecialChar \menuseparator
35848 \begin_inset space ~
35868 \begin_layout Standard
35869 Before the multi-column text the command
35872 \begin_layout Standard
35877 begin{multicols}{column number}
35880 \begin_layout Standard
35881 is written in TeX-mode.
35882 The column number is a number in the range of 2
35883 \begin_inset space \thinspace{}
35887 \begin_inset space \thinspace{}
35891 Before the formula the multi-column text is ended by inserting the command
35894 \begin_layout Standard
35902 \begin_layout Standard
35906 \begin_layout Standard
35907 Due to the command some space is automatically added before the formula.
35909 \begin_inset space \thinspace{}
35912 mm vertical space is inserted before the formula.
35913 When the formula style
35919 \begin_layout Plain Layout
35921 \begin_inset CommandInset ref
35923 reference "sec:Formula-Styles"
35935 \begin_inset space \thinspace{}
35938 mm space is inserted instead.
35941 \begin_layout Standard
35942 As example a multi-column text with a displayed formula:
35945 \begin_layout Standard
35951 \begin_layout Plain Layout
35955 begin{multicols}{2}
35960 Das Spektrum wird fouriertransformiert.
35961 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
35962 , Lösungsmittel) zu trennen.
35963 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
35964 nun das Aussehen des Ausgangssignals.
35965 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
35966 über alle Phasen integrieren muss.
35968 \begin_inset Formula $S$
35971 unser normiertes Ausgangssignal und
35972 \begin_inset Formula $P$
35975 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
35979 \begin_layout Plain Layout
35989 \begin_inset VSpace -6mm
35993 \begin_inset Formula \begin{equation}
35994 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi\end{equation}
36002 \begin_layout Plain Layout
36006 begin{multicols}{2}
36012 \begin_inset Formula $S_{0}$
36015 das Signal ohne Gradient ist und die Normierungsbedingung
36016 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
36020 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
36022 \begin_inset Formula $\nicefrac{\pi}{2}$
36026 \begin_inset space \thinspace{}
36029 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
36030 das Signal zusätzlich abschwächt.
36031 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
36033 \begin_inset Formula $T_{2}$
36039 \begin_layout Standard
36045 \begin_layout Plain Layout
36057 \begin_layout Subsection
36058 Formulas with Description of Variables
36059 \begin_inset Index idx
36062 \begin_layout Plain Layout
36063 Formula ! with description of variables
36071 \begin_layout Standard
36072 To describe variables within a formula, like in formula
36073 \begin_inset CommandInset ref
36075 reference "eq:within"
36084 \begin_inset Formula $n$
36088 \begin_inset space ~
36091 matrix is used with left aligned columns for the
36092 \begin_inset Formula $n$
36099 \begin_layout Plain Layout
36101 \begin_inset CommandInset ref
36103 reference "sec:Matrices"
36112 To set the description in a smaller size, before the matrix e.
36113 \begin_inset space \thinspace{}
36117 \begin_inset space \space{}
36130 \begin_layout Plain Layout
36132 \begin_inset CommandInset ref
36134 reference "sub:Font-Sizes"
36146 \begin_layout Standard
36147 When the formula style
36153 \begin_layout Plain Layout
36155 \begin_inset CommandInset ref
36157 reference "sec:Formula-Styles"
36178 \begin_layout Plain Layout
36185 only works in formulas with the style
36190 \begin_inset CommandInset ref
36192 reference "sub:Variable-Space"
36201 is inserted before and after the matrix to have the same separation of
36202 the matrix from the equation and the side margin.
36205 \begin_layout Standard
36206 When the formula style
36210 is used, the method described in
36211 \begin_inset CommandInset ref
36213 reference "sub:Flalign-Environment"
36217 is used to indent formulas.
36219 \begin_inset CommandInset ref
36221 reference "eq:within"
36225 consists of five columns whereas in the first two columns contain the equation,
36226 the third the matrix and the last one an empty TeX-brace.
36227 \begin_inset Formula \begin{flalign}
36228 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
36229 \rho & \textrm{density}\\
36230 V & \textrm{volume}\\
36231 g & \textrm{gravitational acceleration}
36232 \end{array} & & {}\label{eq:within}\end{flalign}
36239 \begin_layout Subsection
36240 Upright small Greek Letters
36241 \begin_inset CommandInset label
36243 name "sub:Upright-small-Greek"
36248 \begin_inset Index idx
36251 \begin_layout Plain Layout
36252 Greek letters ! upright
36260 \begin_layout Standard
36261 Most of the math fonts only provide italic small Greek letters.
36262 But for symbols of elementary particles like pions and neutrinos, upright
36263 Greek letters are needed.
36272 \begin_layout Plain Layout
36277 is part of the LaTeX-package
36282 \begin_inset Index idx
36285 \begin_layout Plain Layout
36290 \begin_layout Plain Layout
36310 \begin_inset Index idx
36313 \begin_layout Plain Layout
36319 that is loaded with the LaTeX-preamble line
36322 \begin_layout Standard
36327 usepackage{upgreek}
36330 \begin_layout Standard
36336 \begin_layout Plain Layout
36346 \begin_inset Note Note
36349 \begin_layout Plain Layout
36350 The following table will only be displayed when the LaTeX-package
36359 They are created when the command for a small Greek letters is started
36365 For example the command
36372 \begin_inset Formula $\uptau$
36378 \begin_layout Standard
36379 With these commands reactions of elementary particles can be typeset:
36380 \begin_inset Formula \[
36381 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}\]
36388 \begin_layout Standard
36389 The upright letters are more bold and wider than the italic ones.
36390 They should therefore not be used for units like
36391 \begin_inset Quotes eld
36395 \begin_inset Quotes erd
36401 \begin_layout Standard
36405 \begin_layout Plain Layout
36415 \begin_inset Note Note
36418 \begin_layout Plain Layout
36419 The following will be displayed when the LaTeX-package
36431 \begin_layout Standard
36432 You need to install the LaTeX-package
36436 to see the rest of this subsection in the output.
36439 \begin_layout Standard
36443 \begin_layout Plain Layout
36455 \begin_layout Subsection
36456 Text Characters in Formulas
36457 \begin_inset CommandInset label
36459 name "sub:Text-Characters-in"
36464 \begin_inset Index idx
36467 \begin_layout Plain Layout
36476 \begin_layout Standard
36477 In some cases you might want to insert text characters directly into formulas.
36478 When for example the centered dot · is often used in formulas like
36479 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
36482 , one would have to insert the command
36492 \begin_layout Plain Layout
36494 \begin_inset CommandInset ref
36496 reference "sub:Binary-Operators"
36505 all the time, because this character is defined in all encodings as text
36507 But the encoding can be changed by this LaTeX-preamble line:
36510 \begin_layout Standard
36515 Declare Inputtext{183}{
36525 f\SpecialChar \textcompwordmark{}
36529 \begin_layout Standard
36530 The character encoding (menu
36532 Document\SpecialChar \menuseparator
36533 Settings\SpecialChar \menuseparator
36536 ) specifies what character appears when a keyboard key is pressed.
36537 When the key for the character '·' is pressed, internally the command
36544 But this command is not available in a formula so that you would get LaTeX-erro
36546 With the changed encoding the right command is chosen automatically, depending
36547 on if the character was inserted into a formula or not.
36550 \begin_layout Standard
36551 The encoding of several characters is saved in definition files.
36552 Fore example the encoding
36556 is defined in the file
36560 that is in the installation folder of LaTeX.
36561 Encodings should only be changed via the LaTeX-preamble and not in the
36563 Otherwise own documents could not be edited by other LyX users working
36564 on other computers.
36567 \begin_layout Standard
36568 \begin_inset VSpace medskip
36571 Besides the centered dot, in this document the degree sign ° is defined
36572 with the following LaTeX-preamble line so that it can directly be inserted
36576 \begin_layout Standard
36581 DeclareInputtext{176}{
36591 f\SpecialChar \textcompwordmark{}
36595 \begin_layout Standard
36596 \begin_inset Newpage newpage
36602 \begin_layout Section
36605 \begin_inset Index idx
36608 \begin_layout Plain Layout
36617 \begin_layout Standard
36618 This section is a summary of the most important typographic rules, listed
36623 \begin_layout Plain Layout
36624 This collection was partly taken from the German semi-official dictionary
36626 \begin_inset Quotes eld
36630 \begin_inset Quotes erd
36634 \begin_inset CommandInset citation
36640 that lists some of the ISO rules.
36641 More rules are listed in
36642 \begin_inset CommandInset citation
36656 \begin_layout Itemize
36665 \begin_layout Plain Layout
36666 done with font styles, see
36667 \begin_inset CommandInset ref
36669 reference "sub:Font-Styles"
36678 , no matter if they appear in italic text: 30
36679 \begin_inset space \thinspace{}
36683 \begin_inset Newline newline
36686 Between the value and the unit is the smallest space, see
36687 \begin_inset CommandInset ref
36689 reference "sub:Predefined-Space"
36694 \begin_inset Newline newline
36697 This convention is automatically fulfilled when the command
36704 When it is entered to a formula, two boxes appear.
36705 In the first one the value is inserted, in the second one the unit, and
36707 \begin_inset Formula $\unit[30]{km/h}$
36711 \begin_inset space \thinspace{}
36721 is not a real LaTeX command but the command
36727 , therefore you cannot use it in TeX code.
36730 \begin_layout Itemize
36731 Percent and perthousand signs are set like physical units:
36732 \begin_inset Newline newline
36736 \begin_inset space \thinspace{}
36742 \begin_layout Itemize
36743 The degree sign follows directly on the value: 15°, but not when it is used
36745 \begin_inset space \thinspace{}
36751 \begin_layout Itemize
36752 In numbers with more than four digits the smallest space is inserted before
36753 every third digit to group them:
36763 \begin_inset space \thinspace{}
36767 \begin_inset space \thinspace{}
36773 \begin_layout Itemize
36774 For dimensions like 120×90×40
36775 \begin_inset space \thinspace{}
36778 cm the multiplication sign
36779 \begin_inset Quotes eld
36783 \begin_inset Quotes erd
36787 It is available either via the command
36795 Insert\SpecialChar \menuseparator
36796 Special Character\SpecialChar \menuseparator
36802 \begin_layout Itemize
36803 Functions with names consisting of several letters are set upright to avoid
36805 \begin_inset CommandInset ref
36807 reference "sub:Predefined-Functions"
36814 \begin_layout Itemize
36815 Indices consisting of several letters, are set upright:
36816 \begin_inset Formula $E_{\mathrm{kin}}$
36820 \begin_inset Newline newline
36823 Components of matrices are set italic:
36824 \begin_inset Formula $\hat{H}_{kl}$
36830 \begin_layout Itemize
36831 The differentiation/integration operator 'd', the Euler's number 'e' and
36832 the imaginary unit 'i' should be set upright, to avoid mixing them up with
36836 \begin_layout Itemize
36837 The character that denotes a
36841 transformation is inserted either by the command
36849 \begin_layout Plain Layout
36862 Insert\SpecialChar \menuseparator
36863 Special Character\SpecialChar \menuseparator
36864 Symbols\SpecialChar \menuseparator
36866 \begin_inset space ~
36872 \begin_inset Formula $\mathscr{F}$
36878 \begin_layout Standard
36879 \begin_inset Newpage newpage
36885 \begin_layout Section
36887 \begin_inset Index idx
36890 \begin_layout Plain Layout
36899 \begin_layout Standard
36900 Some characters and symbols can be created with several commands.
36901 Here is a list of the synonym commands:
36904 \begin_layout Standard
36905 \begin_inset VSpace bigskip
36909 \begin_inset space \hfill{}
36913 \begin_inset Tabular
36914 <lyxtabular version="3" rows="12" columns="2">
36915 <features tabularvalignment="middle">
36916 <column alignment="center" valignment="top" width="0pt">
36917 <column alignment="center" valignment="top" width="0pt">
36919 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
36922 \begin_layout Plain Layout
36928 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
36931 \begin_layout Plain Layout
36933 \begin_inset Note Note
36936 \begin_layout Plain Layout
36943 is only used as spacer.
36955 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36958 \begin_layout Plain Layout
36966 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36969 \begin_layout Plain Layout
36973 \begin_layout Plain Layout
36986 \begin_layout Plain Layout
37000 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37003 \begin_layout Plain Layout
37011 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37014 \begin_layout Plain Layout
37024 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37027 \begin_layout Plain Layout
37035 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37038 \begin_layout Plain Layout
37048 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37051 \begin_layout Plain Layout
37059 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37062 \begin_layout Plain Layout
37070 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37073 \begin_layout Plain Layout
37081 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37084 \begin_layout Plain Layout
37092 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37095 \begin_layout Plain Layout
37103 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37106 \begin_layout Plain Layout
37116 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37119 \begin_layout Plain Layout
37127 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37130 \begin_layout Plain Layout
37140 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37143 \begin_layout Plain Layout
37151 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37154 \begin_layout Plain Layout
37164 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37167 \begin_layout Plain Layout
37175 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37178 \begin_layout Plain Layout
37188 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37191 \begin_layout Plain Layout
37199 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37202 \begin_layout Plain Layout
37210 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37213 \begin_layout Plain Layout
37221 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37224 \begin_layout Plain Layout
37236 \begin_inset space \hfill{}
37240 \begin_inset Tabular
37241 <lyxtabular version="3" rows="12" columns="2">
37242 <features tabularvalignment="middle">
37243 <column alignment="center" valignment="top" width="0pt">
37244 <column alignment="center" valignment="top" width="0pt">
37246 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37249 \begin_layout Plain Layout
37255 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37258 \begin_layout Plain Layout
37266 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37269 \begin_layout Plain Layout
37277 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37280 \begin_layout Plain Layout
37292 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37295 \begin_layout Plain Layout
37303 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37306 \begin_layout Plain Layout
37316 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37319 \begin_layout Plain Layout
37327 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37330 \begin_layout Plain Layout
37340 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37343 \begin_layout Plain Layout
37351 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37354 \begin_layout Plain Layout
37362 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37365 \begin_layout Plain Layout
37373 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37376 \begin_layout Plain Layout
37384 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37387 \begin_layout Plain Layout
37395 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37398 \begin_layout Plain Layout
37408 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37411 \begin_layout Plain Layout
37419 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37422 \begin_layout Plain Layout
37432 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37435 \begin_layout Plain Layout
37443 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37446 \begin_layout Plain Layout
37456 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37459 \begin_layout Plain Layout
37467 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37470 \begin_layout Plain Layout
37480 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37483 \begin_layout Plain Layout
37491 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37494 \begin_layout Plain Layout
37504 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37507 \begin_layout Plain Layout
37515 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37518 \begin_layout Plain Layout
37532 \begin_inset space \hfill{}
37538 \begin_layout Standard
37539 \begin_inset Newpage newpage
37545 \begin_layout Bibliography
37546 \labelwidthstring References
37547 \begin_inset CommandInset bibitem
37548 LatexCommand bibitem
37560 The LaTeX Companion
37563 Addison Wesley, 2004
37566 \begin_layout Bibliography
37567 \labelwidthstring References
37568 \begin_inset CommandInset bibitem
37569 LatexCommand bibitem
37575 \begin_inset CommandInset href
37578 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
37582 of LaTeX's math abilities
37585 \begin_layout Bibliography
37586 \labelwidthstring References
37587 \begin_inset CommandInset bibitem
37588 LatexCommand bibitem
37594 \begin_inset CommandInset href
37597 target "ftp://ftp.ams.org/pub/tex/doc/amsmath/amsldoc.pdf"
37605 \begin_layout Plain Layout
37617 \begin_layout Bibliography
37618 \labelwidthstring References
37619 \begin_inset CommandInset bibitem
37620 LatexCommand bibitem
37626 \begin_inset CommandInset href
37629 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
37633 of all symbols available with LaTeX-packages
37636 \begin_layout Bibliography
37637 \labelwidthstring References
37638 \begin_inset CommandInset bibitem
37639 LatexCommand bibitem
37645 \begin_inset CommandInset href
37647 name "Documentation"
37648 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
37652 of the LaTeX-package
37657 \begin_inset Index idx
37660 \begin_layout Plain Layout
37661 Packages ! hyperref
37669 \begin_layout Bibliography
37670 \labelwidthstring References
37671 \begin_inset CommandInset bibitem
37672 LatexCommand bibitem
37678 \begin_inset CommandInset href
37680 name "Documentation"
37681 target "http://www.ctan.org/tex-archive/macros/latex/contrib/mhchem/mhchem.pdf"
37685 of the LaTeX-package
37690 \begin_inset Index idx
37693 \begin_layout Plain Layout
37702 \begin_layout Bibliography
37703 \labelwidthstring References
37704 \begin_inset CommandInset bibitem
37705 LatexCommand bibitem
37711 \begin_inset CommandInset href
37714 target "http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf"
37725 \begin_inset CommandInset ref
37727 reference "sub:Operator-Limits"
37732 \begin_inset Index idx
37735 \begin_layout Plain Layout
37746 \begin_layout Bibliography
37747 \labelwidthstring References
37748 \begin_inset CommandInset bibitem
37749 LatexCommand bibitem
37760 Auflage, Duden 2001
37763 \begin_layout Bibliography
37764 \labelwidthstring References
37765 \begin_inset CommandInset bibitem
37766 LatexCommand bibitem
37772 \begin_inset CommandInset href
37775 target "http://physics.nist.gov/Document/checklist.pdf"
37779 for reviewing manuscripts
37782 \begin_layout Standard
37783 \begin_inset CommandInset index_print
37784 LatexCommand printindex