1 #LyX 2.0.0beta1 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}}
2269 \begin_layout Standard
2270 For inline fractions with a sloped fraction stroke you can use the command
2278 \begin_inset Index idx
2281 \begin_layout Plain Layout
2290 \begin_inset Formula $\nicefrac{5}{31}$
2300 \begin_inset Index idx
2303 \begin_layout Plain Layout
2312 \begin_inset Formula $\unitfrac{5}{31}$
2315 There is furthermore the command
2321 that offers to write a fraction in combination with a number:
2322 \begin_inset Formula $\unitfrac[2]{1}{3}$
2328 \begin_layout Standard
2329 \begin_inset Note Greyedout
2332 \begin_layout Plain Layout
2343 is not a real LaTeX command but the command
2344 \begin_inset Newline newline
2351 unitfrac[number]{numerator}{denominator}
2354 Therefore you cannot use it in TeX code.
2362 \begin_layout Standard
2363 How to define own fractions where the fraction stroke can be changed, is
2365 \begin_inset CommandInset ref
2367 reference "sub:Self-defined-Fractions"
2374 \begin_layout Subsection
2376 \begin_inset Index idx
2379 \begin_layout Plain Layout
2388 \begin_layout Standard
2389 Square roots are created with
2396 \begin_inset Index idx
2399 \begin_layout Plain Layout
2407 or the math toolbar button
2408 \begin_inset Graphics
2409 filename ../images/math/sqrt.png
2414 , all other roots with the command
2421 \begin_inset Index idx
2424 \begin_layout Plain Layout
2432 or with the math toolbar button
2433 \begin_inset Graphics
2434 filename ../images/math/root.png
2442 \begin_layout Standard
2444 \begin_inset Tabular
2445 <lyxtabular version="3" rows="3" columns="2">
2446 <features tabularvalignment="middle">
2447 <column alignment="center" valignment="top" width="0pt">
2448 <column alignment="center" valignment="top" width="0pt">
2450 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2453 \begin_layout Plain Layout
2459 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2462 \begin_layout Plain Layout
2464 \begin_inset Note Note
2467 \begin_layout Plain Layout
2474 is only used as spacer.
2486 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2489 \begin_layout Plain Layout
2496 \begin_layout Plain Layout
2510 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2513 \begin_layout Plain Layout
2514 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$
2524 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
2527 \begin_layout Plain Layout
2534 \begin_layout Plain Layout
2544 \begin_inset Formula $\downarrow$
2552 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
2555 \begin_layout Plain Layout
2556 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$
2572 \begin_layout Standard
2573 A square root can also be created with
2579 when the root index field is left empty.
2582 \begin_layout Standard
2583 With certain indices the distance to the root is too small, like in this
2585 \begin_inset Formula $\sqrt[\beta]{B}$
2589 \begin_inset Newline newline
2593 \begin_inset Formula $\beta$
2597 To avoid this, the commands
2604 \begin_inset Index idx
2607 \begin_layout Plain Layout
2622 \begin_inset Index idx
2625 \begin_layout Plain Layout
2633 are used with the following scheme:
2636 \begin_layout Standard
2650 \begin_layout Standard
2651 Distance is the number of Big Points (unit bp;
2652 \begin_inset Formula $\mathrm{72\, bp=1\, inch}$
2655 ), that the index should be moved to the left or top, resp..
2656 The commands are written to the index.
2657 This way the command
2658 \begin_inset Newline newline
2668 \begin_inset Formula $\to$
2674 \begin_inset Formula $\to$
2683 \begin_layout Plain Layout
2693 \begin_inset Formula $\to$
2697 \begin_inset Newline newline
2702 produces a correct typeset formula:
2703 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2709 \begin_layout Subsection
2710 Binomial Coefficients
2711 \begin_inset Index idx
2714 \begin_layout Plain Layout
2715 Binomial coefficients
2723 \begin_layout Standard
2724 Binomial coefficients are inserted with the command
2731 \begin_inset Index idx
2734 \begin_layout Plain Layout
2742 or with the submenu of the math toolbar button
2743 \begin_inset Graphics
2744 filename ../images/math/frac-square.png
2750 Analog to fractions (
2769 \begin_inset Index idx
2772 \begin_layout Plain Layout
2787 \begin_inset Index idx
2790 \begin_layout Plain Layout
2799 For other brackets around binomial coeficients there are the commands
2806 \begin_inset Index idx
2809 \begin_layout Plain Layout
2824 \begin_inset Index idx
2827 \begin_layout Plain Layout
2838 \begin_layout Standard
2840 \begin_inset Tabular
2841 <lyxtabular version="3" rows="6" columns="2">
2842 <features tabularvalignment="middle">
2843 <column alignment="center" valignment="top" width="0pt">
2844 <column alignment="center" valignment="top" width="0pt">
2846 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2849 \begin_layout Plain Layout
2855 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2858 \begin_layout Plain Layout
2860 \begin_inset Note Note
2863 \begin_layout Plain Layout
2870 is only used as spacer.
2882 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2885 \begin_layout Plain Layout
2892 \begin_layout Plain Layout
2902 \begin_inset Formula $\downarrow$
2910 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2913 \begin_layout Plain Layout
2914 \begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$
2924 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2927 \begin_layout Plain Layout
2934 \begin_layout Plain Layout
2944 \begin_inset Formula $\downarrow$
2952 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2955 \begin_layout Plain Layout
2956 \begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$
2966 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2969 \begin_layout Plain Layout
2976 \begin_layout Plain Layout
2986 \begin_inset Formula $\downarrow$
2994 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2997 \begin_layout Plain Layout
2998 \begin_inset Formula $\raisebox{5mm}{}\tbinom{A}{B}\raisebox{-2.5mm}{}$
3008 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3011 \begin_layout Plain Layout
3018 \begin_layout Plain Layout
3028 \begin_inset Formula $\downarrow$
3036 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3039 \begin_layout Plain Layout
3040 \begin_inset Formula $\raisebox{5mm}{}{A \brack B}\raisebox{-2.5mm}{}$
3050 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3053 \begin_layout Plain Layout
3060 \begin_layout Plain Layout
3070 \begin_inset Formula $\downarrow$
3078 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3081 \begin_layout Plain Layout
3082 \begin_inset Formula $\raisebox{5mm}{}{A \brace B}\raisebox{-2.5mm}{}$
3098 \begin_layout Subsection
3099 Case Differentiations
3100 \begin_inset Index idx
3103 \begin_layout Plain Layout
3104 Case differentiations
3112 \begin_layout Standard
3114 \begin_inset Tabular
3115 <lyxtabular version="3" rows="3" columns="2">
3116 <features tabularvalignment="middle">
3117 <column alignment="center" valignment="top" width="0pt">
3118 <column alignment="center" valignment="top" width="0pt">
3120 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3123 \begin_layout Plain Layout
3129 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3132 \begin_layout Plain Layout
3140 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3143 \begin_layout Plain Layout
3150 \begin_layout Plain Layout
3160 \begin_inset Formula $\to$
3164 \begin_inset Index idx
3167 \begin_layout Plain Layout
3180 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3183 \begin_layout Plain Layout
3184 \begin_inset Formula $\begin{cases}
3195 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3198 \begin_layout Plain Layout
3205 \begin_layout Plain Layout
3217 arg "newline-insert newline"
3225 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3228 \begin_layout Plain Layout
3229 \begin_inset Formula $\begin{cases}
3230 A & \textrm{for }x>0\\
3231 B & \textrm{for }x=0
3248 \begin_layout Standard
3255 or the usage of the math toolbar button
3256 \begin_inset Graphics
3257 filename ../images/math/cases.png
3262 you can create new lines with the shortcut
3265 arg "newline-insert newline"
3268 or the table toolbar button
3269 \begin_inset Graphics
3270 filename ../images/tabular-feature_append-row.png
3278 \begin_layout Standard
3285 is also available via the menu
3287 Insert\SpecialChar \menuseparator
3288 Math\SpecialChar \menuseparator
3294 \begin_layout Subsection
3296 \begin_inset Index idx
3299 \begin_layout Plain Layout
3308 \begin_layout Standard
3316 \begin_inset Index idx
3319 \begin_layout Plain Layout
3327 every character can be displayed canceled.
3328 The characters are quasi accentuated by a slash.
3331 \begin_layout Standard
3333 \begin_inset Tabular
3334 <lyxtabular version="3" rows="4" columns="2">
3335 <features tabularvalignment="middle">
3336 <column alignment="center" valignment="top" width="0pt">
3337 <column alignment="center" valignment="top" width="0pt">
3339 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3342 \begin_layout Plain Layout
3348 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3351 \begin_layout Plain Layout
3359 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3362 \begin_layout Plain Layout
3370 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3373 \begin_layout Plain Layout
3374 \begin_inset Formula $\not=$
3384 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3387 \begin_layout Plain Layout
3397 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3400 \begin_layout Plain Layout
3401 \begin_inset Formula $\not\le$
3411 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3414 \begin_layout Plain Layout
3424 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3427 \begin_layout Plain Layout
3428 \begin_inset Formula $\not\parallel$
3444 \begin_layout Standard
3445 The last example shows, that not all negations look good.
3446 Therefore there are for some negations special commands (see
3447 \begin_inset CommandInset ref
3449 reference "sub:Mathematical-Symbols"
3454 \begin_inset CommandInset ref
3456 reference "sec:Relations"
3463 \begin_layout Subsection
3465 \begin_inset CommandInset label
3467 name "sub:Placeholders"
3472 \begin_inset Index idx
3475 \begin_layout Plain Layout
3482 \begin_inset Index idx
3485 \begin_layout Plain Layout
3486 Chemical characters ! Isotopes
3492 \begin_inset Index idx
3495 \begin_layout Plain Layout
3500 \begin_layout Plain Layout
3511 \begin_layout Plain Layout
3526 \begin_layout Standard
3528 \begin_inset space \thinspace{}
3532 \begin_inset space \space{}
3539 \begin_layout Plain Layout
3540 Typesetting isotopes and chemical symbols is described in
3541 \begin_inset CommandInset ref
3543 reference "sub:Chemical-Symbols-and"
3552 the following problem occurs:
3555 \begin_layout Standard
3557 \begin_inset Tabular
3558 <lyxtabular version="3" rows="2" columns="2">
3559 <features tabularvalignment="middle">
3560 <column alignment="center" valignment="top" width="0pt">
3561 <column alignment="center" valignment="top" width="0pt">
3563 <cell alignment="center" valignment="top" usebox="none">
3566 \begin_layout Plain Layout
3567 Indices created with sub- and superscripts:
3572 <cell alignment="center" valignment="top" usebox="none">
3575 \begin_layout Plain Layout
3576 \begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
3586 <cell alignment="center" valignment="top" usebox="none">
3589 \begin_layout Plain Layout
3595 <cell alignment="center" valignment="top" usebox="none">
3598 \begin_layout Plain Layout
3599 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3613 \begin_inset Note Note
3616 \begin_layout Plain Layout
3623 is only used as spacer.
3631 \begin_layout Standard
3632 The shorter index is by default placed below or above the first character
3633 of the longer index.
3634 To avoid this there is the command
3641 \begin_inset Index idx
3644 \begin_layout Plain Layout
3652 or the math toolbar button
3653 \begin_inset space \thinspace{}
3660 \begin_layout Plain Layout
3661 can be found in the submenu of the toolbar button
3662 \begin_inset Graphics
3663 filename ../images/math/space.png
3674 \begin_inset Graphics
3675 filename ../images/math/phantom.png
3680 that creates one or more phantom characters.
3687 a small blue box appears that is superposed with two red arrows.
3688 The arrows indicate that the complete width and height of the box content
3689 will be created as placeholder.
3690 Phantom characters are accordingly placeholders with the size of the characters.
3693 \begin_layout Standard
3695 \begin_inset Tabular
3696 <lyxtabular version="3" rows="4" columns="2">
3697 <features tabularvalignment="middle">
3698 <column alignment="center" valignment="top" width="0">
3699 <column alignment="center" valignment="top" width="0">
3701 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3704 \begin_layout Plain Layout
3710 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3713 \begin_layout Plain Layout
3715 \begin_inset Note Note
3718 \begin_layout Plain Layout
3725 is only used as spacer.
3737 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3740 \begin_layout Plain Layout
3745 \begin_layout Plain Layout
3760 \begin_layout Plain Layout
3770 \begin_inset Formula $\to$
3777 \begin_layout Plain Layout
3791 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3794 \begin_layout Plain Layout
3795 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
3805 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3808 \begin_layout Plain Layout
3813 \begin_layout Plain Layout
3828 \begin_layout Plain Layout
3838 \begin_inset Formula $\to$
3845 \begin_layout Plain Layout
3859 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3862 \begin_layout Plain Layout
3863 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
3873 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3876 \begin_layout Plain Layout
3883 \begin_layout Plain Layout
3898 \begin_layout Plain Layout
3908 \begin_inset Formula $\to$
3915 \begin_layout Plain Layout
3929 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3932 \begin_layout Plain Layout
3933 \begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
3949 \begin_layout Standard
3950 Furthermore there are the commands
3957 \begin_inset Index idx
3960 \begin_layout Plain Layout
3969 \begin_inset space ~
3973 \begin_inset Graphics
3974 filename ../images/math/vphantom.png
3986 \begin_inset Index idx
3989 \begin_layout Plain Layout
3998 \begin_inset space ~
4002 \begin_inset Graphics
4003 filename ../images/math/hphantom.png
4015 creates only space for the maximal height of the characters in the box
4016 but not for its width.
4023 creates only space for the width of the box content.
4024 Therefore the boxes of both commands have only one red arrow.
4027 \begin_layout Standard
4038 \begin_layout Plain Layout
4053 space for the height of the integral sign,
4057 \begin_layout Plain Layout
4064 creates an integral sign, see
4065 \begin_inset CommandInset ref
4067 reference "sub:Big-Operators"
4076 because this is the larger character.
4077 An example application is in
4078 \begin_inset CommandInset ref
4080 reference "sub:Multiline-Brackets"
4087 \begin_layout Standard
4088 Placeholders can also be used for text when it is inserted via the menu
4091 Insert\SpecialChar \menuseparator
4092 Formatting\SpecialChar \menuseparator
4098 \begin_layout Standard
4100 \begin_inset Newline newline
4104 \begin_inset Phantom Phantom
4107 \begin_layout Plain Layout
4116 \begin_layout Subsection
4118 \begin_inset Index idx
4121 \begin_layout Plain Layout
4128 \begin_inset Index idx
4131 \begin_layout Plain Layout
4132 Formula ! underlined
4140 \begin_layout Standard
4142 \begin_inset Tabular
4143 <lyxtabular version="3" rows="4" columns="2">
4144 <features tabularvalignment="middle">
4145 <column alignment="center" valignment="top" width="0pt">
4146 <column alignment="center" valignment="top" width="0pt">
4148 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4151 \begin_layout Plain Layout
4157 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4160 \begin_layout Plain Layout
4162 \begin_inset Note Note
4165 \begin_layout Plain Layout
4172 is only used as spacer.
4184 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4187 \begin_layout Plain Layout
4194 \begin_layout Plain Layout
4204 \begin_inset Index idx
4207 \begin_layout Plain Layout
4220 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4223 \begin_layout Plain Layout
4224 \begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
4234 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
4237 \begin_layout Plain Layout
4244 \begin_layout Plain Layout
4254 \begin_inset Index idx
4257 \begin_layout Plain Layout
4270 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
4273 \begin_layout Plain Layout
4274 \begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
4284 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4287 \begin_layout Plain Layout
4294 \begin_layout Plain Layout
4309 \begin_layout Plain Layout
4323 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4326 \begin_layout Plain Layout
4327 \begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
4343 \begin_layout Standard
4344 In the last example it doesn't matter if first
4359 \begin_layout Standard
4360 To double underline e.
4361 \begin_inset space \thinspace{}
4365 \begin_inset space \space{}
4377 \begin_layout Standard
4378 It is possible to place up to 6 lines above or below characters.
4381 \begin_layout Standard
4382 \begin_inset VSpace bigskip
4385 Custom lines can be created using the command
4392 \begin_inset Index idx
4395 \begin_layout Plain Layout
4403 which has the following scheme:
4406 \begin_layout Standard
4411 rule[vertical offset]{length}{thickness}
4414 \begin_layout Standard
4415 The optional vertical offset shifts the line upwards (or downwards, when
4416 the value is negative).
4418 \begin_inset CommandInset ref
4420 reference "tab:Available-units"
4424 can be used for the values.
4425 Here are two example lines created with the commands
4426 \begin_inset Newline newline
4433 rule[-2ex]{3cm}{2pt}
4444 \begin_layout Standard
4446 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4452 \begin_layout Standard
4459 can also be used for text when a line is inserted via the menu
4461 Insert\SpecialChar \menuseparator
4462 Formatting\SpecialChar \menuseparator
4464 \begin_inset space ~
4472 \begin_layout Standard
4474 \begin_inset CommandInset line
4485 \begin_layout Subsection
4487 \begin_inset CommandInset label
4494 \begin_inset Index idx
4497 \begin_layout Plain Layout
4506 \begin_layout Standard
4507 There are different types of ellipses available.
4511 \begin_layout Plain Layout
4512 In the math toolbar in the submenu of the button
4513 \begin_inset Graphics
4514 filename ../images/math/ldots.png
4524 For listings dots at the baseline are used (
4531 \begin_inset Index idx
4534 \begin_layout Plain Layout
4542 ), while for operations dots are needed that are on the same height as the
4550 \begin_inset Index idx
4553 \begin_layout Plain Layout
4562 When using the command
4569 \begin_inset Index idx
4572 \begin_layout Plain Layout
4580 , LaTeX decides on the basis of the next character what type is used.
4583 \begin_layout Standard
4585 \begin_inset Tabular
4586 <lyxtabular version="3" rows="9" columns="2">
4587 <features tabularvalignment="middle">
4588 <column alignment="center" valignment="top" width="0pt">
4589 <column alignment="center" valignment="top" width="0pt">
4591 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4594 \begin_layout Plain Layout
4600 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4603 \begin_layout Plain Layout
4611 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4614 \begin_layout Plain Layout
4619 \begin_layout Plain Layout
4634 \begin_layout Plain Layout
4648 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4651 \begin_layout Plain Layout
4652 \begin_inset Formula $A_{1},\dots,A_{n}$
4662 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4665 \begin_layout Plain Layout
4670 \begin_layout Plain Layout
4685 \begin_layout Plain Layout
4699 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4702 \begin_layout Plain Layout
4703 \begin_inset Formula $A_{1}+\dots+A_{n}$
4713 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4716 \begin_layout Plain Layout
4721 \begin_layout Plain Layout
4736 \begin_layout Plain Layout
4750 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4753 \begin_layout Plain Layout
4754 \begin_inset Formula $A_{1},\ldots,A_{n}$
4764 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4767 \begin_layout Plain Layout
4772 \begin_layout Plain Layout
4787 \begin_layout Plain Layout
4801 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4804 \begin_layout Plain Layout
4805 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4815 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4818 \begin_layout Plain Layout
4826 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4829 \begin_layout Plain Layout
4830 \begin_inset Formula $\vdots$
4840 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4843 \begin_layout Plain Layout
4851 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4854 \begin_layout Plain Layout
4855 \begin_inset Formula $\ddots$
4865 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4868 \begin_layout Plain Layout
4876 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4879 \begin_layout Plain Layout
4880 \begin_inset Formula $\iddots$
4890 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4893 \begin_layout Plain Layout
4895 \begin_inset space \thinspace{}
4898 matrix with the different dots
4903 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4906 \begin_layout Plain Layout
4907 \begin_inset Formula $\begin{array}{ccc}
4908 A_{11} & \cdots & A_{1m}\\
4909 \vdots & \ddots & \vdots\\
4910 A_{n1} & \cdots & A_{nm}
4927 \begin_layout Standard
4928 The ellipses available in menu
4930 Insert\SpecialChar \menuseparator
4932 \begin_inset space ~
4946 \begin_layout Standard
4947 \begin_inset VSpace medskip
4956 , one of the options
4958 Use mathdots package (automatically)
4960 must be set in the document settings under
4963 \begin_inset space ~
4969 \begin_inset Newline newline
4974 Use mathdots package
4976 will improve the appearance of all dots in the documents if their font
4977 style or size is not the default.
4980 \begin_layout Standard
4981 \begin_inset VSpace medskip
4984 Specially for matrices there are ellipses that span over several columns.
4985 They are created with the command
4992 \begin_inset Index idx
4995 \begin_layout Plain Layout
5003 , that has the following scheme:
5006 \begin_layout Standard
5011 hdotsfor[distance]{number of columns}
5014 \begin_layout Standard
5015 The number of columns specifies how many columns should be spanned.
5016 Distance is a factor for the distance between the dots.
5019 \begin_layout Standard
5020 In the following matrix the command
5026 was inserted in the first box of the second line, to get an ellipsis with
5027 a dot distance twice as long as with the command
5034 \begin_inset Formula \[
5035 \left(\begin{array}{cccc}
5044 Note that the matrix fields that should be spanned must be empty, otherwise
5045 you get LaTeX-errors.
5048 \begin_layout Standard
5049 \begin_inset VSpace bigskip
5052 Furthermore you can fill with the command
5059 \begin_inset Index idx
5062 \begin_layout Plain Layout
5070 the rest of a line with dots.
5071 The effect of these commands is the same like with
5078 \begin_inset CommandInset ref
5080 reference "sub:Variable-Space"
5087 \begin_layout Standard
5088 For example the command
5096 \begin_layout Plain Layout
5110 \begin_layout Standard
5111 \begin_inset Formula $A\dotfill B$
5117 \begin_layout Standard
5124 there is for a line the command
5131 \begin_inset Index idx
5134 \begin_layout Plain Layout
5145 \begin_layout Standard
5146 \begin_inset Formula $A\hrulefill B$
5152 \begin_layout Standard
5153 To use the commands for text, they have to be inserted in TeX-mode.
5156 \begin_layout Section
5158 \begin_inset CommandInset label
5165 \begin_inset Index idx
5168 \begin_layout Plain Layout
5177 \begin_layout Standard
5178 Matrices can be inserted via the math toolbar button
5179 \begin_inset Graphics
5180 filename ../images/dialog-show_mathmatrix.png
5187 Insert\SpecialChar \menuseparator
5188 Math\SpecialChar \menuseparator
5192 In the matrix dialog you can specify the number of columns and rows, the
5193 alignment and the decoration.
5194 The vertical alignment is hereby only of importance for matrices in inline
5198 \begin_layout Standard
5199 The first matrix is top
5200 \begin_inset Formula $\begin{array}[t]{cccc}
5208 \begin_inset Formula $\begin{array}{cccc}
5215 and the third bottom
5216 \begin_inset Formula $\begin{array}[b]{cccc}
5226 \begin_layout Standard
5227 The horizontal alignment specifies how the column entries should be aligned.
5228 It is set by entering a letter for every column.
5233 denotes left aligned,
5242 To create for example a 4
5247 \begin_inset space ~
5250 matrix where the first column is left aligned, the second and third are
5251 centered and the last one is right aligned, one enters for the horizontal
5257 Normally are in a matrix all columns centered, therefore the default is
5258 for every column is a
5265 \begin_layout Standard
5266 Horizontal alignment:
5269 \begin_layout Standard
5275 \begin_inset Formula $\begin{array}{lll}
5287 \begin_inset Formula $\begin{array}{ccc}
5299 \begin_inset Formula $\begin{array}{rrr}
5309 \begin_layout Standard
5310 To add or delete rows and columns subsequently, the math toolbar buttons
5312 \begin_inset Graphics
5313 filename ../images/tabular-feature_append-row.png
5319 \begin_inset Graphics
5320 filename ../images/tabular-feature_delete-row.png
5326 \begin_inset space \thinspace{}
5331 Edit\SpecialChar \menuseparator
5335 New rows can also be created with
5338 arg "newline-insert newline"
5344 \begin_layout Standard
5345 \begin_inset VSpace bigskip
5352 adds parentheses in the selected style around the matrix.
5353 Alternatively, parentheses can can either be created with the commands
5361 \begin_inset Index idx
5364 \begin_layout Plain Layout
5379 \begin_inset Index idx
5382 \begin_layout Plain Layout
5393 \begin_inset space ~
5399 \begin_inset CommandInset ref
5401 reference "sub:Automatic-Bracket-Size"
5405 , or by using the following commands:
5406 \begin_inset VSpace medskip
5412 \begin_layout Standard
5413 \begin_inset space \hfill{}
5417 \begin_inset Tabular
5418 <lyxtabular version="3" rows="4" columns="2">
5419 <features tabularvalignment="middle">
5420 <column alignment="center" valignment="top" width="0">
5421 <column alignment="center" valignment="top" width="0">
5423 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5426 \begin_layout Plain Layout
5432 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5435 \begin_layout Plain Layout
5437 \begin_inset Note Note
5440 \begin_layout Plain Layout
5447 is only used as spacer.
5459 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5462 \begin_layout Plain Layout
5469 \begin_layout Plain Layout
5483 \begin_inset space \thinspace{}
5491 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5494 \begin_layout Plain Layout
5495 \begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
5496 0 & \textrm{-}\mathrm{i}\\
5498 \end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
5508 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5511 \begin_layout Plain Layout
5518 \begin_layout Plain Layout
5532 \begin_inset space \thinspace{}
5540 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5543 \begin_layout Plain Layout
5544 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
5545 0 & \textrm{-}\mathrm{i}\\
5547 \end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
5557 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5560 \begin_layout Plain Layout
5567 \begin_layout Plain Layout
5581 \begin_inset space \thinspace{}
5589 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5592 \begin_layout Plain Layout
5593 \begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
5594 0 & \textrm{-}\mathrm{i}\\
5596 \end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
5610 \begin_inset space \hfill{}
5614 \begin_inset Tabular
5615 <lyxtabular version="3" rows="4" columns="2">
5616 <features tabularvalignment="middle">
5617 <column alignment="center" valignment="top" width="0">
5618 <column alignment="center" valignment="top" width="0">
5620 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5623 \begin_layout Plain Layout
5629 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5632 \begin_layout Plain Layout
5640 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5643 \begin_layout Plain Layout
5650 \begin_layout Plain Layout
5664 \begin_inset space \thinspace{}
5672 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5675 \begin_layout Plain Layout
5676 \begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
5677 0 & \textrm{-}\mathrm{i}\\
5679 \end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
5689 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5692 \begin_layout Plain Layout
5699 \begin_layout Plain Layout
5713 \begin_inset space \thinspace{}
5721 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5724 \begin_layout Plain Layout
5725 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
5726 0 & \textrm{-}\mathrm{i}\\
5728 \end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
5738 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5741 \begin_layout Plain Layout
5748 \begin_layout Plain Layout
5762 \begin_inset space \thinspace{}
5770 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5773 \begin_layout Plain Layout
5774 \begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
5775 0 & \textrm{-}\mathrm{i}\\
5777 \end{array}\end{matrix}\raisebox{-5.3mm}{}$
5791 \begin_inset space \hfill{}
5797 \begin_layout Standard
5798 \begin_inset VSpace medskip
5802 \begin_inset space \thinspace{}
5806 \begin_inset space \space{}
5815 is inserted, a blue box appears between two vertical lines where the matrix
5817 \begin_inset Newline newline
5820 Note that decorated matrices ignore the vertical alignment.
5823 \begin_layout Standard
5824 \begin_inset VSpace bigskip
5827 As all multiline formulas are matrices, the length
5834 \begin_inset Index idx
5837 \begin_layout Plain Layout
5845 that is described in
5846 \begin_inset CommandInset ref
5848 reference "sub:Column-Separation"
5852 can also be used to change the column separation of matrices.
5855 \begin_layout Standard
5856 To change the row separation, the command
5863 \begin_inset Index idx
5866 \begin_layout Plain Layout
5875 It is used as follows:
5878 \begin_layout Standard
5885 arraystretch}{stretch factor}
5886 \begin_inset Index idx
5889 \begin_layout Plain Layout
5900 \begin_layout Standard
5907 assigns the stretch factor to the predefined command
5915 \begin_inset space \thinspace{}
5919 \begin_inset space \space{}
5922 the row separation, use the factor 2.
5923 This is then used for all following matrices.
5924 To go back to the original separation, assign the factor 1 to
5933 \begin_layout Standard
5934 To set matrices into a text line, the command
5941 \begin_inset Index idx
5944 \begin_layout Plain Layout
5953 When it is inserted a blue box with two dashed lines appears.
5954 In this box the matrix is inserted.
5957 \begin_layout Standard
5959 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5961 \end{smallmatrix}\right)$
5967 \begin_layout Section
5968 Brackets and Delimiters
5969 \begin_inset Index idx
5972 \begin_layout Plain Layout
5979 \begin_inset Index idx
5982 \begin_layout Plain Layout
5991 \begin_layout Subsection
5992 Vertical Brackets and Delimiters
5993 \begin_inset Index idx
5996 \begin_layout Plain Layout
6005 \begin_layout Standard
6006 \begin_inset space \hfill{}
6010 \begin_inset Tabular
6011 <lyxtabular version="3" rows="9" columns="2">
6012 <features tabularvalignment="middle">
6013 <column alignment="center" valignment="top" width="0pt">
6014 <column alignment="center" valignment="top" width="0pt">
6016 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6019 \begin_layout Plain Layout
6025 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6028 \begin_layout Plain Layout
6036 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6039 \begin_layout Plain Layout
6045 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6048 \begin_layout Plain Layout
6049 \begin_inset Formula $($
6059 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6062 \begin_layout Plain Layout
6068 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6071 \begin_layout Plain Layout
6072 \begin_inset Formula $\{$
6082 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6085 \begin_layout Plain Layout
6091 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6094 \begin_layout Plain Layout
6095 \begin_inset Formula $[$
6105 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6108 \begin_layout Plain Layout
6116 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6119 \begin_layout Plain Layout
6120 \begin_inset Formula $\langle$
6130 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6133 \begin_layout Plain Layout
6141 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6144 \begin_layout Plain Layout
6145 \begin_inset Formula $\lceil$
6155 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6158 \begin_layout Plain Layout
6166 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6169 \begin_layout Plain Layout
6170 \begin_inset Formula $\lfloor$
6180 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6183 \begin_layout Plain Layout
6189 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6192 \begin_layout Plain Layout
6193 \begin_inset Formula $/$
6203 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6206 \begin_layout Plain Layout
6212 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6215 \begin_layout Plain Layout
6216 \begin_inset Formula $|$
6230 \begin_inset space \hfill{}
6234 \begin_inset Tabular
6235 <lyxtabular version="3" rows="9" columns="2">
6236 <features tabularvalignment="middle">
6237 <column alignment="center" valignment="top" width="0pt">
6238 <column alignment="center" valignment="top" width="0pt">
6240 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6243 \begin_layout Plain Layout
6249 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6252 \begin_layout Plain Layout
6260 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6263 \begin_layout Plain Layout
6269 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6272 \begin_layout Plain Layout
6273 \begin_inset Formula $)$
6283 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6286 \begin_layout Plain Layout
6292 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6295 \begin_layout Plain Layout
6296 \begin_inset Formula $\}$
6306 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6309 \begin_layout Plain Layout
6315 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6318 \begin_layout Plain Layout
6319 \begin_inset Formula $]$
6329 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6332 \begin_layout Plain Layout
6340 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6343 \begin_layout Plain Layout
6344 \begin_inset Formula $\rangle$
6354 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6357 \begin_layout Plain Layout
6365 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6368 \begin_layout Plain Layout
6369 \begin_inset Formula $\rceil$
6379 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6382 \begin_layout Plain Layout
6390 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6393 \begin_layout Plain Layout
6394 \begin_inset Formula $\rfloor$
6404 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6407 \begin_layout Plain Layout
6417 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6420 \begin_layout Plain Layout
6421 \begin_inset Formula $\backslash$
6431 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6434 \begin_layout Plain Layout
6442 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6445 \begin_layout Plain Layout
6446 \begin_inset Formula $\|$
6460 \begin_inset space \hfill{}
6466 \begin_layout Standard
6469 \begin_inset Note Greyedout
6472 \begin_layout Plain Layout
6477 In TeX-mode the command
6484 \begin_inset Index idx
6487 \begin_layout Plain Layout
6495 must be used for the backslash, because the command
6503 produces there a line break.
6511 \begin_layout Standard
6512 For all characters listed above the size can be adjusted with the commands
6513 described in the following two subsections.
6514 When using these commands, the characters < and > can directly be used
6515 instead of the commands
6530 \begin_layout Subsubsection
6532 \begin_inset CommandInset label
6534 name "sub:Manual-Bracket-Size"
6539 \begin_inset Index idx
6542 \begin_layout Plain Layout
6543 Bracket size ! manual
6551 \begin_layout Standard
6552 The bracket size can be specified manually by the LaTeX-commands
6559 \begin_inset Index idx
6562 \begin_layout Plain Layout
6595 denotes the smallest and
6601 the largest bracket size.
6604 \begin_layout Standard
6605 These commands are used to emphasize levels of brackets:
6608 \begin_layout Standard
6610 \begin_inset Tabular
6611 <lyxtabular version="3" rows="2" columns="2">
6612 <features tabularvalignment="middle">
6613 <column alignment="center" valignment="top" width="0pt">
6614 <column alignment="center" valignment="top" width="0pt">
6616 <cell alignment="center" valignment="top" usebox="none">
6619 \begin_layout Plain Layout
6620 all brackets in the same size:
6625 <cell alignment="center" valignment="top" usebox="none">
6628 \begin_layout Plain Layout
6629 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
6639 <cell alignment="center" valignment="top" usebox="none">
6642 \begin_layout Plain Layout
6648 <cell alignment="center" valignment="top" usebox="none">
6651 \begin_layout Plain Layout
6652 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6666 \begin_inset Note Note
6669 \begin_layout Plain Layout
6676 is only used as spacer.
6684 \begin_layout Standard
6685 For the second formula the command
6695 \begin_layout Plain Layout
6709 \begin_layout Standard
6710 Here is an overview about all bracket sizes:
6713 \begin_layout Standard
6733 \begin_layout Plain Layout
6750 \begin_layout Plain Layout
6763 \begin_layout Plain Layout
6779 \begin_layout Standard
6781 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6787 \begin_layout Standard
6794 -commands there is the variant
6801 \begin_inset Index idx
6804 \begin_layout Plain Layout
6812 that adds a bit more space between the bracket and its content, and the
6826 \begin_inset Index idx
6829 \begin_layout Plain Layout
6839 , that don't add additional space.
6844 at the end of the command
6850 is for a left bracket; for a right bracket this will be replaced by an
6856 A left or right bracket can each be an opening or closing bracket.
6859 \begin_layout Standard
6860 In the following table is a comparison of the variants:
6863 \begin_layout Standard
6865 \begin_inset Tabular
6866 <lyxtabular version="3" rows="5" columns="2">
6867 <features tabularvalignment="middle">
6868 <column alignment="center" valignment="middle" width="0">
6869 <column alignment="center" valignment="middle" width="0">
6871 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6874 \begin_layout Plain Layout
6880 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6883 \begin_layout Plain Layout
6885 \begin_inset Note Note
6888 \begin_layout Plain Layout
6895 is only used as spacer.
6907 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6910 \begin_layout Plain Layout
6925 \begin_layout Plain Layout
6943 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6946 \begin_layout Plain Layout
6947 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
6957 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6960 \begin_layout Plain Layout
6975 \begin_layout Plain Layout
6993 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6996 \begin_layout Plain Layout
6997 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
7007 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7010 \begin_layout Plain Layout
7025 \begin_layout Plain Layout
7043 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7046 \begin_layout Plain Layout
7047 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
7057 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7060 \begin_layout Plain Layout
7072 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7075 \begin_layout Plain Layout
7076 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
7092 \begin_layout Subsubsection
7093 Automatic Bracket Size
7094 \begin_inset CommandInset label
7096 name "sub:Automatic-Bracket-Size"
7101 \begin_inset Index idx
7104 \begin_layout Plain Layout
7105 Bracket size ! automatic
7113 \begin_layout Standard
7114 Brackets with variable size can be inserted with the commands
7121 \begin_inset Index idx
7124 \begin_layout Plain Layout
7139 \begin_inset Index idx
7142 \begin_layout Plain Layout
7150 or via the math toolbar button
7151 \begin_inset Graphics
7152 filename ../images/dialog-show_mathdelimiter.png
7170 the wanted bracket must be inserted.
7171 The bracket size will then automatically be calculated for the output.
7174 \begin_layout Standard
7176 normal bracket: The command
7186 \begin_layout Plain Layout
7196 \begin_inset Formula $\downarrow$
7203 \begin_layout Plain Layout
7215 \begin_inset Formula \[
7224 \begin_layout Standard
7226 multiline bracket: The command
7238 \begin_layout Plain Layout
7248 \begin_inset Formula $\downarrow$
7255 \begin_layout Plain Layout
7269 \begin_inset Formula \[
7270 \ln\left(\frac{A}{C}\right)
7278 \begin_layout Standard
7294 \begin_inset space ~
7300 This has the advantage that you can see in LyX immediately the real bracket
7301 size and that the matching right bracket will be created too.
7302 \begin_inset Newline newline
7305 The command for the last example would then be:
7319 \begin_layout Plain Layout
7329 \begin_inset Formula $\downarrow$
7335 \begin_layout Standard
7336 To omit a left or right bracket, a dot is inserted for the omitted bracket.
7337 For example the command
7347 \begin_layout Plain Layout
7357 \begin_inset Formula $\downarrow$
7364 \begin_layout Plain Layout
7380 \begin_inset Formula \[
7381 \left.\frac{A}{B}\right\}
7400 will be converted by LyX to brackets in the right size when the document
7401 is reloaded and an omitted bracket will appear as dashed line.
7404 \begin_layout Standard
7405 \begin_inset VSpace bigskip
7408 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
7416 \begin_inset Index idx
7419 \begin_layout Plain Layout
7427 is additionally available for all brackets and limits.
7428 With this command the height of the following character is adapted to the
7429 one of the surrounding brackets, what is e.
7430 \begin_inset space \thinspace{}
7434 \begin_inset space \space{}
7437 needed for physical vectors:
7438 \begin_inset Formula \[
7439 \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle
7444 For physical vectors there is a special LaTeX-package, described in
7445 \begin_inset CommandInset ref
7447 reference "sub:Physical-Vectors"
7454 \begin_layout Subsection
7456 \begin_inset Index idx
7459 \begin_layout Plain Layout
7460 Brackets ! horizontal
7468 \begin_layout Standard
7470 \begin_inset Tabular
7471 <lyxtabular version="3" rows="4" columns="2">
7472 <features tabularvalignment="middle">
7473 <column alignment="center" valignment="top" width="0pt">
7474 <column alignment="center" valignment="top" width="0pt">
7476 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7479 \begin_layout Plain Layout
7481 \begin_inset Note Note
7484 \begin_layout Plain Layout
7491 is only used as spacer.
7501 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7504 \begin_layout Plain Layout
7512 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7515 \begin_layout Plain Layout
7519 \begin_layout Plain Layout
7534 \begin_layout Plain Layout
7547 \begin_layout Plain Layout
7560 \begin_layout Plain Layout
7573 \begin_layout Plain Layout
7581 \begin_inset Index idx
7584 \begin_layout Plain Layout
7597 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7600 \begin_layout Plain Layout
7601 \begin_inset Formula $\overbrace{A+B}^{3}$
7611 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7614 \begin_layout Plain Layout
7618 \begin_layout Plain Layout
7633 \begin_layout Plain Layout
7646 \begin_layout Plain Layout
7659 \begin_layout Plain Layout
7667 \begin_inset Index idx
7670 \begin_layout Plain Layout
7683 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7686 \begin_layout Plain Layout
7687 \begin_inset Formula $\underbrace{A+B}_{5}$
7697 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7700 \begin_layout Plain Layout
7707 \begin_layout Plain Layout
7722 \begin_layout Plain Layout
7735 \begin_layout Plain Layout
7748 \begin_layout Plain Layout
7761 \begin_layout Plain Layout
7774 \begin_layout Plain Layout
7787 \begin_layout Plain Layout
7801 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7804 \begin_layout Plain Layout
7805 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
7821 \begin_layout Standard
7822 In the last example it doesn't matter if
7834 is inserted at first.
7837 \begin_layout Standard
7838 \begin_inset VSpace bigskip
7841 When brackets are needed that overlap each other, multiline formulas, as
7843 \begin_inset CommandInset ref
7845 reference "sec:Multiline-Formulas"
7850 \begin_inset Formula \begin{eqnarray*}
7851 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
7852 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
7857 In the first row the formula is inserted together with the first brace.
7858 It is hereby important that the space command
7862 \begin_layout Plain Layout
7863 Space commands are explained in
7864 \begin_inset CommandInset ref
7866 reference "sub:Predefined-Space"
7881 is inserted before the first
7882 \begin_inset Formula $d$
7885 , because the brace that ends behind the
7886 \begin_inset Formula $q$
7889 prevents that the following
7890 \begin_inset Quotes eld
7894 \begin_inset Quotes erd
7897 is surrounded by space.
7901 \begin_layout Plain Layout
7902 because a bracket is not handled as character, see
7903 \begin_inset CommandInset ref
7905 reference "sub:Binary-Operators"
7914 In the second row the second brace is inserted.
7915 As it should begin before the
7916 \begin_inset Formula $b$
7931 \begin_layout Plain Layout
7939 \begin_inset CommandInset ref
7941 reference "sub:Placeholders"
7950 This space is needed because the
7951 \begin_inset Quotes eld
7955 \begin_inset Quotes erd
7958 is also surrounded by space in the formula.
7959 The brace is placed under the command
7968 \begin_layout Standard
7969 It gets more complicated when brackets overlap each other, like in the following
7974 \begin_layout Plain Layout
7986 \begin_inset Formula \begin{eqnarray*}
7987 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7988 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd
7997 \begin_layout Plain Layout
8008 The first formula row is the same as the second row of the previous example,
8009 with the difference that the brace is above.
8010 The second row contains the formula together with the second brace.
8011 To avoid that there is space between the upper brace in the first row and
8012 the formula, the row spacing need to be reduced.
8013 This is not easily possible due to a bug in LyX
8017 \begin_layout Plain Layout
8018 \begin_inset CommandInset href
8020 name "LyX-bug #1505"
8021 target "http://www.lyx.org/trac/ticket/1505"
8031 As solution for the problem, the global formula row separation
8038 \begin_inset Index idx
8041 \begin_layout Plain Layout
8049 must be changed to -6
8050 \begin_inset space \thinspace{}
8053 pt before the formula with the command
8068 is set back after the formula to the standard value of 3
8069 \begin_inset space \thinspace{}
8072 pt using the same command.
8073 More about the row separation in formulas is explained in
8074 \begin_inset CommandInset ref
8076 reference "sub:Line-Separation"
8083 \begin_layout Section
8085 \begin_inset Index idx
8088 \begin_layout Plain Layout
8097 \begin_layout Standard
8098 Arrows can be inserted via the math toolbar button
8099 \begin_inset Graphics
8100 filename ../images/math/leftarrow.png
8105 or the commands listed in the following subsections.
8108 \begin_layout Standard
8109 \begin_inset Newpage newpage
8115 \begin_layout Subsection
8117 \begin_inset Index idx
8120 \begin_layout Plain Layout
8129 \begin_layout Standard
8130 \begin_inset space \hfill{}
8134 \begin_inset Tabular
8135 <lyxtabular version="3" rows="8" columns="2">
8136 <features tabularvalignment="middle">
8137 <column alignment="center" valignment="top" width="0pt">
8138 <column alignment="center" valignment="top" width="0pt">
8140 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8143 \begin_layout Plain Layout
8149 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8152 \begin_layout Plain Layout
8160 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8163 \begin_layout Plain Layout
8171 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8174 \begin_layout Plain Layout
8175 \begin_inset Formula $\gets$
8185 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8188 \begin_layout Plain Layout
8196 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8199 \begin_layout Plain Layout
8200 \begin_inset Formula $\Leftarrow$
8210 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8213 \begin_layout Plain Layout
8221 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8224 \begin_layout Plain Layout
8225 \begin_inset Formula $\longleftarrow$
8235 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8238 \begin_layout Plain Layout
8246 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8249 \begin_layout Plain Layout
8250 \begin_inset Formula $\Longleftarrow$
8260 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8263 \begin_layout Plain Layout
8271 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8274 \begin_layout Plain Layout
8275 \begin_inset Formula $\leftharpoonup$
8285 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8288 \begin_layout Plain Layout
8296 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8299 \begin_layout Plain Layout
8300 \begin_inset Formula $\leftharpoondown$
8310 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8313 \begin_layout Plain Layout
8321 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8324 \begin_layout Plain Layout
8325 \begin_inset Formula $\hookleftarrow$
8339 \begin_inset space \hfill{}
8343 \begin_inset Tabular
8344 <lyxtabular version="3" rows="8" columns="2">
8345 <features tabularvalignment="middle">
8346 <column alignment="center" valignment="top" width="0pt">
8347 <column alignment="center" valignment="top" width="0pt">
8349 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8352 \begin_layout Plain Layout
8358 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8361 \begin_layout Plain Layout
8369 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8372 \begin_layout Plain Layout
8380 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8383 \begin_layout Plain Layout
8384 \begin_inset Formula $\to$
8394 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8397 \begin_layout Plain Layout
8405 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8408 \begin_layout Plain Layout
8409 \begin_inset Formula $\Rightarrow$
8419 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8422 \begin_layout Plain Layout
8430 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8433 \begin_layout Plain Layout
8434 \begin_inset Formula $\longrightarrow$
8444 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8447 \begin_layout Plain Layout
8455 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8458 \begin_layout Plain Layout
8459 \begin_inset Formula $\Longrightarrow$
8469 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8472 \begin_layout Plain Layout
8480 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8483 \begin_layout Plain Layout
8484 \begin_inset Formula $\rightharpoonup$
8494 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8497 \begin_layout Plain Layout
8505 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8508 \begin_layout Plain Layout
8509 \begin_inset Formula $\rightharpoondown$
8519 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8522 \begin_layout Plain Layout
8530 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8533 \begin_layout Plain Layout
8534 \begin_inset Formula $\hookrightarrow$
8548 \begin_inset space \hfill{}
8554 \begin_layout Standard
8555 \begin_inset space \hfill{}
8559 \begin_inset Tabular
8560 <lyxtabular version="3" rows="6" columns="2">
8561 <features tabularvalignment="middle">
8562 <column alignment="center" valignment="top" width="0pt">
8563 <column alignment="center" valignment="top" width="0pt">
8565 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8568 \begin_layout Plain Layout
8574 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8577 \begin_layout Plain Layout
8585 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8588 \begin_layout Plain Layout
8596 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8599 \begin_layout Plain Layout
8600 \begin_inset Formula $\leftrightarrow$
8610 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8613 \begin_layout Plain Layout
8621 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8624 \begin_layout Plain Layout
8625 \begin_inset Formula $\Leftrightarrow$
8635 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8638 \begin_layout Plain Layout
8646 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8649 \begin_layout Plain Layout
8650 \begin_inset Formula $\longleftrightarrow$
8660 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8663 \begin_layout Plain Layout
8671 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8674 \begin_layout Plain Layout
8675 \begin_inset Formula $\Longleftrightarrow$
8685 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8688 \begin_layout Plain Layout
8696 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8699 \begin_layout Plain Layout
8700 \begin_inset Formula $\rightleftharpoons$
8714 \begin_inset space \hspace{}
8719 \begin_inset space \hfill{}
8723 \begin_inset Tabular
8724 <lyxtabular version="3" rows="5" columns="2">
8725 <features tabularvalignment="middle">
8726 <column alignment="center" valignment="top" width="0pt">
8727 <column alignment="center" valignment="top" width="0pt">
8729 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8732 \begin_layout Plain Layout
8738 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8741 \begin_layout Plain Layout
8749 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8752 \begin_layout Plain Layout
8760 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8763 \begin_layout Plain Layout
8764 \begin_inset Formula $\mapsto$
8774 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8777 \begin_layout Plain Layout
8785 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8788 \begin_layout Plain Layout
8789 \begin_inset Formula $\longmapsto$
8799 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8802 \begin_layout Plain Layout
8810 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8813 \begin_layout Plain Layout
8814 \begin_inset Formula $\leadsto$
8824 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8827 \begin_layout Plain Layout
8835 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8838 \begin_layout Plain Layout
8839 \begin_inset Formula $\dasharrow$
8853 \begin_inset space \hfill{}
8859 \begin_layout Standard
8860 \begin_inset VSpace medskip
8863 Arrows used as accent like e.
8864 \begin_inset space \thinspace{}
8868 \begin_inset space \space{}
8871 vector arrows are listed in
8872 \begin_inset CommandInset ref
8874 reference "sec:Accents"
8881 \begin_layout Standard
8882 \begin_inset VSpace bigskip
8885 Furthermore there are the labeled arrows
8886 \begin_inset Index idx
8889 \begin_layout Plain Layout
8902 \begin_inset Index idx
8905 \begin_layout Plain Layout
8920 \begin_inset Index idx
8923 \begin_layout Plain Layout
8930 \begin_layout Plain Layout
8945 When inserting one of these commands in a formula, an arrow with two blue
8946 boxes appear where the label can be inserted.
8947 The length of the arrow adapts to the label width.
8950 \begin_layout Standard
8952 \begin_inset Tabular
8953 <lyxtabular version="3" rows="3" columns="2">
8954 <features tabularvalignment="middle">
8955 <column alignment="center" valignment="top" width="0pt">
8956 <column alignment="center" valignment="top" width="0pt">
8958 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8961 \begin_layout Plain Layout
8967 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8970 \begin_layout Plain Layout
8972 \begin_inset Note Note
8975 \begin_layout Plain Layout
8982 is only used as spacer.
8994 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8997 \begin_layout Plain Layout
9004 \begin_layout Plain Layout
9014 \begin_inset Formula $\downarrow$
9018 \begin_inset Formula $\to$
9026 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9029 \begin_layout Plain Layout
9030 \begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
9040 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9043 \begin_layout Plain Layout
9050 \begin_layout Plain Layout
9060 \begin_inset Formula $\downarrow$
9064 \begin_inset Formula $\to$
9072 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9075 \begin_layout Plain Layout
9076 \begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
9092 \begin_layout Subsection
9093 Vertical and diagonal Arrows
9094 \begin_inset Index idx
9097 \begin_layout Plain Layout
9104 \begin_inset Index idx
9107 \begin_layout Plain Layout
9116 \begin_layout Standard
9117 \begin_inset space \hfill{}
9121 \begin_inset Tabular
9122 <lyxtabular version="3" rows="7" columns="2">
9123 <features tabularvalignment="middle">
9124 <column alignment="center" valignment="top" width="0pt">
9125 <column alignment="center" valignment="top" width="0pt">
9127 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9130 \begin_layout Plain Layout
9136 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9139 \begin_layout Plain Layout
9147 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9150 \begin_layout Plain Layout
9158 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9161 \begin_layout Plain Layout
9162 \begin_inset Formula $\uparrow$
9172 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9175 \begin_layout Plain Layout
9183 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9186 \begin_layout Plain Layout
9187 \begin_inset Formula $\Uparrow$
9197 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9200 \begin_layout Plain Layout
9208 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9211 \begin_layout Plain Layout
9212 \begin_inset Formula $\updownarrow$
9222 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9225 \begin_layout Plain Layout
9233 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9236 \begin_layout Plain Layout
9237 \begin_inset Formula $\Updownarrow$
9247 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9250 \begin_layout Plain Layout
9258 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9261 \begin_layout Plain Layout
9262 \begin_inset Formula $\Downarrow$
9272 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9275 \begin_layout Plain Layout
9283 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9286 \begin_layout Plain Layout
9287 \begin_inset Formula $\downarrow$
9301 \begin_inset space \hfill{}
9305 \begin_inset Tabular
9306 <lyxtabular version="3" rows="5" columns="2">
9307 <features tabularvalignment="middle">
9308 <column alignment="center" valignment="top" width="0pt">
9309 <column alignment="center" valignment="top" width="0pt">
9311 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9314 \begin_layout Plain Layout
9320 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9323 \begin_layout Plain Layout
9331 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9334 \begin_layout Plain Layout
9342 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9345 \begin_layout Plain Layout
9346 \begin_inset Formula $\nearrow$
9356 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9359 \begin_layout Plain Layout
9367 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9370 \begin_layout Plain Layout
9371 \begin_inset Formula $\searrow$
9381 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9384 \begin_layout Plain Layout
9392 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9395 \begin_layout Plain Layout
9396 \begin_inset Formula $\swarrow$
9406 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9409 \begin_layout Plain Layout
9417 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9420 \begin_layout Plain Layout
9421 \begin_inset Formula $\nwarrow$
9435 \begin_inset space \hfill{}
9441 \begin_layout Standard
9442 \begin_inset VSpace medskip
9445 Vertical arrows can be used also as delimiter together with the commands
9447 \begin_inset CommandInset ref
9449 reference "sub:Manual-Bracket-Size"
9454 \begin_inset CommandInset ref
9456 reference "sub:Automatic-Bracket-Size"
9463 \begin_layout Standard
9464 \begin_inset Newpage newpage
9470 \begin_layout Section
9472 \begin_inset CommandInset label
9479 \begin_inset Index idx
9482 \begin_layout Plain Layout
9491 \begin_layout Standard
9492 Accents can be inserted via the math toolbar button
9493 \begin_inset Graphics
9494 filename ../images/math/hat.png
9499 or the commands listed in the following subsections.
9502 \begin_layout Subsection
9503 Accents for one Character
9507 \begin_layout Plain Layout
9520 \begin_layout Plain Layout
9522 \begin_inset CommandInset ref
9524 reference "sub:Accents-in-Text"
9537 \begin_layout Plain Layout
9545 \begin_inset Note Note
9548 \begin_layout Plain Layout
9555 is used to avoid that the footnote appears in the PDF-bookmark.
9558 \begin_layout Plain Layout
9566 \begin_inset CommandInset ref
9568 reference "sub:Formulas-in-Section"
9578 \begin_inset CommandInset label
9580 name "sub:Accents-for-one"
9585 \begin_inset Index idx
9588 \begin_layout Plain Layout
9589 Accents ! for one character
9597 \begin_layout Standard
9598 \begin_inset space \hfill{}
9602 \begin_inset Tabular
9603 <lyxtabular version="3" rows="8" columns="2">
9604 <features tabularvalignment="middle">
9605 <column alignment="center" valignment="top" width="0pt">
9606 <column alignment="center" valignment="top" width="0pt">
9608 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9611 \begin_layout Plain Layout
9617 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9620 \begin_layout Plain Layout
9622 \begin_inset Note Note
9625 \begin_layout Plain Layout
9632 is only used as spacer.
9644 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9647 \begin_layout Plain Layout
9654 \begin_layout Plain Layout
9668 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9671 \begin_layout Plain Layout
9672 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
9682 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9685 \begin_layout Plain Layout
9692 \begin_layout Plain Layout
9706 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9709 \begin_layout Plain Layout
9710 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
9720 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9723 \begin_layout Plain Layout
9730 \begin_layout Plain Layout
9744 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9747 \begin_layout Plain Layout
9748 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
9758 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9761 \begin_layout Plain Layout
9768 \begin_layout Plain Layout
9782 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9785 \begin_layout Plain Layout
9786 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
9796 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9799 \begin_layout Plain Layout
9806 \begin_layout Plain Layout
9816 \begin_inset Index idx
9819 \begin_layout Plain Layout
9830 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9833 \begin_layout Plain Layout
9834 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
9844 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9847 \begin_layout Plain Layout
9854 \begin_layout Plain Layout
9868 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9871 \begin_layout Plain Layout
9872 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
9882 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9885 \begin_layout Plain Layout
9892 \begin_layout Plain Layout
9906 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9909 \begin_layout Plain Layout
9910 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
9924 \begin_inset space \hfill{}
9928 \begin_inset Tabular
9929 <lyxtabular version="3" rows="7" columns="2">
9930 <features tabularvalignment="middle">
9931 <column alignment="center" valignment="top" width="0pt">
9932 <column alignment="center" valignment="top" width="0pt">
9934 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9937 \begin_layout Plain Layout
9943 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9946 \begin_layout Plain Layout
9954 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9957 \begin_layout Plain Layout
9964 \begin_layout Plain Layout
9978 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9981 \begin_layout Plain Layout
9982 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
9992 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9995 \begin_layout Plain Layout
10002 \begin_layout Plain Layout
10016 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10019 \begin_layout Plain Layout
10020 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
10030 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10033 \begin_layout Plain Layout
10040 \begin_layout Plain Layout
10054 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10057 \begin_layout Plain Layout
10058 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
10068 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10071 \begin_layout Plain Layout
10078 \begin_layout Plain Layout
10092 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10095 \begin_layout Plain Layout
10096 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
10106 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10109 \begin_layout Plain Layout
10116 \begin_layout Plain Layout
10130 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10133 \begin_layout Plain Layout
10134 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
10144 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10147 \begin_layout Plain Layout
10154 \begin_layout Plain Layout
10168 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10171 \begin_layout Plain Layout
10172 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
10186 \begin_inset space \hfill{}
10192 \begin_layout Standard
10193 \begin_inset VSpace bigskip
10199 \begin_layout Standard
10200 You can directly insert accents like é to formulas.
10201 LyX will transform them to the corresponding accent command.
10203 \begin_inset Index idx
10206 \begin_layout Plain Layout
10212 it is better to insert a quotation mark before the vowel.
10213 These two characters are then treated by LaTeX as
10217 character when the formula part with the umlaut is marked as German.
10225 \begin_inset Quotes eld
10229 \begin_inset Quotes erd
10232 umlauts are created as demonstrated in the following example:
10235 \begin_layout Standard
10236 \begin_inset VSpace -2mm
10242 \begin_layout Standard
10244 \begin_inset Tabular
10245 <lyxtabular version="3" rows="3" columns="2">
10246 <features tabularvalignment="middle">
10247 <column alignment="center" valignment="top" width="0">
10248 <column alignment="center" valignment="top" width="0">
10250 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10253 \begin_layout Plain Layout
10259 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10262 \begin_layout Plain Layout
10264 \begin_inset Note Note
10267 \begin_layout Plain Layout
10275 \begin_inset space \thinspace{}
10278 pt space are only used as spacer.
10290 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10293 \begin_layout Plain Layout
10296 \begin_inset Quotes grd
10304 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10307 \begin_layout Plain Layout
10308 \begin_inset space \hspace{}
10315 \begin_inset Formula $"i$
10325 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10328 \begin_layout Plain Layout
10335 \begin_layout Plain Layout
10349 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10352 \begin_layout Plain Layout
10353 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
10369 \begin_layout Standard
10370 Another advantage to
10376 is that umlauts can directly be converted to mathematical text because
10377 the accent commands above are
10383 in mathematical text
10386 To convert an accented character to mathematical text, only the character
10387 under the accent may be converted.
10388 This applies also for all other conversions, e.
10389 \begin_inset space \thinspace{}
10393 \begin_inset space \space{}
10399 \begin_layout Standard
10400 In mathematical text, umlauts and other accented characters can directly
10404 \begin_layout Subsection
10405 Accents for Operators
10406 \begin_inset Index idx
10409 \begin_layout Plain Layout
10410 Accents ! for operators
10418 \begin_layout Standard
10426 \begin_inset Index idx
10429 \begin_layout Plain Layout
10444 \begin_inset Index idx
10447 \begin_layout Plain Layout
10455 characters can be placed above or below an operator, respectively, to accent
10464 \begin_inset Index idx
10467 \begin_layout Plain Layout
10475 characters can be set before and behind an operator.
10476 The command scheme is:
10479 \begin_layout Standard
10495 \begin_layout Standard
10502 must always be before the operator that should be accented.
10503 You can accent with several characters and even with other operators and
10511 for example only characters behind an operator, write nothing between the
10512 first braces but don't omit the braces.
10515 \begin_layout Standard
10516 For example the command
10521 \begin_inset Formula $\to$
10531 \begin_inset Formula $\to$
10540 \begin_layout Plain Layout
10556 \begin_inset Formula \[
10557 \sideset{}{'}\sum_{k=1}^{n}
10565 \begin_layout Standard
10574 \begin_layout Plain Layout
10589 \begin_layout Plain Layout
10601 \begin_inset Formula $\uparrow$
10609 \begin_inset Formula \[
10610 \overset{a}{\maltese}
10615 As seen in the last example, with
10627 also symbols and characters can be accented; with
10633 this is not possible.
10636 \begin_layout Subsection
10637 Accents for several Characters
10638 \begin_inset Index idx
10641 \begin_layout Plain Layout
10642 Accents ! for several characters
10650 \begin_layout Standard
10651 \begin_inset space \hfill{}
10655 \begin_inset Tabular
10656 <lyxtabular version="3" rows="5" columns="2">
10657 <features tabularvalignment="middle">
10658 <column alignment="center" valignment="top" width="0pt">
10659 <column alignment="center" valignment="top" width="0pt">
10661 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10664 \begin_layout Plain Layout
10670 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10673 \begin_layout Plain Layout
10675 \begin_inset Note Note
10678 \begin_layout Plain Layout
10685 is only used as spacer.
10697 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10700 \begin_layout Plain Layout
10707 \begin_layout Plain Layout
10721 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10724 \begin_layout Plain Layout
10725 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
10735 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10738 \begin_layout Plain Layout
10745 \begin_layout Plain Layout
10759 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10762 \begin_layout Plain Layout
10763 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
10773 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10776 \begin_layout Plain Layout
10783 \begin_layout Plain Layout
10797 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10800 \begin_layout Plain Layout
10801 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
10811 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10814 \begin_layout Plain Layout
10817 underleftrightarrow
10821 \begin_layout Plain Layout
10835 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10838 \begin_layout Plain Layout
10839 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
10853 \begin_inset space \hfill{}
10857 \begin_inset Tabular
10858 <lyxtabular version="3" rows="5" columns="2">
10859 <features tabularvalignment="middle">
10860 <column alignment="center" valignment="top" width="0pt">
10861 <column alignment="center" valignment="top" width="0pt">
10863 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10866 \begin_layout Plain Layout
10872 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10875 \begin_layout Plain Layout
10883 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10886 \begin_layout Plain Layout
10893 \begin_layout Plain Layout
10907 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10910 \begin_layout Plain Layout
10911 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
10921 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10924 \begin_layout Plain Layout
10931 \begin_layout Plain Layout
10945 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10948 \begin_layout Plain Layout
10949 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
10959 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10962 \begin_layout Plain Layout
10969 \begin_layout Plain Layout
10983 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10986 \begin_layout Plain Layout
10987 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
10997 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11000 \begin_layout Plain Layout
11007 \begin_layout Plain Layout
11021 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11024 \begin_layout Plain Layout
11025 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
11039 \begin_inset space \hfill{}
11045 \begin_layout Standard
11046 \begin_inset VSpace medskip
11049 With these commands as many characters as you like can be accented.
11062 will only be set in the output with a length of three characters, as shown
11063 in the following example:
11064 \begin_inset Formula \[
11065 \widetilde{A+B=C-D}
11073 \begin_layout Standard
11081 \begin_inset Index idx
11084 \begin_layout Plain Layout
11099 \begin_inset Index idx
11102 \begin_layout Plain Layout
11110 described in the previous subsection it is also possible to accent several
11120 \begin_layout Plain Layout
11130 \begin_inset Formula $\downarrow$
11136 \begin_inset Formula \[
11137 \underset{***}{A=B}
11145 \begin_layout Section
11147 \begin_inset CommandInset label
11154 \begin_inset Index idx
11157 \begin_layout Plain Layout
11166 \begin_layout Subsection
11168 \begin_inset CommandInset label
11170 name "sub:Predefined-Space"
11175 \begin_inset Index idx
11178 \begin_layout Plain Layout
11179 Space ! horizontal ! predefined
11187 \begin_layout Standard
11188 Sometimes it is necessary to insert horizontal space to a formula.
11189 This is done by inserting a protected space (shortcut
11192 arg "space-insert protected"
11197 \begin_inset Quotes eld
11206 \begin_layout Plain Layout
11218 \begin_inset Quotes erd
11221 appears and by pressing
11225 several times one can select one of eight different space sizes.
11226 The spaces can also be inserted using the math toolbar button
11227 \begin_inset Graphics
11228 filename ../images/math/space.png
11233 or special commands.
11234 Independent from the inserted command, one can select the size again by
11242 \begin_layout Standard
11245 \begin_inset VSpace -5mm
11249 \begin_inset Tabular
11250 <lyxtabular version="3" rows="3" columns="7">
11251 <features tabularvalignment="middle">
11252 <column alignment="center" valignment="middle" width="6.8cm">
11253 <column alignment="center" valignment="top" width="0">
11254 <column alignment="center" valignment="top" width="0">
11255 <column alignment="center" valignment="top" width="0">
11256 <column alignment="center" valignment="top" width="0">
11257 <column alignment="center" valignment="top" width="0">
11258 <column alignment="center" valignment="top" width="0">
11260 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11263 \begin_layout Plain Layout
11269 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11272 \begin_layout Plain Layout
11280 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11283 \begin_layout Plain Layout
11291 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11294 \begin_layout Plain Layout
11302 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11305 \begin_layout Plain Layout
11313 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11316 \begin_layout Plain Layout
11324 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11327 \begin_layout Plain Layout
11337 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11340 \begin_layout Plain Layout
11345 keystrokes after inserting the protected space
11350 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11353 \begin_layout Plain Layout
11359 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11362 \begin_layout Plain Layout
11368 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11371 \begin_layout Plain Layout
11377 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11380 \begin_layout Plain Layout
11386 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11389 \begin_layout Plain Layout
11395 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11398 \begin_layout Plain Layout
11406 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11409 \begin_layout Plain Layout
11415 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11418 \begin_layout Plain Layout
11419 \begin_inset Formula $A\, B$
11427 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11430 \begin_layout Plain Layout
11431 \begin_inset Formula $A\: B$
11439 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11442 \begin_layout Plain Layout
11443 \begin_inset Formula $A\; B$
11451 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11454 \begin_layout Plain Layout
11455 \begin_inset Formula $A\quad B$
11463 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11466 \begin_layout Plain Layout
11467 \begin_inset Formula $A\qquad B$
11475 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11478 \begin_layout Plain Layout
11479 \begin_inset Formula $A\! B$
11495 \begin_layout Standard
11496 The last size seem to produce no space.
11497 It is displayed red in LyX contrary to the other sizes, because it is a
11499 There are two more negative spaces:
11502 \begin_layout Standard
11504 \begin_inset Tabular
11505 <lyxtabular version="3" rows="3" columns="3">
11506 <features tabularvalignment="middle">
11507 <column alignment="center" valignment="middle" width="6.8cm">
11508 <column alignment="center" valignment="top" width="0pt">
11509 <column alignment="center" valignment="top" width="0pt">
11511 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11514 \begin_layout Plain Layout
11520 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11523 \begin_layout Plain Layout
11531 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11534 \begin_layout Plain Layout
11544 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11547 \begin_layout Plain Layout
11552 keystrokes after inserting the protected space
11557 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11560 \begin_layout Plain Layout
11566 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11569 \begin_layout Plain Layout
11577 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11580 \begin_layout Plain Layout
11586 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11589 \begin_layout Plain Layout
11590 \begin_inset Formula $A\negmedspace B$
11598 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11601 \begin_layout Plain Layout
11602 \begin_inset Formula $A\negthickspace B$
11618 \begin_layout Standard
11619 Negative spaces can lead to characters overlapping each other.
11620 Thus they can be used to enforce ligatures, what is e.
11621 \begin_inset space \thinspace{}
11625 \begin_inset space \space{}
11628 useful for summation operators:
11631 \begin_layout Standard
11633 \begin_inset Tabular
11634 <lyxtabular version="3" rows="3" columns="2">
11635 <features tabularvalignment="middle">
11636 <column alignment="center" valignment="top" width="0">
11637 <column alignment="center" valignment="top" width="0">
11639 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11642 \begin_layout Plain Layout
11648 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11651 \begin_layout Plain Layout
11653 \begin_inset Note Note
11656 \begin_layout Plain Layout
11663 is only used as spacer.
11675 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11678 \begin_layout Plain Layout
11687 \begin_layout Plain Layout
11701 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11704 \begin_layout Plain Layout
11705 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
11715 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11718 \begin_layout Plain Layout
11729 \begin_layout Plain Layout
11743 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11746 \begin_layout Plain Layout
11747 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
11763 \begin_layout Standard
11764 Relations like for example equal signs, are always surrounded by space.
11765 To suppress this, the equal sign is placed into a TeX-brace.
11766 The following example demonstrates this:
11769 \begin_layout Standard
11771 \begin_inset Tabular
11772 <lyxtabular version="3" rows="2" columns="2">
11773 <features tabularvalignment="middle">
11774 <column alignment="center" valignment="top" width="0pt">
11775 <column alignment="center" valignment="top" width="0pt">
11777 <cell alignment="center" valignment="top" usebox="none">
11780 \begin_layout Plain Layout
11786 <cell alignment="center" valignment="top" usebox="none">
11789 \begin_layout Plain Layout
11790 \begin_inset Formula $A=B$
11800 <cell alignment="center" valignment="top" usebox="none">
11803 \begin_layout Plain Layout
11804 \begin_inset Note Note
11807 \begin_layout Plain Layout
11814 is only used as spacer.
11820 \begin_inset Formula $\raisebox{5mm}{}$
11823 equation without space
11828 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11831 \begin_layout Plain Layout
11832 \begin_inset Formula $A{=}B$
11848 \begin_layout Standard
11850 The command for the last formula is:
11855 \begin_inset Formula $\to$
11861 \begin_layout Standard
11862 \begin_inset VSpace bigskip
11865 Spaces are needed for physical units, because the space between the value
11866 and the unit is the smallest one and not a normal space.
11867 For units in text, the smallest space is inserted via the menu
11869 Insert\SpecialChar \menuseparator
11870 Formatting\SpecialChar \menuseparator
11872 \begin_inset space ~
11880 arg "space-insert thin"
11886 \begin_layout Standard
11887 An example to visualize the difference:
11890 \begin_layout Standard
11891 \begin_inset Tabular
11892 <lyxtabular version="3" rows="2" columns="2">
11893 <features tabularvalignment="middle">
11894 <column alignment="left" valignment="top" width="0">
11895 <column alignment="left" valignment="top" width="0">
11897 <cell alignment="center" valignment="top" usebox="none">
11900 \begin_layout Plain Layout
11902 \begin_inset Formula $\cdot$
11910 <cell alignment="center" valignment="top" usebox="none">
11913 \begin_layout Plain Layout
11914 space between value and unit
11921 <cell alignment="center" valignment="top" usebox="none">
11924 \begin_layout Plain Layout
11926 \begin_inset space \thinspace{}
11930 \begin_inset Formula $\cdot$
11938 <cell alignment="center" valignment="top" usebox="none">
11941 \begin_layout Plain Layout
11942 smallest space between value and unit
11955 \begin_layout Subsection
11960 \begin_layout Plain Layout
11973 \begin_layout Plain Layout
11974 for vertical space in formulas see
11975 \begin_inset CommandInset ref
11977 reference "sub:Line-Separation"
11990 \begin_layout Plain Layout
11998 \begin_inset Note Note
12001 \begin_layout Plain Layout
12004 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
12007 \begin_layout Plain Layout
12010 texorpdfstring is in section
12011 \begin_inset CommandInset ref
12013 reference "sub:Formulas-in-Section"
12023 \begin_inset CommandInset label
12025 name "sub:Variable-Space"
12030 \begin_inset Index idx
12033 \begin_layout Plain Layout
12034 Space ! horizontal ! variable
12042 \begin_layout Standard
12043 Space with a defined length can be inserted with the command
12050 \begin_inset Index idx
12053 \begin_layout Plain Layout
12063 \begin_inset Quotes eld
12072 \begin_layout Plain Layout
12084 \begin_inset Quotes erd
12088 The length can be specified by left-clicking on the
12089 \begin_inset Quotes eld
12098 \begin_layout Plain Layout
12110 \begin_inset Quotes erd
12114 The length may also be negative.
12115 To insert so many space that the formula uses all available space, the
12123 \begin_inset Index idx
12126 \begin_layout Plain Layout
12137 \begin_layout Standard
12138 \begin_inset VSpace -1mm
12144 \begin_layout Standard
12146 \begin_inset Tabular
12147 <lyxtabular version="3" rows="4" columns="2">
12148 <features tabularvalignment="middle">
12149 <column alignment="center" valignment="top" width="0">
12150 <column alignment="center" valignment="top" width="0">
12152 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12155 \begin_layout Plain Layout
12163 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12166 \begin_layout Plain Layout
12174 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12177 \begin_layout Plain Layout
12184 \begin_layout Plain Layout
12194 \begin_inset Formula $\to$
12200 \begin_inset space \thinspace{}
12208 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12211 \begin_layout Plain Layout
12212 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
12222 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12225 \begin_layout Plain Layout
12232 \begin_layout Plain Layout
12242 \begin_inset Formula $\to$
12248 \begin_inset space \thinspace{}
12256 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12259 \begin_layout Plain Layout
12260 \begin_inset Formula $A\hspace{-1mm}A\not=A$
12270 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12273 \begin_layout Plain Layout
12280 \begin_layout Plain Layout
12294 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12297 \begin_layout Plain Layout
12298 \begin_inset Formula $A=A\hfill B=B$
12314 \begin_layout Standard
12315 In the last example the available space is given by the longest column entry
12317 In an inline formula the space depends on the length of the line in which
12325 Thus, when the line uses the full width, no space will be created.
12332 only has an effect on displayed formulas when the formula style
12337 (Formula styles are explained in
12338 \begin_inset CommandInset ref
12340 reference "sec:Formula-Styles"
12347 \begin_layout Standard
12354 , there are the commands
12366 that fill the space with a pattern, see
12367 \begin_inset CommandInset ref
12369 reference "sub:Ellipses"
12376 \begin_layout Standard
12377 For text, variable space can be inserted via the menu
12379 Insert\SpecialChar \menuseparator
12380 Formatting\SpecialChar \menuseparator
12382 \begin_inset space ~
12390 \begin_layout Standard
12391 This is a line with
12392 \begin_inset space \hspace{}
12397 \begin_inset space \thinspace{}
12403 \begin_layout Standard
12404 This is a line with
12405 \begin_inset space \hfill{}
12411 \begin_layout Subsection
12412 Space besides inline Formulas
12413 \begin_inset Index idx
12416 \begin_layout Plain Layout
12417 Space ! besides inline formulas
12425 \begin_layout Standard
12426 The space that surrounds inline formulas can be adjusted with the length
12434 \begin_inset Index idx
12437 \begin_layout Plain Layout
12446 The value of a length is set with the command
12453 \begin_inset Index idx
12456 \begin_layout Plain Layout
12464 that has the following scheme:
12467 \begin_layout Standard
12472 setlength{length name}{value}
12475 \begin_layout Standard
12483 \begin_inset space \thinspace{}
12489 \begin_layout Standard
12499 \begin_layout Standard
12500 is inserted in TeX-mode.
12502 \begin_inset space \thinspace{}
12505 mm space will now be set around all inline formulas:
12509 \begin_layout Plain Layout
12523 \begin_layout Standard
12524 This is a line with an inline formula
12525 \begin_inset Formula $A=B$
12529 \begin_inset space \thinspace{}
12532 mm surrounding space.
12536 \begin_layout Plain Layout
12550 \begin_layout Standard
12551 To return to the predefined value,
12557 is set to the value 0
12558 \begin_inset space \thinspace{}
12564 \begin_layout Section
12566 \begin_inset Index idx
12569 \begin_layout Plain Layout
12576 \begin_inset Index idx
12579 \begin_layout Plain Layout
12584 \begin_layout Plain Layout
12595 \begin_layout Plain Layout
12610 \begin_layout Standard
12611 Boxes for text are described in chapter
12618 \begin_inset space ~
12626 \begin_layout Subsection
12628 \begin_inset CommandInset label
12630 name "sub:Boxes-with-Frame"
12635 \begin_inset Index idx
12638 \begin_layout Plain Layout
12647 \begin_layout Standard
12648 It is possible to frame formulas or parts of it with the commands
12655 \begin_inset Index idx
12658 \begin_layout Plain Layout
12673 \begin_inset Index idx
12676 \begin_layout Plain Layout
12687 \begin_layout Standard
12688 When one of these commands is inserted to a formula, a blue box appears
12689 within a frame to enter formula parts.
12696 an additional formula has to be created by
12700 within this box, because the box content will otherwise be treated as mathemati
12708 is used, a new formula is automatically created inside the frame.
12711 \begin_layout Standard
12718 is not suitable to frame displayed formulas because the formula will always
12719 be set in the size of the text.
12726 is in contrary not suitable to frame inline formulas, because the formula
12727 will always be set in the size of a displayed formula.
12730 \begin_layout Standard
12737 there is the command
12744 \begin_inset Index idx
12747 \begin_layout Plain Layout
12755 where additionally the frame width and the alignment can be specified.
12762 is used in the following scheme:
12765 \begin_layout Standard
12770 framebox[frame width][position]{box content}
12773 \begin_layout Standard
12774 The position can either be
12791 right aligns the formula in the box.
12792 When no position is given, the formula will be centered.
12793 \begin_inset Newline newline
12796 Is no width given, also no position can be given.
12797 In this case the frame width is adjusted to the box content like for
12806 \begin_layout Standard
12813 is inserted, a box appears containing three blue boxes.
12814 The first two boxes are surrounded by brackets and denote the two optional
12816 The third box is for formula parts like for
12825 \begin_layout Standard
12827 \begin_inset Tabular
12828 <lyxtabular version="3" rows="5" columns="2">
12829 <features tabularvalignment="middle">
12830 <column alignment="center" valignment="top" width="0">
12831 <column alignment="center" valignment="top" width="0">
12833 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12836 \begin_layout Plain Layout
12842 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12845 \begin_layout Plain Layout
12847 \begin_inset Note Note
12850 \begin_layout Plain Layout
12857 is only used as spacer.
12869 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12872 \begin_layout Plain Layout
12879 \begin_layout Plain Layout
12898 \begin_layout Plain Layout
12912 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12915 \begin_layout Plain Layout
12916 \begin_inset Formula $\raisebox{6mm}{}\fbox{\ensuremath{\int A=B}}\raisebox{-4mm}{}$
12926 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12929 \begin_layout Plain Layout
12936 \begin_layout Plain Layout
12951 \begin_layout Plain Layout
12965 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12968 \begin_layout Plain Layout
12969 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
12979 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12982 \begin_layout Plain Layout
12989 \begin_layout Plain Layout
13003 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13006 \begin_layout Plain Layout
13007 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
13017 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13020 \begin_layout Plain Layout
13027 \begin_layout Plain Layout
13037 \begin_inset Formula $\to$
13041 \begin_inset Formula $\to$
13054 \begin_layout Plain Layout
13064 \begin_inset Formula $\downarrow$
13072 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13075 \begin_layout Plain Layout
13076 \begin_inset Formula $\raisebox{6mm}{}$
13080 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
13084 \begin_inset Formula $\raisebox{-4mm}{}$
13100 \begin_layout Standard
13101 The frame thickness can also be adjusted.
13102 To do this the following commands have to be inserted in TeX-mode before
13106 \begin_layout Standard
13116 \begin_inset Quotes eld
13120 \begin_inset Quotes erd
13134 \begin_inset Quotes eld
13138 \begin_inset Quotes erd
13144 \begin_layout Standard
13145 \begin_inset Quotes eld
13149 \begin_inset Quotes erd
13152 specifies the minimal distance between the frame and the first character
13154 An example for this is the following framed formula:
13158 \begin_layout Plain Layout
13170 \begin_inset Formula \[
13176 Before this formula the commands
13179 \begin_layout Standard
13201 \begin_layout Standard
13202 were inserted in TeX-mode.
13203 The given values are used for all following boxes.
13206 \begin_layout Standard
13207 To return to the standard frame size, the command
13210 \begin_layout Standard
13235 \begin_layout Plain Layout
13249 \begin_layout Standard
13250 is inserted in TeX-mode before the next formula.
13253 \begin_layout Subsection
13254 Boxes without Frame
13255 \begin_inset CommandInset label
13257 name "sub:Boxes-without-Frame"
13262 \begin_inset Index idx
13265 \begin_layout Plain Layout
13266 Boxes ! without frame
13274 \begin_layout Standard
13275 For boxes without a frame there are the following box commands:
13282 \begin_inset Index idx
13285 \begin_layout Plain Layout
13300 \begin_inset Index idx
13303 \begin_layout Plain Layout
13318 \begin_inset Index idx
13321 \begin_layout Plain Layout
13332 \begin_layout Standard
13339 a box can be super- or subscripted.
13340 But in contrary to normal super- and subscripting, the characters in the
13341 box keep their font size.
13348 is used in the following scheme:
13351 \begin_layout Standard
13356 raisebox{height}{box content}
13359 \begin_layout Standard
13360 When the box should contain a formula, an extra formula is needed like for
13371 \begin_inset Note Greyedout
13374 \begin_layout Plain Layout
13385 this extra formula is created by pressing
13389 twice instead of once because LyX doesn't yet support
13403 \begin_layout Standard
13405 \begin_inset Tabular
13406 <lyxtabular version="3" rows="4" columns="2">
13407 <features tabularvalignment="middle">
13408 <column alignment="center" valignment="top" width="0">
13409 <column alignment="center" valignment="top" width="0">
13411 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13414 \begin_layout Plain Layout
13420 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13423 \begin_layout Plain Layout
13431 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13434 \begin_layout Plain Layout
13438 \begin_inset Formula $\to$
13444 \begin_inset Formula $\to$
13452 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13455 \begin_layout Plain Layout
13456 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13466 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13469 \begin_layout Plain Layout
13473 \begin_inset Formula $\to$
13479 \begin_inset Formula $\to$
13487 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13490 \begin_layout Plain Layout
13491 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13501 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13504 \begin_layout Plain Layout
13508 \begin_inset Formula $\to$
13527 \begin_layout Plain Layout
13541 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13544 \begin_layout Plain Layout
13545 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
13561 \begin_layout Standard
13586 , with the difference that there is no frame.
13589 \begin_layout Subsection
13591 \begin_inset CommandInset label
13593 name "sub:Colored-Boxes"
13598 \begin_inset Index idx
13601 \begin_layout Plain Layout
13610 \begin_layout Standard
13611 To be able to use all commands explained in this section, the LaTeX-package
13620 \begin_layout Plain Layout
13625 is part of every LaTeX standard installation.
13631 \begin_inset Index idx
13634 \begin_layout Plain Layout
13640 has to be loaded in the LaTeX-preamble with the line
13644 \begin_layout Plain Layout
13645 When text is colored somewhere in the document with a predefined color,
13646 LyX loads the LaTeX-package
13651 Thus it is possible that the package is loaded twice, but this doesn't
13658 \begin_inset Note Note
13661 \begin_layout Plain Layout
13662 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
13671 \begin_layout Standard
13679 \begin_layout Standard
13680 \begin_inset VSpace medskip
13683 To color boxes, the command
13690 \begin_inset Index idx
13693 \begin_layout Plain Layout
13701 is used in the following scheme:
13704 \begin_layout Standard
13709 colorbox{color}{box content}
13712 \begin_layout Standard
13713 The box content can also be a box and a
13719 can also be part of another box (see the 2nd and 3rd example).
13720 When the box should contain a formula, an extra formula has to be created,
13721 the same way as for
13731 \begin_layout Plain Layout
13732 This also applies for the command
13746 \begin_layout Standard
13747 One of the following predefined colors can be chosen:
13750 \begin_layout Standard
13784 \begin_layout Standard
13786 \begin_inset Tabular
13787 <lyxtabular version="3" rows="4" columns="2">
13788 <features tabularvalignment="middle">
13789 <column alignment="center" valignment="top" width="0">
13790 <column alignment="center" valignment="top" width="0">
13792 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13795 \begin_layout Plain Layout
13801 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13804 \begin_layout Plain Layout
13806 \begin_inset Note Note
13809 \begin_layout Plain Layout
13816 is only used as spacer.
13828 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13831 \begin_layout Plain Layout
13835 \begin_inset Formula $\to$
13845 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13848 \begin_layout Plain Layout
13849 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
13859 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13862 \begin_layout Plain Layout
13866 \begin_inset Formula $\to$
13877 \begin_layout Plain Layout
13891 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13894 \begin_layout Plain Layout
13895 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
13905 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13908 \begin_layout Plain Layout
13915 \begin_layout Plain Layout
13927 \begin_inset Formula $\to$
13946 \begin_layout Plain Layout
13960 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13963 \begin_layout Plain Layout
13964 \begin_inset Formula $\raisebox{7mm}{}\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}\raisebox{-5mm}{}$
13980 \begin_layout Standard
13987 only colors the box but not the characters in the box.
13988 To color all characters, the whole formula is highlighted and the wanted
13989 color is chosen in the
13992 \begin_inset space ~
13998 The dialog can be called with the toolbar button
13999 \begin_inset Graphics
14000 filename ../images/dialog-show_character.png
14007 Edit\SpecialChar \menuseparator
14009 \begin_inset space ~
14012 Style\SpecialChar \menuseparator
14016 The formula number has then the same color as the formula.
14017 When the formula number should get another color than the formula characters,
14018 the color must be changed within the formula.
14021 \begin_layout Standard
14025 \begin_layout Standard
14028 \begin_inset Formula \begin{equation}
14029 \int A=B\label{eq:red}
14037 \begin_inset Formula \begin{equation}
14038 \textcolor{red}{\int A=B}\label{eq:redgreen}
14046 \begin_layout Standard
14048 \begin_inset CommandInset ref
14054 is completely colored red.
14055 \begin_inset Newline newline
14059 \begin_inset CommandInset ref
14061 reference "eq:redgreen"
14065 was first completely colored green to set the color for the formula number.
14066 Subsequently the formula characters were colored red.
14069 \begin_layout Standard
14070 \begin_inset VSpace bigskip
14073 To color the frame different than the rest of the box, the command
14080 \begin_inset Index idx
14083 \begin_layout Plain Layout
14091 is used in the following scheme:
14094 \begin_layout Standard
14099 fcolorbox{frame color}{color}{box content}
14102 \begin_layout Standard
14109 is an extension of the command
14116 The frame width is set, like for
14139 \begin_layout Plain Layout
14151 \begin_inset Formula \[
14152 \fcolorbox{cyan}{magenta}{A=B}
14161 \begin_layout Plain Layout
14175 \begin_layout Standard
14176 This formula was created with the command
14177 \begin_inset Newline newline
14185 \begin_inset Formula $\to$
14191 \begin_inset Formula $\to$
14201 \begin_layout Standard
14202 \begin_inset VSpace bigskip
14205 To use other colors than the predefined ones, they have to be defined first.
14208 \begin_layout Standard
14209 One can for example define the color
14210 \begin_inset Quotes eld
14218 \begin_inset Quotes erd
14221 with the LaTeX-preamble line:
14224 \begin_layout Standard
14229 definecolor{darkgreen}{cmyk}{0.5,
14244 \begin_inset Index idx
14247 \begin_layout Plain Layout
14258 \begin_layout Standard
14263 is the color space that denotes the colors
14280 The four comma separated numbers are the portion factor for the corresponding
14281 colors of the color space.
14282 The factors can be in the range of 0
14283 \begin_inset space \thinspace{}
14287 \begin_inset space \thinspace{}
14295 also the color space
14299 can be used for definitions.
14316 , so that there are in this case three portion factors for the corresponding
14318 Furthermore there is the color space
14322 with one portion factor for the gray value.
14325 \begin_layout Standard
14326 As example a framed box with the new defined color
14330 where the characters have been colored
14335 \begin_inset Formula \begin{equation}
14336 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}
14344 \begin_layout Standard
14345 Self-defined colors can also be used for text with the help of the command
14353 \begin_inset Index idx
14356 \begin_layout Plain Layout
14365 \begin_layout Standard
14369 \begin_layout Plain Layout
14373 textcolor{darkgreen}{
14379 \begin_inset Quotes eld
14383 \begin_inset Quotes erd
14390 \begin_layout Plain Layout
14400 \begin_layout Standard
14408 \begin_inset Index idx
14411 \begin_layout Plain Layout
14419 is used in the scheme
14423 textcolor{color}{characters to color}
14428 \begin_layout Subsection
14430 \begin_inset CommandInset label
14432 name "sub:Paragraph-Boxes"
14437 \begin_inset Index idx
14440 \begin_layout Plain Layout
14441 Boxes ! as paragraph
14449 \begin_layout Standard
14450 A box that can contain several lines and paragraphs, a so called paragraph
14451 box (parbox), can be created with the menu
14453 Insert\SpecialChar \menuseparator
14456 or the toolbar button
14457 \begin_inset Graphics
14458 filename ../images/box-insert.png
14466 \begin_layout Standard
14467 The following example shows a framed parbox in a line:
14470 \begin_layout Standard
14471 \begin_inset VSpace medskip
14475 \begin_inset Box Boxed
14485 height_special "totalheight"
14488 \begin_layout Plain Layout
14489 This is a paragraph box.
14491 \begin_inset space \thinspace{}
14494 cm long and can also contain formulas:
14495 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14506 \begin_layout Standard
14507 \begin_inset VSpace medskip
14513 \begin_layout Standard
14514 Such a box is created by right-clicking on the gray box inset.
14515 A dialog pops up showing the box properties.
14529 \begin_inset space \thinspace{}
14534 Vertical Box Alignment
14539 \begin_layout Standard
14540 \begin_inset VSpace medskip
14543 In LaTeX a parbox is created with the command
14550 \begin_inset Index idx
14553 \begin_layout Plain Layout
14561 that has the following scheme:
14564 \begin_layout Standard
14569 parbox[position]{width}{box content}
14572 \begin_layout Standard
14586 for bottom means that the box is aligned within the surrounding text with
14592 for top this is done with the first line.
14593 When no position is given, the box will be vertically centered, see section
14601 \begin_inset space ~
14606 manual for examples.
14609 \begin_layout Standard
14610 \begin_inset VSpace bigskip
14613 To frame formulas completely, including the formula number, the formula
14614 must be set into a parbox.
14615 To do this, the command
14629 is inserted in TeX-mode before the formula.
14637 \begin_inset Index idx
14640 \begin_layout Plain Layout
14648 is hereby the line width set for the document.
14649 Because the frame is outside the parbox, 2
14650 \begin_inset space \thinspace{}
14653 times the frame separation and the frame thickness must be subtracted from
14655 As this is not automatically done by LyX due to a bug
14659 \begin_layout Plain Layout
14660 \begin_inset CommandInset href
14662 name "LyX-bug #4483"
14663 target "http://www.lyx.org/trac/ticket/4483"
14672 , TeX-mode has to be used.
14673 To be able to multiply and subtract in arguments, the LaTeX-package
14681 \begin_layout Plain Layout
14686 is part of every LaTeX standard installation.
14692 \begin_inset Index idx
14695 \begin_layout Plain Layout
14701 must be loaded in the LaTeX-preamble with the line
14704 \begin_layout Standard
14712 \begin_layout Standard
14713 Behind the formula both boxes are closed by entering
14718 Here is an example:
14722 \begin_layout Plain Layout
14736 \begin_layout Standard
14740 \begin_layout Plain Layout
14758 \begin_inset Formula \begin{equation}
14759 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}
14768 \begin_layout Plain Layout
14779 \begin_layout Plain Layout
14793 \begin_layout Standard
14794 \begin_inset VSpace medskip
14797 As a parbox is used as argument of
14803 , there is in this case no difference between
14818 \begin_layout Standard
14819 \begin_inset VSpace bigskip
14822 Paragraph boxes are very useful to comment formulas directly.
14829 is used in combination with the command
14843 \begin_inset CommandInset ref
14845 reference "sub:User-defined-Numbering"
14852 \begin_layout Standard
14853 An example of a formula commented with
14862 \begin_layout Standard
14866 \begin_layout Plain Layout
14879 This is a description.
14880 It is distinctly separated from the formula and multiline.
14884 \begin_layout Plain Layout
14896 \begin_layout Standard
14897 Such a formula must be inserted completely in TeX-mode because LyX does
14898 not yet support the command
14905 The formula is created with the following command sequence:
14908 \begin_layout Standard
14921 is inserted in TeX-mode.
14925 \begin_layout Plain Layout
14926 When the formula style
14938 can also be replaced by
14945 (formula styles see
14946 \begin_inset CommandInset ref
14948 reference "sec:Formula-Styles"
14957 Then the description follows as normal text and finally
14963 is inserted in TeX-mode.
14976 hereby create a displayed formula.
14979 \begin_layout Standard
14986 can be seen in this example that was
14987 \begin_inset Quotes eld
14991 \begin_inset Quotes erd
14994 using the mathematical textmode:
14995 \begin_inset Formula \[
14996 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}
15004 \begin_layout Section
15006 \begin_inset Index idx
15009 \begin_layout Plain Layout
15018 \begin_layout Subsection
15020 \begin_inset CommandInset label
15022 name "sub:Big-Operators"
15027 \begin_inset Index idx
15030 \begin_layout Plain Layout
15037 \begin_inset Index idx
15040 \begin_layout Plain Layout
15047 \begin_inset Index idx
15050 \begin_layout Plain Layout
15059 \begin_layout Standard
15060 To be able to use all integral operators listed here, the option
15062 Use esint package automatically
15064 must be set in the document settings under
15067 \begin_inset space ~
15075 \begin_layout Standard
15076 \begin_inset space \hfill{}
15080 \begin_inset Tabular
15081 <lyxtabular version="3" rows="11" columns="2">
15082 <features tabularvalignment="middle">
15083 <column alignment="center" valignment="top" width="0pt">
15084 <column alignment="center" valignment="top" width="0pt">
15086 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15089 \begin_layout Plain Layout
15095 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15098 \begin_layout Plain Layout
15106 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15109 \begin_layout Plain Layout
15113 \begin_inset Index idx
15116 \begin_layout Plain Layout
15129 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15132 \begin_layout Plain Layout
15133 \begin_inset Formula $\int$
15143 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15146 \begin_layout Plain Layout
15154 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15157 \begin_layout Plain Layout
15158 \begin_inset Formula $\oint$
15168 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15171 \begin_layout Plain Layout
15179 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15182 \begin_layout Plain Layout
15183 \begin_inset Formula $\ointctrclockwise$
15193 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15196 \begin_layout Plain Layout
15204 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15207 \begin_layout Plain Layout
15208 \begin_inset Formula $\ointclockwise$
15218 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15221 \begin_layout Plain Layout
15229 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15232 \begin_layout Plain Layout
15233 \begin_inset Formula $\sqint$
15243 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15246 \begin_layout Plain Layout
15254 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15257 \begin_layout Plain Layout
15259 \begin_inset Formula $\fint$
15269 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15272 \begin_layout Plain Layout
15280 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15283 \begin_layout Plain Layout
15285 \begin_inset Formula $\landupint$
15295 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15298 \begin_layout Plain Layout
15306 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15309 \begin_layout Plain Layout
15311 \begin_inset Formula $\landdownint$
15321 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15324 \begin_layout Plain Layout
15332 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15335 \begin_layout Plain Layout
15336 \begin_inset Formula $\bigcap$
15346 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15349 \begin_layout Plain Layout
15357 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15360 \begin_layout Plain Layout
15361 \begin_inset Formula $\bigcup$
15375 \begin_inset space \hfill{}
15379 \begin_inset Tabular
15380 <lyxtabular version="3" rows="11" columns="2">
15381 <features tabularvalignment="middle">
15382 <column alignment="center" valignment="top" width="0pt">
15383 <column alignment="center" valignment="top" width="0pt">
15385 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15388 \begin_layout Plain Layout
15394 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15397 \begin_layout Plain Layout
15405 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15408 \begin_layout Plain Layout
15412 \begin_inset Index idx
15415 \begin_layout Plain Layout
15428 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15431 \begin_layout Plain Layout
15432 \begin_inset Formula $\sum$
15442 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15445 \begin_layout Plain Layout
15449 \begin_inset Index idx
15452 \begin_layout Plain Layout
15465 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15468 \begin_layout Plain Layout
15469 \begin_inset Formula $\prod$
15479 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15482 \begin_layout Plain Layout
15490 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15493 \begin_layout Plain Layout
15494 \begin_inset Formula $\coprod$
15504 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15507 \begin_layout Plain Layout
15515 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15518 \begin_layout Plain Layout
15519 \begin_inset Formula $\bigodot$
15529 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15532 \begin_layout Plain Layout
15540 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15543 \begin_layout Plain Layout
15544 \begin_inset Formula $\bigotimes$
15554 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15557 \begin_layout Plain Layout
15565 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15568 \begin_layout Plain Layout
15569 \begin_inset Formula $\bigoplus$
15579 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15582 \begin_layout Plain Layout
15590 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15593 \begin_layout Plain Layout
15594 \begin_inset Formula $\bigwedge$
15604 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15607 \begin_layout Plain Layout
15615 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15618 \begin_layout Plain Layout
15619 \begin_inset Formula $\bigvee$
15629 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15632 \begin_layout Plain Layout
15640 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15643 \begin_layout Plain Layout
15644 \begin_inset Formula $\bigsqcup$
15654 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15657 \begin_layout Plain Layout
15665 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15668 \begin_layout Plain Layout
15669 \begin_inset Formula $\biguplus$
15683 \begin_inset space \hfill{}
15689 \begin_layout Standard
15690 All big operators can also be inserted via the math toolbar button
15691 \begin_inset Graphics
15692 filename ../images/math/intop.png
15700 \begin_layout Standard
15701 The operators are called big because they are bigger than the sometimes
15702 equal looking binary operators.
15703 All big operators can have limits as described in the next subsection.
15706 \begin_layout Standard
15707 For all integral operators there is a second version available, ending on
15725 These operators are different from
15732 \begin_inset space \space{}
15735 in the style the operator limits are displayed, see
15736 \begin_inset CommandInset ref
15738 reference "sub:Operator-Limits"
15746 \begin_layout Subsubsection*
15747 Advice for Integrals
15750 \begin_layout Standard
15755 in an integral is an operator, that therefore has to be set upright.
15756 This is done by highlighting the
15760 and using the keyboard shortcut
15770 \begin_layout Plain Layout
15776 \begin_inset CommandInset ref
15778 reference "sub:Font-Styles"
15788 Finally the smallest space is inserted before the
15792 , as this is usual for operators.
15796 \begin_layout Standard
15798 \begin_inset Formula $\int A(x)dx$
15802 \begin_inset Newline newline
15806 \begin_inset Phantom HPhantom
15809 \begin_layout Plain Layout
15816 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15822 \begin_layout Standard
15823 For multiple integrals there are the following commands:
15824 \begin_inset VSpace medskip
15830 \begin_layout Standard
15831 \begin_inset space \hfill{}
15835 \begin_inset Tabular
15836 <lyxtabular version="3" rows="4" columns="2">
15837 <features tabularvalignment="middle">
15838 <column alignment="center" valignment="top" width="0">
15839 <column alignment="center" valignment="top" width="0">
15841 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15844 \begin_layout Plain Layout
15850 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15853 \begin_layout Plain Layout
15855 \begin_inset Note Note
15858 \begin_layout Plain Layout
15865 is only used as spacer.
15877 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15880 \begin_layout Plain Layout
15888 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15891 \begin_layout Plain Layout
15892 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
15902 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15905 \begin_layout Plain Layout
15913 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15916 \begin_layout Plain Layout
15917 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
15927 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15930 \begin_layout Plain Layout
15938 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15941 \begin_layout Plain Layout
15942 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
15956 \begin_inset space \hfill{}
15960 \begin_inset Tabular
15961 <lyxtabular version="3" rows="4" columns="2">
15962 <features tabularvalignment="middle">
15963 <column alignment="center" valignment="top" width="0">
15964 <column alignment="center" valignment="top" width="0">
15966 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15969 \begin_layout Plain Layout
15975 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15978 \begin_layout Plain Layout
15986 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15989 \begin_layout Plain Layout
15997 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16000 \begin_layout Plain Layout
16001 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
16011 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16014 \begin_layout Plain Layout
16022 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16025 \begin_layout Plain Layout
16026 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
16036 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16039 \begin_layout Plain Layout
16047 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16050 \begin_layout Plain Layout
16051 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
16065 \begin_inset space \hfill{}
16071 \begin_layout Subsection
16073 \begin_inset CommandInset label
16075 name "sub:Operator-Limits"
16080 \begin_inset Index idx
16083 \begin_layout Plain Layout
16092 \begin_layout Standard
16093 Limits are created by super- and subscripts:
16096 \begin_layout Standard
16098 \begin_inset Tabular
16099 <lyxtabular version="3" rows="2" columns="2">
16100 <features tabularvalignment="middle">
16101 <column alignment="center" valignment="top" width="0pt">
16102 <column alignment="center" valignment="top" width="0pt">
16104 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16107 \begin_layout Plain Layout
16113 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16116 \begin_layout Plain Layout
16118 \begin_inset Note Note
16121 \begin_layout Plain Layout
16128 is only used as spacer.
16140 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16143 \begin_layout Plain Layout
16152 \begin_layout Plain Layout
16162 \begin_inset Formula $\to$
16166 \begin_inset Formula $\to$
16174 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16177 \begin_layout Plain Layout
16178 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
16194 \begin_layout Standard
16195 Limits of inline formulas are set right beside the operator.
16196 Limits in displayed formulas are set above or below the operator, except
16197 for integral limits.
16200 \begin_layout Standard
16201 To force that the limits are set beside the operator, the cursor is set
16202 directly behind the operator and the limits type is changed with the menu
16205 Edit\SpecialChar \menuseparator
16206 Math\SpecialChar \menuseparator
16225 \begin_layout Standard
16226 The default limits type is this:
16227 \begin_inset Formula \[
16228 \sum_{x=0}^{\infty}\frac{1}{x^{2}}
16233 This is how it looks when the limits type was changed to
16240 \begin_inset Formula \[
16241 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}
16246 For integrals, except those ending with
16262 etc., the limits are by default set beside the operator.
16263 But for multiple integrals the limits are often set below the operator.
16264 In the following example the limits type was therefore set to
16268 and so set below the integrals:
16269 \begin_inset Formula \begin{equation}
16270 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}
16278 \begin_layout Standard
16279 \begin_inset VSpace medskip
16282 To specify conditions for limits, the commands
16289 \begin_inset Index idx
16292 \begin_layout Plain Layout
16307 \begin_inset Index idx
16310 \begin_layout Plain Layout
16319 To create for example this expression
16320 \begin_inset Formula \begin{equation}
16321 \sum_{\begin{subarray}{c}
16325 \end{subarray}}^{n}k^{-2}\label{eq:substack}
16333 \begin_layout Standard
16334 the following has to be done:
16335 \begin_inset Newline newline
16350 \begin_layout Plain Layout
16362 One is now in a blue box under the summation operator and insert there
16371 \begin_layout Plain Layout
16383 The blue box is now within a purple box and now several lines can be written
16385 A new line is created by inserting a line break (
16388 arg "newline-insert newline"
16393 \begin_inset Newline newline
16398 0<k<1000 Ctrl+Return
16399 \begin_inset Newline newline
16404 is typed in, a new box appears below for the new line.
16407 \begin_layout Standard
16408 The alignment of the lines can be changed to left aligned with the
16418 Edit\SpecialChar \menuseparator
16422 To get right alignment,
16430 \begin_layout Plain Layout
16441 is inserted at the beginning of the line.
16444 \begin_layout Standard
16457 with the difference that the lines are always centered.
16460 \begin_layout Standard
16461 \begin_inset VSpace bigskip
16465 \begin_inset CommandInset ref
16467 reference "eq:substack"
16471 there can be too much space beside an operator, because the characters
16472 following the operator are set beside the limits.
16475 \begin_layout Standard
16476 To avoid this, the following macro can be used in the LaTeX-preamble:
16479 \begin_layout Standard
16493 \begin_inset Newline newline
16505 \begin_inset Newline newline
16512 mathclapinternal #1#2{
16516 mathsurround =0pt #1{#2}$}}
16519 \begin_layout Standard
16520 This defines the command
16527 \begin_inset Index idx
16530 \begin_layout Plain Layout
16538 that sets the width of the limit to 0
16539 \begin_inset space \thinspace{}
16543 The command scheme is
16546 \begin_layout Standard
16554 \begin_layout Standard
16555 where the limit can consist of several conditions.
16558 \begin_layout Standard
16560 \begin_inset CommandInset ref
16562 reference "eq:substack"
16566 , one uses the command
16569 \begin_layout Standard
16582 \begin_layout Plain Layout
16591 0<k<1000 Ctrl+Return
16594 \begin_layout Standard
16595 to create the lower limit.
16596 The summand is now directly behind the summation operator:
16597 \begin_inset Formula \[
16598 \sum_{\mathclap{\substack{0<k<1000\\
16610 \begin_layout Standard
16611 \begin_inset VSpace bigskip
16614 How to use one limit for several operators is described in
16615 \begin_inset CommandInset ref
16617 reference "sub:Self-defined-Operators"
16624 \begin_layout Subsection
16626 \begin_inset CommandInset label
16628 name "sub:Binary-Operators"
16633 \begin_inset Index idx
16636 \begin_layout Plain Layout
16645 \begin_layout Standard
16646 Binary operators are surrounded by space when there is a character before
16648 \begin_inset VSpace medskip
16654 \begin_layout Standard
16655 \begin_inset space \hfill{}
16659 \begin_inset Tabular
16660 <lyxtabular version="3" rows="13" columns="2">
16661 <features tabularvalignment="middle">
16662 <column alignment="center" valignment="top" width="0pt">
16663 <column alignment="center" valignment="top" width="0pt">
16665 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16668 \begin_layout Plain Layout
16670 \begin_inset Note Note
16673 \begin_layout Plain Layout
16680 is only used as spacer.
16690 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16693 \begin_layout Plain Layout
16701 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16704 \begin_layout Plain Layout
16710 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16713 \begin_layout Plain Layout
16714 \begin_inset Formula $+$
16724 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16727 \begin_layout Plain Layout
16733 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16736 \begin_layout Plain Layout
16737 \begin_inset Formula $-$
16747 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16750 \begin_layout Plain Layout
16758 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16761 \begin_layout Plain Layout
16762 \begin_inset Formula $\pm$
16772 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16775 \begin_layout Plain Layout
16783 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16786 \begin_layout Plain Layout
16787 \begin_inset Formula $\mp$
16797 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16800 \begin_layout Plain Layout
16808 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16811 \begin_layout Plain Layout
16812 \begin_inset Formula $\cdot$
16822 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16825 \begin_layout Plain Layout
16833 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16836 \begin_layout Plain Layout
16837 \begin_inset Formula $\times$
16847 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16850 \begin_layout Plain Layout
16858 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16861 \begin_layout Plain Layout
16862 \begin_inset Formula $\div$
16872 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16875 \begin_layout Plain Layout
16879 \begin_layout Plain Layout
16892 \begin_layout Plain Layout
16904 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16907 \begin_layout Plain Layout
16908 \begin_inset Formula $*$
16918 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16921 \begin_layout Plain Layout
16929 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16932 \begin_layout Plain Layout
16933 \begin_inset Formula $\star$
16943 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16946 \begin_layout Plain Layout
16954 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16957 \begin_layout Plain Layout
16958 \begin_inset Formula $\circ$
16968 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16971 \begin_layout Plain Layout
16979 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16982 \begin_layout Plain Layout
16983 \begin_inset Formula $\diamond$
16993 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16996 \begin_layout Plain Layout
17004 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17007 \begin_layout Plain Layout
17008 \begin_inset Formula $\bullet$
17022 \begin_inset space \hfill{}
17026 \begin_inset Tabular
17027 <lyxtabular version="3" rows="13" columns="2">
17028 <features tabularvalignment="middle">
17029 <column alignment="center" valignment="top" width="0pt">
17030 <column alignment="center" valignment="top" width="0pt">
17032 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17035 \begin_layout Plain Layout
17041 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17044 \begin_layout Plain Layout
17052 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17055 \begin_layout Plain Layout
17063 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17066 \begin_layout Plain Layout
17067 \begin_inset Formula $\nabla$
17077 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17080 \begin_layout Plain Layout
17088 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17091 \begin_layout Plain Layout
17092 \begin_inset Formula $\bigtriangledown$
17102 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17105 \begin_layout Plain Layout
17113 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17116 \begin_layout Plain Layout
17117 \begin_inset Formula $\bigtriangleup$
17127 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17130 \begin_layout Plain Layout
17138 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17141 \begin_layout Plain Layout
17142 \begin_inset Formula $\Box$
17152 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17155 \begin_layout Plain Layout
17163 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17166 \begin_layout Plain Layout
17167 \begin_inset Formula $\cap$
17177 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17180 \begin_layout Plain Layout
17188 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17191 \begin_layout Plain Layout
17192 \begin_inset Formula $\cup$
17202 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17205 \begin_layout Plain Layout
17213 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17216 \begin_layout Plain Layout
17217 \begin_inset Formula $\dagger$
17227 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17230 \begin_layout Plain Layout
17238 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17241 \begin_layout Plain Layout
17242 \begin_inset Formula $\ddagger$
17252 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17255 \begin_layout Plain Layout
17263 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17266 \begin_layout Plain Layout
17267 \begin_inset Formula $\wr$
17277 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17280 \begin_layout Plain Layout
17288 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17291 \begin_layout Plain Layout
17292 \begin_inset Formula $\bigcirc$
17302 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17305 \begin_layout Plain Layout
17313 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17316 \begin_layout Plain Layout
17317 \begin_inset Formula $\wedge$
17327 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17330 \begin_layout Plain Layout
17338 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17341 \begin_layout Plain Layout
17342 \begin_inset Formula $\vee$
17356 \begin_inset space \hfill{}
17360 \begin_inset Tabular
17361 <lyxtabular version="3" rows="13" columns="2">
17362 <features tabularvalignment="middle">
17363 <column alignment="center" valignment="top" width="0pt">
17364 <column alignment="center" valignment="top" width="0pt">
17366 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17369 \begin_layout Plain Layout
17375 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17378 \begin_layout Plain Layout
17386 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17389 \begin_layout Plain Layout
17397 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17400 \begin_layout Plain Layout
17401 \begin_inset Formula $\oplus$
17411 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17414 \begin_layout Plain Layout
17422 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17425 \begin_layout Plain Layout
17426 \begin_inset Formula $\ominus$
17436 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17439 \begin_layout Plain Layout
17447 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17450 \begin_layout Plain Layout
17451 \begin_inset Formula $\otimes$
17461 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17464 \begin_layout Plain Layout
17472 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17475 \begin_layout Plain Layout
17476 \begin_inset Formula $\oslash$
17486 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17489 \begin_layout Plain Layout
17497 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17500 \begin_layout Plain Layout
17501 \begin_inset Formula $\odot$
17511 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17514 \begin_layout Plain Layout
17522 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17525 \begin_layout Plain Layout
17526 \begin_inset Formula $\amalg$
17536 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17539 \begin_layout Plain Layout
17547 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17550 \begin_layout Plain Layout
17551 \begin_inset Formula $\uplus$
17561 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17564 \begin_layout Plain Layout
17572 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17575 \begin_layout Plain Layout
17576 \begin_inset Formula $\setminus$
17586 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17589 \begin_layout Plain Layout
17597 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17600 \begin_layout Plain Layout
17601 \begin_inset Formula $\sqcap$
17611 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17614 \begin_layout Plain Layout
17622 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17625 \begin_layout Plain Layout
17626 \begin_inset Formula $\sqcup$
17636 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17639 \begin_layout Plain Layout
17647 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17650 \begin_layout Plain Layout
17651 \begin_inset Formula $\triangleleft$
17661 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17664 \begin_layout Plain Layout
17672 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17675 \begin_layout Plain Layout
17676 \begin_inset Formula $\triangleright$
17690 \begin_inset space \hfill{}
17696 \begin_layout Standard
17697 All binary operators can also be inserted via the math toolbar button
17698 \begin_inset Graphics
17699 filename ../images/math/pm.png
17707 \begin_layout Standard
17708 To typeset the Laplace operator also
17725 \begin_inset Formula $\nabla^{2}$
17728 ) can be used instead of
17737 \begin_layout Standard
17744 Insert\SpecialChar \menuseparator
17756 \begin_layout Subsection
17757 Self-defined Operators
17758 \begin_inset CommandInset label
17760 name "sub:Self-defined-Operators"
17765 \begin_inset Index idx
17768 \begin_layout Plain Layout
17769 Operators ! self-defined
17777 \begin_layout Standard
17778 With the help of the command
17782 DeclareMathOperator
17785 \begin_inset Index idx
17788 \begin_layout Plain Layout
17793 DeclareMathOperator
17798 custom operators can be defined in the LaTeX-preamble.
17799 Its command scheme is:
17802 \begin_layout Standard
17807 DeclareMathOperator{new command}{display}
17810 \begin_layout Standard
17811 Display can be characters or symbols that define how the operator looks
17813 To define a big operator a * is set behind the command.
17814 All self-defined big operators can have limits as described in
17815 \begin_inset CommandInset ref
17817 reference "sub:Operator-Limits"
17824 \begin_layout Standard
17825 For example the LaTeX-preamble line
17828 \begin_layout Standard
17833 DeclareMathOperator*{
17840 \begin_layout Standard
17841 defines the command
17847 , that inserts a big operator consisting of the lozenge symbol from
17848 \begin_inset CommandInset ref
17850 reference "sub:Miscellaneous-Symbols"
17855 \begin_inset Formula \[
17856 \Lozenge_{n=1}^{\infty}
17861 The command for this formula is:
17872 \begin_inset Formula $\to$
17878 \begin_layout Standard
17879 \begin_inset VSpace bigskip
17882 When self-defined operators are not used several times in the document,
17883 they can also be defined with the commands
17890 \begin_inset Index idx
17893 \begin_layout Plain Layout
17908 \begin_inset Index idx
17911 \begin_layout Plain Layout
17919 , which have the following scheme:
17922 \begin_layout Standard
17936 \begin_layout Standard
17943 defines big operators,
17952 \begin_layout Standard
17960 \begin_inset space \thinspace{}
17964 \begin_inset space \space{}
17967 be used to use one limit for several operators:
17970 \begin_layout Standard
17971 \begin_inset Formula \[
17972 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
17980 \begin_layout Standard
17981 The command for the formula above is:
17982 \begin_inset Newline newline
18001 \begin_layout Plain Layout
18013 \begin_inset Formula $\to$
18022 \begin_layout Plain Layout
18036 \begin_layout Section
18038 \begin_inset Index idx
18041 \begin_layout Plain Layout
18050 \begin_layout Subsection
18052 \begin_inset CommandInset label
18054 name "sub:Font-Styles"
18059 \begin_inset Index idx
18062 \begin_layout Plain Layout
18071 \begin_layout Standard
18072 Latin letters in formulas can be set in one of the following font styles:
18073 \begin_inset VSpace -2mm
18079 \begin_layout Standard
18081 \begin_inset Tabular
18082 <lyxtabular version="3" rows="7" columns="3">
18083 <features tabularvalignment="middle">
18084 <column alignment="center" valignment="top" width="0">
18085 <column alignment="center" valignment="top" width="0">
18086 <column alignment="center" valignment="top" width="0">
18088 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18091 \begin_layout Plain Layout
18097 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18100 \begin_layout Plain Layout
18106 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18109 \begin_layout Plain Layout
18117 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18120 \begin_layout Plain Layout
18129 \begin_layout Plain Layout
18145 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18148 \begin_layout Plain Layout
18149 \begin_inset Formula $\mathbb{ABC}$
18157 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18160 \begin_layout Plain Layout
18173 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18176 \begin_layout Plain Layout
18185 \begin_layout Plain Layout
18201 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18204 \begin_layout Plain Layout
18205 \begin_inset Formula $\mathbf{AbC}$
18213 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18216 \begin_layout Plain Layout
18229 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18232 \begin_layout Plain Layout
18241 \begin_layout Plain Layout
18257 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18260 \begin_layout Plain Layout
18261 \begin_inset Formula $\boldsymbol{AbC}$
18269 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18272 \begin_layout Plain Layout
18275 arg "font-boldsymbol"
18285 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18288 \begin_layout Plain Layout
18297 \begin_layout Plain Layout
18313 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18316 \begin_layout Plain Layout
18317 \begin_inset Formula $\mathcal{ABC}$
18325 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18328 \begin_layout Plain Layout
18341 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18344 \begin_layout Plain Layout
18353 \begin_layout Plain Layout
18369 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18372 \begin_layout Plain Layout
18373 \begin_inset Formula $\mathfrak{AbC}$
18381 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18384 \begin_layout Plain Layout
18392 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18395 \begin_layout Plain Layout
18404 \begin_layout Plain Layout
18420 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18423 \begin_layout Plain Layout
18424 \begin_inset Formula $\mathscr{AbC}$
18432 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18435 \begin_layout Plain Layout
18449 \begin_layout Standard
18451 \begin_inset Tabular
18452 <lyxtabular version="3" rows="5" columns="3">
18453 <features tabularvalignment="middle">
18454 <column alignment="center" valignment="top" width="0">
18455 <column alignment="center" valignment="top" width="0">
18456 <column alignment="center" valignment="top" width="0">
18458 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18461 \begin_layout Plain Layout
18467 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18470 \begin_layout Plain Layout
18476 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18479 \begin_layout Plain Layout
18487 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18490 \begin_layout Plain Layout
18499 \begin_layout Plain Layout
18515 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18518 \begin_layout Plain Layout
18519 \begin_inset Formula $\mathit{AbC}$
18527 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18530 \begin_layout Plain Layout
18538 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18541 \begin_layout Plain Layout
18550 \begin_layout Plain Layout
18566 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18569 \begin_layout Plain Layout
18570 \begin_inset Formula $\mathrm{AbC}$
18578 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18581 \begin_layout Plain Layout
18594 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18597 \begin_layout Plain Layout
18606 \begin_layout Plain Layout
18622 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18625 \begin_layout Plain Layout
18626 \begin_inset Formula $\mathsf{AbC}$
18634 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18637 \begin_layout Plain Layout
18650 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18653 \begin_layout Plain Layout
18662 \begin_layout Plain Layout
18678 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18681 \begin_layout Plain Layout
18682 \begin_inset Formula $\mathtt{AbC}$
18690 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18693 \begin_layout Plain Layout
18696 arg "font-typewriter"
18712 \begin_layout Standard
18713 \begin_inset Note Greyedout
18716 \begin_layout Plain Layout
18733 can only be used for big letters.
18741 \begin_layout Standard
18742 Predefined is the style
18751 \begin_layout Standard
18752 The style commands work also for letters in mathematical constructs:
18753 \begin_inset Formula \[
18754 \mathfrak{A=\frac{b}{C}}
18762 \begin_layout Standard
18763 Characters in mathematical text don't appear in a math font style but in
18764 the text font style
18771 That their style can't be set correctly via the text style dialog is a
18776 \begin_layout Plain Layout
18777 \begin_inset CommandInset href
18779 name "LyX-bug #4629"
18780 target "http://www.lyx.org/trac/ticket/4629"
18792 \begin_layout Standard
18793 Instead of the style commands the dialog
18795 Edit\SpecialChar \menuseparator
18796 Math\SpecialChar \menuseparator
18799 or the toolbar button
18800 \begin_inset Graphics
18801 filename ../images/math/font.png
18809 \begin_layout Subsection
18811 \begin_inset CommandInset label
18813 name "sub:Bold-Formulas"
18818 \begin_inset Index idx
18821 \begin_layout Plain Layout
18830 \begin_layout Standard
18831 To make a complete formula bold, the command
18837 from the previous subsection cannot be used, because it doesn't work for
18838 small Greek letters.
18839 Furthermore it prints Latin letters always upright, like in the following
18843 \begin_layout Standard
18844 \begin_inset Formula \[
18845 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
18853 \begin_layout Standard
18854 To display the formula correctly, the command
18861 \begin_inset Formula \[
18862 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
18867 It is also possible to set the formula in a
18869 boldmath environment
18872 This environment is created by inserting the command
18879 \begin_inset Index idx
18882 \begin_layout Plain Layout
18891 To end the environment, the command
18898 \begin_inset Index idx
18901 \begin_layout Plain Layout
18909 is inserted in TeX-mode.
18913 \begin_layout Plain Layout
18923 \begin_inset Formula \[
18924 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
18933 \begin_layout Plain Layout
18945 \begin_layout Subsection
18947 \begin_inset Index idx
18950 \begin_layout Plain Layout
18959 \begin_layout Standard
18960 Formulas can be colored like normal text: Highlight a formula or a formula
18966 Here is a formula in magenta:
18967 \begin_inset Formula \[
18968 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
18976 \begin_layout Standard
18977 You can also define your own colors as described in
18978 \begin_inset CommandInset ref
18980 reference "sub:Colored-Boxes"
18985 They can be used with the TeX code command
18992 \begin_inset Index idx
18995 \begin_layout Plain Layout
19006 \begin_layout Standard
19011 textcolor{color}{characters or formula}
19014 \begin_layout Standard
19015 The following example was colored completely dark green and partly red:
19018 \begin_layout Standard
19022 \begin_layout Plain Layout
19026 textcolor{darkgreen}{
19032 \begin_inset Formula \[
19033 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
19042 \begin_layout Plain Layout
19052 \begin_layout Standard
19053 Due to a bug in LyX only complete formulas can be colored with self-defined
19058 \begin_layout Plain Layout
19059 \begin_inset CommandInset href
19061 name "LyX-bug #5269"
19062 target "http://www.lyx.org/trac/ticket/5269"
19074 \begin_layout Subsection
19076 \begin_inset CommandInset label
19078 name "sub:Font-Sizes"
19083 \begin_inset Index idx
19086 \begin_layout Plain Layout
19095 \begin_layout Standard
19096 For characters in formulas there are, analog to characters in text, the
19097 following size commands:
19100 \begin_layout Standard
19144 \begin_inset Newline newline
19166 \begin_layout Standard
19167 The size produced by the commands depends on the document font size, that
19168 corresponds with the command
19175 The other commands produce smaller or larger sizes than
19182 The font size can however not exceed a certain value.
19183 Is for example the document font size 12
19184 \begin_inset space \thinspace{}
19193 switches to the same size as
19203 \begin_layout Standard
19204 A size command is inserted in TeX-mode before the formula and sets the size
19205 for all following formula and text characters.
19206 To switch back to the initial size, the command
19212 is inserted behind the formula in TeX-mode.
19215 \begin_layout Standard
19216 \begin_inset Newpage newpage
19222 \begin_layout Standard
19223 Within a formula the size can be changed using the following size commands:
19226 \begin_layout Standard
19229 \begin_inset Tabular
19230 <lyxtabular version="3" rows="5" columns="2">
19231 <features tabularvalignment="middle">
19232 <column alignment="center" valignment="top" width="0">
19233 <column alignment="center" valignment="top" width="0">
19235 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19238 \begin_layout Plain Layout
19244 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19247 \begin_layout Plain Layout
19249 \begin_inset Note Note
19252 \begin_layout Plain Layout
19259 is only used as spacer.
19271 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19274 \begin_layout Plain Layout
19278 \begin_inset Index idx
19281 \begin_layout Plain Layout
19294 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19297 \begin_layout Plain Layout
19298 \begin_inset Formula $\raisebox{6.5mm}{}{\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-5.5mm}{}$
19308 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19311 \begin_layout Plain Layout
19319 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19322 \begin_layout Plain Layout
19323 \begin_inset Formula $\raisebox{4.5mm}{}{\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-4mm}{}$
19333 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19336 \begin_layout Plain Layout
19344 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19347 \begin_layout Plain Layout
19348 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
19358 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19361 \begin_layout Plain Layout
19369 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19372 \begin_layout Plain Layout
19373 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
19389 \begin_layout Standard
19390 After entering these commands, a blue box appears in which the formula parts
19394 \begin_layout Standard
19395 There is a further method to change the font size, that though only works
19396 for symbols or letters in mathematical text.
19397 To use it, one of the above text size commands is inserted in mathematical
19399 All following characters until the end of the mathematical text or until
19400 another size command will have the selected size.
19402 \begin_inset VSpace -2mm
19408 \begin_layout Standard
19412 \begin_layout Plain Layout
19422 \begin_inset Formula \[
19423 A=\frac{B}{c}\cdot\maltese
19429 \begin_inset Formula \[
19430 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
19439 \begin_layout Plain Layout
19451 \begin_layout Standard
19452 \begin_inset VSpace medskip
19455 Before both formulas the command
19462 The command for the second formula is:
19463 \begin_inset Newline newline
19474 \begin_layout Plain Layout
19489 \begin_layout Plain Layout
19504 \begin_layout Plain Layout
19519 \begin_layout Plain Layout
19529 \begin_inset Formula $\to$
19533 \begin_inset Formula $\to$
19537 \begin_inset Newline newline
19541 \begin_inset space \hspace*{}
19555 \begin_layout Plain Layout
19570 \begin_layout Plain Layout
19585 \begin_layout Plain Layout
19597 \begin_layout Standard
19598 If a symbol cannot be displayed in different sizes, it will always be displayed
19599 in the default size.
19602 \begin_layout Standard
19603 \begin_inset Newpage newpage
19609 \begin_layout Section
19611 \begin_inset Index idx
19614 \begin_layout Plain Layout
19623 \begin_layout Standard
19624 Greek letters can also be inserted via the toolbar button
19625 \begin_inset Graphics
19626 filename ../images/math/alpha.png
19632 All international typesetting norms purport that Greek letters in math
19633 have to be typeset italic/slanted.
19634 In some languages, like French or Russian, they are nevertheless sometimes
19638 \begin_layout Subsection
19640 \begin_inset Index idx
19643 \begin_layout Plain Layout
19644 Greek letters ! small
19652 \begin_layout Standard
19653 \begin_inset space \hfill{}
19657 \begin_inset Tabular
19658 <lyxtabular version="3" rows="11" columns="2">
19659 <features tabularvalignment="middle">
19660 <column alignment="center" valignment="top" width="0pt">
19661 <column alignment="center" valignment="top" width="0pt">
19663 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19666 \begin_layout Plain Layout
19672 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19675 \begin_layout Plain Layout
19683 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19686 \begin_layout Plain Layout
19694 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19697 \begin_layout Plain Layout
19698 \begin_inset Formula $\alpha$
19708 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19711 \begin_layout Plain Layout
19719 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19722 \begin_layout Plain Layout
19723 \begin_inset Formula $\beta$
19733 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19736 \begin_layout Plain Layout
19744 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19747 \begin_layout Plain Layout
19748 \begin_inset Formula $\gamma$
19758 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19761 \begin_layout Plain Layout
19769 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19772 \begin_layout Plain Layout
19773 \begin_inset Formula $\delta$
19783 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19786 \begin_layout Plain Layout
19794 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19797 \begin_layout Plain Layout
19798 \begin_inset Formula $\epsilon$
19808 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19811 \begin_layout Plain Layout
19819 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19822 \begin_layout Plain Layout
19823 \begin_inset Formula $\varepsilon$
19833 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19836 \begin_layout Plain Layout
19844 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19847 \begin_layout Plain Layout
19848 \begin_inset Formula $\zeta$
19858 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19861 \begin_layout Plain Layout
19869 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19872 \begin_layout Plain Layout
19873 \begin_inset Formula $\eta$
19883 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19886 \begin_layout Plain Layout
19894 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19897 \begin_layout Plain Layout
19898 \begin_inset Formula $\theta$
19908 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19911 \begin_layout Plain Layout
19919 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19922 \begin_layout Plain Layout
19923 \begin_inset Formula $\vartheta$
19937 \begin_inset space \hfill{}
19941 \begin_inset Tabular
19942 <lyxtabular version="3" rows="12" columns="2">
19943 <features tabularvalignment="middle">
19944 <column alignment="center" valignment="top" width="0pt">
19945 <column alignment="center" valignment="top" width="0pt">
19947 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19950 \begin_layout Plain Layout
19956 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19959 \begin_layout Plain Layout
19967 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19970 \begin_layout Plain Layout
19978 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19981 \begin_layout Plain Layout
19982 \begin_inset Formula $\iota$
19992 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19995 \begin_layout Plain Layout
20003 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20006 \begin_layout Plain Layout
20007 \begin_inset Formula $\kappa$
20017 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20020 \begin_layout Plain Layout
20028 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20031 \begin_layout Plain Layout
20032 \begin_inset Formula $\varkappa$
20042 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20045 \begin_layout Plain Layout
20053 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20056 \begin_layout Plain Layout
20057 \begin_inset Formula $\lambda$
20067 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20070 \begin_layout Plain Layout
20078 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20081 \begin_layout Plain Layout
20082 \begin_inset Formula $\mu$
20092 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20095 \begin_layout Plain Layout
20103 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20106 \begin_layout Plain Layout
20107 \begin_inset Formula $\nu$
20117 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20120 \begin_layout Plain Layout
20128 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20131 \begin_layout Plain Layout
20132 \begin_inset Formula $\xi$
20142 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20145 \begin_layout Plain Layout
20151 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20154 \begin_layout Plain Layout
20155 \begin_inset Formula $o$
20165 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20168 \begin_layout Plain Layout
20176 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20179 \begin_layout Plain Layout
20180 \begin_inset Formula $\pi$
20190 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20193 \begin_layout Plain Layout
20201 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20204 \begin_layout Plain Layout
20205 \begin_inset Formula $\varpi$
20215 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20218 \begin_layout Plain Layout
20226 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20229 \begin_layout Plain Layout
20230 \begin_inset Formula $\rho$
20244 \begin_inset space \hfill{}
20248 \begin_inset Tabular
20249 <lyxtabular version="3" rows="11" columns="2">
20250 <features tabularvalignment="middle">
20251 <column alignment="center" valignment="top" width="0pt">
20252 <column alignment="center" valignment="top" width="0pt">
20254 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20257 \begin_layout Plain Layout
20263 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20266 \begin_layout Plain Layout
20274 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20277 \begin_layout Plain Layout
20285 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20288 \begin_layout Plain Layout
20289 \begin_inset Formula $\varrho$
20299 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20302 \begin_layout Plain Layout
20310 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20313 \begin_layout Plain Layout
20314 \begin_inset Formula $\sigma$
20324 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20327 \begin_layout Plain Layout
20335 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20338 \begin_layout Plain Layout
20339 \begin_inset Formula $\varsigma$
20349 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20352 \begin_layout Plain Layout
20360 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20363 \begin_layout Plain Layout
20364 \begin_inset Formula $\tau$
20374 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20377 \begin_layout Plain Layout
20385 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20388 \begin_layout Plain Layout
20389 \begin_inset Formula $\upsilon$
20399 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20402 \begin_layout Plain Layout
20410 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20413 \begin_layout Plain Layout
20414 \begin_inset Formula $\phi$
20424 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20427 \begin_layout Plain Layout
20435 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20438 \begin_layout Plain Layout
20439 \begin_inset Formula $\varphi$
20449 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20452 \begin_layout Plain Layout
20460 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20463 \begin_layout Plain Layout
20464 \begin_inset Formula $\chi$
20474 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20477 \begin_layout Plain Layout
20485 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20488 \begin_layout Plain Layout
20489 \begin_inset Formula $\psi$
20499 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20502 \begin_layout Plain Layout
20510 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20513 \begin_layout Plain Layout
20514 \begin_inset Formula $\omega$
20528 \begin_inset space \hfill{}
20534 \begin_layout Standard
20535 \begin_inset VSpace medskip
20541 \begin_layout Standard
20542 How to create special upright Greek letters is explained in
20543 \begin_inset CommandInset ref
20545 reference "sub:Upright-small-Greek"
20552 \begin_layout Subsection
20554 \begin_inset Index idx
20557 \begin_layout Plain Layout
20558 Greek letters ! big
20566 \begin_layout Standard
20567 \begin_inset space \hfill{}
20571 \begin_inset Tabular
20572 <lyxtabular version="3" rows="7" columns="2">
20573 <features tabularvalignment="middle">
20574 <column alignment="center" valignment="top" width="0pt">
20575 <column alignment="center" valignment="top" width="0pt">
20577 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20580 \begin_layout Plain Layout
20586 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20589 \begin_layout Plain Layout
20597 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20600 \begin_layout Plain Layout
20608 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20611 \begin_layout Plain Layout
20612 \begin_inset Formula $\Gamma$
20622 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20625 \begin_layout Plain Layout
20633 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20636 \begin_layout Plain Layout
20637 \begin_inset Formula $\Delta$
20647 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20650 \begin_layout Plain Layout
20658 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20661 \begin_layout Plain Layout
20662 \begin_inset Formula $\Theta$
20672 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20675 \begin_layout Plain Layout
20683 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20686 \begin_layout Plain Layout
20687 \begin_inset Formula $\Lambda$
20697 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20700 \begin_layout Plain Layout
20708 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20711 \begin_layout Plain Layout
20712 \begin_inset Formula $\Xi$
20722 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20725 \begin_layout Plain Layout
20733 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20736 \begin_layout Plain Layout
20737 \begin_inset Formula $\Pi$
20751 \begin_inset space \hfill{}
20755 \begin_inset Tabular
20756 <lyxtabular version="3" rows="6" columns="2">
20757 <features tabularvalignment="middle">
20758 <column alignment="center" valignment="top" width="0pt">
20759 <column alignment="center" valignment="top" width="0pt">
20761 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20764 \begin_layout Plain Layout
20770 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20773 \begin_layout Plain Layout
20781 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20784 \begin_layout Plain Layout
20792 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20795 \begin_layout Plain Layout
20796 \begin_inset Formula $\Sigma$
20806 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20809 \begin_layout Plain Layout
20817 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20820 \begin_layout Plain Layout
20821 \begin_inset Formula $\Upsilon$
20831 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20834 \begin_layout Plain Layout
20842 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20845 \begin_layout Plain Layout
20846 \begin_inset Formula $\Phi$
20856 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20859 \begin_layout Plain Layout
20867 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20870 \begin_layout Plain Layout
20871 \begin_inset Formula $\Psi$
20881 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20884 \begin_layout Plain Layout
20892 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20895 \begin_layout Plain Layout
20896 \begin_inset Formula $\Omega$
20910 \begin_inset space \hfill{}
20916 \begin_layout Standard
20917 \begin_inset VSpace medskip
20920 That the big Greek letters appear upright is caused by a design bug when
20922 To get correct italic big letters, begin every command with
20927 For example the command
20934 \begin_inset Formula $\varGamma$
20938 Another way is to load the package
20946 \begin_layout Plain Layout
20951 is part of the LaTeX-package
20956 \begin_inset Index idx
20959 \begin_layout Plain Layout
20964 \begin_layout Plain Layout
20984 \begin_inset Index idx
20987 \begin_layout Plain Layout
20993 with the LaTeX-preamble line
20996 \begin_layout Standard
21001 usepackage{fixmath}
21004 \begin_layout Standard
21005 Then all big Greek letters in a document will automatically be typeset upright.
21008 \begin_layout Subsection
21010 \begin_inset Index idx
21013 \begin_layout Plain Layout
21014 Greek letters ! bold
21022 \begin_layout Standard
21023 Greek letters cannot be set with different font styles like Latin letters.
21024 They can only be made bold with the command
21031 \begin_inset Index idx
21034 \begin_layout Plain Layout
21045 \begin_layout Standard
21047 \begin_inset Tabular
21048 <lyxtabular version="3" rows="3" columns="2">
21049 <features tabularvalignment="middle">
21050 <column alignment="center" valignment="top" width="0">
21051 <column alignment="center" valignment="top" width="0">
21053 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21056 \begin_layout Plain Layout
21062 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21065 \begin_layout Plain Layout
21073 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21076 \begin_layout Plain Layout
21088 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21091 \begin_layout Plain Layout
21092 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
21102 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21105 \begin_layout Plain Layout
21117 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21120 \begin_layout Plain Layout
21121 \begin_inset Formula $\theta\boldsymbol{\theta}$
21137 \begin_layout Section
21142 \begin_layout Plain Layout
21155 \begin_layout Plain Layout
21156 A list with all symbols of most of the LaTeX-packages can be found in
21157 \begin_inset CommandInset citation
21172 \begin_layout Plain Layout
21180 \begin_inset Note Note
21183 \begin_layout Plain Layout
21186 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
21189 \begin_layout Plain Layout
21192 texorpdfstring is in section
21193 \begin_inset CommandInset ref
21195 reference "sub:Formulas-in-Section"
21205 \begin_inset Index idx
21208 \begin_layout Plain Layout
21217 \begin_layout Standard
21218 Many of the symbols listed in this section can also be inserted via the
21220 \begin_inset Graphics
21221 filename ../images/math/nabla.png
21227 \begin_inset Graphics
21228 filename ../images/math/digamma.png
21236 \begin_layout Subsection
21237 Mathematical Symbols
21238 \begin_inset CommandInset label
21240 name "sub:Mathematical-Symbols"
21245 \begin_inset Index idx
21248 \begin_layout Plain Layout
21249 Symbols ! mathematical
21257 \begin_layout Standard
21258 \begin_inset space \hfill{}
21262 \begin_inset Tabular
21263 <lyxtabular version="3" rows="10" columns="2">
21264 <features tabularvalignment="middle">
21265 <column alignment="center" valignment="top" width="0pt">
21266 <column alignment="center" valignment="top" width="0pt">
21268 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21271 \begin_layout Plain Layout
21277 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21280 \begin_layout Plain Layout
21288 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21291 \begin_layout Plain Layout
21299 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21302 \begin_layout Plain Layout
21303 \begin_inset Formula $\neg$
21313 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21316 \begin_layout Plain Layout
21324 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21327 \begin_layout Plain Layout
21328 \begin_inset Formula $\Im$
21338 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21341 \begin_layout Plain Layout
21349 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21352 \begin_layout Plain Layout
21353 \begin_inset Formula $\Re$
21363 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21366 \begin_layout Plain Layout
21374 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21377 \begin_layout Plain Layout
21378 \begin_inset Formula $\aleph$
21388 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21391 \begin_layout Plain Layout
21399 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21402 \begin_layout Plain Layout
21403 \begin_inset Formula $\partial$
21413 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21416 \begin_layout Plain Layout
21424 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21427 \begin_layout Plain Layout
21428 \begin_inset Formula $\infty$
21438 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21441 \begin_layout Plain Layout
21449 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21452 \begin_layout Plain Layout
21453 \begin_inset Formula $\wp$
21463 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21466 \begin_layout Plain Layout
21474 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21477 \begin_layout Plain Layout
21478 \begin_inset Formula $\imath$
21488 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21491 \begin_layout Plain Layout
21499 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21502 \begin_layout Plain Layout
21503 \begin_inset Formula $\jmath$
21517 \begin_inset space \hfill{}
21521 \begin_inset Tabular
21522 <lyxtabular version="3" rows="10" columns="2">
21523 <features tabularvalignment="middle">
21524 <column alignment="center" valignment="top" width="0pt">
21525 <column alignment="center" valignment="top" width="0pt">
21527 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21530 \begin_layout Plain Layout
21536 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21539 \begin_layout Plain Layout
21541 \begin_inset Note Note
21544 \begin_layout Plain Layout
21551 is only used as spacer.
21563 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21566 \begin_layout Plain Layout
21574 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21577 \begin_layout Plain Layout
21578 \begin_inset Formula $\forall$
21588 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21591 \begin_layout Plain Layout
21599 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21602 \begin_layout Plain Layout
21603 \begin_inset Formula $\exists$
21613 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21616 \begin_layout Plain Layout
21624 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21627 \begin_layout Plain Layout
21628 \begin_inset Formula $\nexists$
21638 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21641 \begin_layout Plain Layout
21649 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21652 \begin_layout Plain Layout
21653 \begin_inset Formula $\emptyset$
21663 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21666 \begin_layout Plain Layout
21674 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21677 \begin_layout Plain Layout
21678 \begin_inset Formula $\varnothing$
21688 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21691 \begin_layout Plain Layout
21699 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21702 \begin_layout Plain Layout
21703 \begin_inset Formula $\dag$
21713 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21716 \begin_layout Plain Layout
21724 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21727 \begin_layout Plain Layout
21728 \begin_inset Formula $\ddag$
21738 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21741 \begin_layout Plain Layout
21749 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21752 \begin_layout Plain Layout
21756 \begin_layout Plain Layout
21766 \begin_inset Formula $\complement$
21773 \begin_layout Plain Layout
21787 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21790 \begin_layout Plain Layout
21798 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21801 \begin_layout Plain Layout
21802 \begin_inset Formula $\Bbbk$
21816 \begin_inset space \hfill{}
21820 \begin_inset Tabular
21821 <lyxtabular version="3" rows="10" columns="2">
21822 <features tabularvalignment="middle">
21823 <column alignment="center" valignment="top" width="0pt">
21824 <column alignment="center" valignment="top" width="0pt">
21826 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21829 \begin_layout Plain Layout
21835 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21838 \begin_layout Plain Layout
21846 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21849 \begin_layout Plain Layout
21857 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21860 \begin_layout Plain Layout
21861 \begin_inset Formula $\prime$
21871 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21874 \begin_layout Plain Layout
21882 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21885 \begin_layout Plain Layout
21886 \begin_inset Formula $\backprime$
21896 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21899 \begin_layout Plain Layout
21907 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21910 \begin_layout Plain Layout
21911 \begin_inset Formula $\mho$
21921 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21924 \begin_layout Plain Layout
21932 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21935 \begin_layout Plain Layout
21936 \begin_inset Formula $\triangle$
21946 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21949 \begin_layout Plain Layout
21957 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21960 \begin_layout Plain Layout
21961 \begin_inset Formula $\angle$
21971 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21974 \begin_layout Plain Layout
21982 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21985 \begin_layout Plain Layout
21986 \begin_inset Formula $\measuredangle$
21996 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21999 \begin_layout Plain Layout
22007 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22010 \begin_layout Plain Layout
22011 \begin_inset Formula $\sphericalangle$
22021 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22024 \begin_layout Plain Layout
22032 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22035 \begin_layout Plain Layout
22036 \begin_inset Formula $\top$
22046 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22049 \begin_layout Plain Layout
22057 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22060 \begin_layout Plain Layout
22061 \begin_inset Formula $\bot$
22075 \begin_inset space \hfill{}
22081 \begin_layout Subsection
22082 Miscellaneous Symbols
22083 \begin_inset CommandInset label
22085 name "sub:Miscellaneous-Symbols"
22090 \begin_inset Index idx
22093 \begin_layout Plain Layout
22094 Symbols ! miscellaneous
22102 \begin_layout Standard
22105 \begin_inset Tabular
22106 <lyxtabular version="3" rows="10" columns="2">
22107 <features tabularvalignment="middle">
22108 <column alignment="center" valignment="top" width="0pt">
22109 <column alignment="center" valignment="top" width="0pt">
22111 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22114 \begin_layout Plain Layout
22120 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22123 \begin_layout Plain Layout
22131 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22134 \begin_layout Plain Layout
22142 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22145 \begin_layout Plain Layout
22146 \begin_inset Formula $\flat$
22156 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22159 \begin_layout Plain Layout
22167 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22170 \begin_layout Plain Layout
22171 \begin_inset Formula $\natural$
22181 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22184 \begin_layout Plain Layout
22192 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22195 \begin_layout Plain Layout
22196 \begin_inset Formula $\sharp$
22206 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22209 \begin_layout Plain Layout
22217 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22220 \begin_layout Plain Layout
22221 \begin_inset Formula $\surd$
22231 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22234 \begin_layout Plain Layout
22242 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22245 \begin_layout Plain Layout
22246 \begin_inset Formula $\checkmark$
22256 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22259 \begin_layout Plain Layout
22267 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22270 \begin_layout Plain Layout
22271 \begin_inset Formula $\yen$
22281 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22284 \begin_layout Plain Layout
22292 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22295 \begin_layout Plain Layout
22296 \begin_inset Formula $\pounds$
22306 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22309 \begin_layout Plain Layout
22315 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22318 \begin_layout Plain Layout
22319 \begin_inset Formula $\$$
22329 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22332 \begin_layout Plain Layout
22338 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22341 \begin_layout Plain Layout
22342 \begin_inset Formula $§$
22356 \begin_inset Tabular
22357 <lyxtabular version="3" rows="10" columns="2">
22358 <features tabularvalignment="middle">
22359 <column alignment="center" valignment="top" width="0">
22360 <column alignment="center" valignment="top" width="0">
22362 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22365 \begin_layout Plain Layout
22371 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22374 \begin_layout Plain Layout
22382 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22385 \begin_layout Plain Layout
22393 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22396 \begin_layout Plain Layout
22397 \begin_inset Formula $\hbar$
22407 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22410 \begin_layout Plain Layout
22418 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22421 \begin_layout Plain Layout
22422 \begin_inset Formula $\hslash$
22432 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22435 \begin_layout Plain Layout
22443 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22446 \begin_layout Plain Layout
22447 \begin_inset Formula $\clubsuit$
22457 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22460 \begin_layout Plain Layout
22468 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22471 \begin_layout Plain Layout
22472 \begin_inset Formula $\spadesuit$
22482 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22485 \begin_layout Plain Layout
22493 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22496 \begin_layout Plain Layout
22497 \begin_inset Formula $\bigstar$
22507 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22510 \begin_layout Plain Layout
22518 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22521 \begin_layout Plain Layout
22522 \begin_inset Formula $\blacklozenge$
22532 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22535 \begin_layout Plain Layout
22543 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22546 \begin_layout Plain Layout
22547 \begin_inset Formula $\blacktriangle$
22557 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22560 \begin_layout Plain Layout
22568 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22571 \begin_layout Plain Layout
22572 \begin_inset Formula $\blacktriangledown$
22582 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22585 \begin_layout Plain Layout
22593 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22596 \begin_layout Plain Layout
22597 \begin_inset Formula $\bullet$
22611 \begin_inset Tabular
22612 <lyxtabular version="3" rows="10" columns="2">
22613 <features tabularvalignment="middle">
22614 <column alignment="center" valignment="top" width="0pt">
22615 <column alignment="center" valignment="top" width="0pt">
22617 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22620 \begin_layout Plain Layout
22626 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22629 \begin_layout Plain Layout
22637 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22640 \begin_layout Plain Layout
22648 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22651 \begin_layout Plain Layout
22652 \begin_inset Formula $\diamondsuit$
22662 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22665 \begin_layout Plain Layout
22673 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22676 \begin_layout Plain Layout
22677 \begin_inset Formula $\Diamond$
22687 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22690 \begin_layout Plain Layout
22698 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22701 \begin_layout Plain Layout
22702 \begin_inset Formula $\heartsuit$
22712 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22715 \begin_layout Plain Layout
22723 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22726 \begin_layout Plain Layout
22727 \begin_inset Formula $\P$
22737 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22740 \begin_layout Plain Layout
22748 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22751 \begin_layout Plain Layout
22752 \begin_inset Formula $\copyright$
22762 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22765 \begin_layout Plain Layout
22773 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22776 \begin_layout Plain Layout
22777 \begin_inset Formula $\circledR$
22787 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22790 \begin_layout Plain Layout
22798 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22801 \begin_layout Plain Layout
22802 \begin_inset Formula $\maltese$
22812 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22815 \begin_layout Plain Layout
22823 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22826 \begin_layout Plain Layout
22827 \begin_inset Formula $\diagup$
22837 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22840 \begin_layout Plain Layout
22848 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22851 \begin_layout Plain Layout
22852 \begin_inset Formula $\diagdown$
22868 \begin_layout Standard
22869 \begin_inset VSpace medskip
22872 More symbols are listed in
22873 \begin_inset CommandInset ref
22875 reference "sub:Miscellaneous-special-Characters"
22882 \begin_layout Standard
22883 Some symbols can be displayed in different sizes, see
22884 \begin_inset CommandInset ref
22886 reference "sub:Font-Sizes"
22893 \begin_layout Subsection
22895 \begin_inset Index idx
22898 \begin_layout Plain Layout
22899 Symbols ! Euro-symbol
22905 \begin_inset Index idx
22908 \begin_layout Plain Layout
22915 \begin_layout Plain Layout
22932 \begin_layout Standard
22933 To use the Euro symbol in formulas, the LaTeX-package
22938 \begin_inset Index idx
22941 \begin_layout Plain Layout
22947 must be installed and loaded with the LaTeX-preamble line
22950 \begin_layout Standard
22955 usepackage[gennarrow]{eurosym}
22958 \begin_layout Standard
22959 The Euro symbol can now be inserted with the command
22966 \begin_inset Index idx
22969 \begin_layout Plain Layout
22980 \begin_layout Standard
22981 The Euro symbol can directly be inserted with the € key in mathematical
22982 text, without having
22997 can also be inserted in TeX-mode.
22998 The official currency symbol can then be inserted with the command
23005 \begin_inset Index idx
23008 \begin_layout Plain Layout
23016 , that is only available in TeX-mode.
23019 \begin_layout Standard
23023 \begin_layout Plain Layout
23033 \begin_inset Note Note
23036 \begin_layout Plain Layout
23037 The following table will only be displayed when the LaTeX-package
23049 \begin_layout Standard
23050 An overview about the different Euro symbols:
23053 \begin_layout Standard
23055 \begin_inset Tabular
23056 <lyxtabular version="3" rows="4" columns="3">
23057 <features tabularvalignment="middle">
23058 <column alignment="center" valignment="top" width="0pt">
23059 <column alignment="center" valignment="top" width="0pt">
23060 <column alignment="center" valignment="top" width="0pt">
23062 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
23065 \begin_layout Plain Layout
23071 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23074 \begin_layout Plain Layout
23080 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23083 \begin_layout Plain Layout
23091 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23094 \begin_layout Plain Layout
23100 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23103 \begin_layout Plain Layout
23111 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23114 \begin_layout Plain Layout
23115 \begin_inset Formula $\euro$
23125 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23128 \begin_layout Plain Layout
23134 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23137 \begin_layout Plain Layout
23143 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23146 \begin_layout Plain Layout
23147 \begin_inset Formula $\mbox{€}$
23157 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23160 \begin_layout Plain Layout
23166 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23169 \begin_layout Plain Layout
23177 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23180 \begin_layout Plain Layout
23184 \begin_layout Plain Layout
23206 \begin_layout Standard
23210 \begin_layout Plain Layout
23220 \begin_inset Note Note
23223 \begin_layout Plain Layout
23224 The following will be displayed when the LaTeX-package
23236 \begin_layout Standard
23237 You need to install the LaTeX-package
23241 to see the rest of this subsection in the output.
23244 \begin_layout Standard
23248 \begin_layout Plain Layout
23260 \begin_layout Section
23262 \begin_inset CommandInset label
23264 name "sec:Relations"
23269 \begin_inset Index idx
23272 \begin_layout Plain Layout
23279 \begin_inset Index idx
23282 \begin_layout Plain Layout
23287 \begin_layout Plain Layout
23298 \begin_layout Plain Layout
23313 \begin_layout Standard
23314 All relations can also be inserted via the toolbar button
23315 \begin_inset Graphics
23316 filename ../images/math/leq.png
23324 \begin_layout Standard
23325 \begin_inset space \hfill{}
23329 \begin_inset Tabular
23330 <lyxtabular version="3" rows="17" columns="2">
23331 <features tabularvalignment="middle">
23332 <column alignment="center" valignment="top" width="0pt">
23333 <column alignment="center" valignment="top" width="0pt">
23335 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23338 \begin_layout Plain Layout
23344 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23347 \begin_layout Plain Layout
23355 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23358 \begin_layout Plain Layout
23364 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23367 \begin_layout Plain Layout
23368 \begin_inset Formula $<$
23378 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23381 \begin_layout Plain Layout
23389 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23392 \begin_layout Plain Layout
23393 \begin_inset Formula $\le$
23403 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23406 \begin_layout Plain Layout
23414 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23417 \begin_layout Plain Layout
23418 \begin_inset Formula $\ll$
23428 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23431 \begin_layout Plain Layout
23439 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23442 \begin_layout Plain Layout
23443 \begin_inset Formula $\prec$
23453 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23456 \begin_layout Plain Layout
23464 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23467 \begin_layout Plain Layout
23468 \begin_inset Formula $\preceq$
23478 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23481 \begin_layout Plain Layout
23489 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23492 \begin_layout Plain Layout
23493 \begin_inset Formula $\subset$
23503 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23506 \begin_layout Plain Layout
23514 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23517 \begin_layout Plain Layout
23518 \begin_inset Formula $\subseteq$
23528 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23531 \begin_layout Plain Layout
23539 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23542 \begin_layout Plain Layout
23543 \begin_inset Formula $\sqsubseteq$
23553 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23556 \begin_layout Plain Layout
23564 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23567 \begin_layout Plain Layout
23568 \begin_inset Formula $\in$
23578 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23581 \begin_layout Plain Layout
23589 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23592 \begin_layout Plain Layout
23593 \begin_inset Formula $\vdash$
23603 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23606 \begin_layout Plain Layout
23614 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23617 \begin_layout Plain Layout
23618 \begin_inset Formula $\smile$
23628 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23631 \begin_layout Plain Layout
23639 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23642 \begin_layout Plain Layout
23643 \begin_inset Formula $\lhd$
23653 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23656 \begin_layout Plain Layout
23664 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23667 \begin_layout Plain Layout
23668 \begin_inset Formula $\unlhd$
23678 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23681 \begin_layout Plain Layout
23689 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23692 \begin_layout Plain Layout
23693 \begin_inset Formula $\gtrless$
23703 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23706 \begin_layout Plain Layout
23714 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23717 \begin_layout Plain Layout
23718 \begin_inset Formula $\mid$
23728 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23731 \begin_layout Plain Layout
23739 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23742 \begin_layout Plain Layout
23743 \begin_inset Formula $\nmid$
23757 \begin_inset space \hfill{}
23761 \begin_inset Tabular
23762 <lyxtabular version="3" rows="17" columns="2">
23763 <features tabularvalignment="middle">
23764 <column alignment="center" valignment="top" width="0pt">
23765 <column alignment="center" valignment="top" width="0pt">
23767 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23770 \begin_layout Plain Layout
23776 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23779 \begin_layout Plain Layout
23787 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23790 \begin_layout Plain Layout
23796 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23799 \begin_layout Plain Layout
23800 \begin_inset Formula $=$
23810 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23813 \begin_layout Plain Layout
23821 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23824 \begin_layout Plain Layout
23825 \begin_inset Formula $\not=$
23835 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23838 \begin_layout Plain Layout
23846 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23849 \begin_layout Plain Layout
23850 \begin_inset Formula $\equiv$
23860 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23863 \begin_layout Plain Layout
23871 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23874 \begin_layout Plain Layout
23875 \begin_inset Formula $\sim$
23885 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23888 \begin_layout Plain Layout
23896 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23899 \begin_layout Plain Layout
23900 \begin_inset Formula $\simeq$
23910 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23913 \begin_layout Plain Layout
23921 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23924 \begin_layout Plain Layout
23925 \begin_inset Formula $\approx$
23935 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23938 \begin_layout Plain Layout
23946 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23949 \begin_layout Plain Layout
23950 \begin_inset Formula $\cong$
23960 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23963 \begin_layout Plain Layout
23971 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23974 \begin_layout Plain Layout
23975 \begin_inset Formula $\bowtie$
23985 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23988 \begin_layout Plain Layout
23996 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23999 \begin_layout Plain Layout
24000 \begin_inset Formula $\notin$
24010 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24013 \begin_layout Plain Layout
24021 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24024 \begin_layout Plain Layout
24025 \begin_inset Formula $\perp$
24035 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24038 \begin_layout Plain Layout
24046 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24049 \begin_layout Plain Layout
24050 \begin_inset Formula $\propto$
24060 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24063 \begin_layout Plain Layout
24071 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24074 \begin_layout Plain Layout
24075 \begin_inset Formula $\asymp$
24085 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24088 \begin_layout Plain Layout
24096 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24099 \begin_layout Plain Layout
24100 \begin_inset Formula $\doteq$
24110 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24113 \begin_layout Plain Layout
24121 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24124 \begin_layout Plain Layout
24125 \begin_inset Formula $\circeq$
24135 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24138 \begin_layout Plain Layout
24146 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24149 \begin_layout Plain Layout
24150 \begin_inset Formula $\models$
24160 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24163 \begin_layout Plain Layout
24171 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24174 \begin_layout Plain Layout
24175 \begin_inset Formula $\widehat{=}$
24189 \begin_inset space \hfill{}
24193 \begin_inset Tabular
24194 <lyxtabular version="3" rows="17" columns="2">
24195 <features tabularvalignment="middle">
24196 <column alignment="center" valignment="top" width="0pt">
24197 <column alignment="center" valignment="top" width="0pt">
24199 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24202 \begin_layout Plain Layout
24208 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24211 \begin_layout Plain Layout
24219 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24222 \begin_layout Plain Layout
24228 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24231 \begin_layout Plain Layout
24232 \begin_inset Formula $>$
24242 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24245 \begin_layout Plain Layout
24253 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24256 \begin_layout Plain Layout
24257 \begin_inset Formula $\ge$
24267 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24270 \begin_layout Plain Layout
24278 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24281 \begin_layout Plain Layout
24282 \begin_inset Formula $\gg$
24292 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24295 \begin_layout Plain Layout
24303 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24306 \begin_layout Plain Layout
24307 \begin_inset Formula $\succ$
24317 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24320 \begin_layout Plain Layout
24328 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24331 \begin_layout Plain Layout
24332 \begin_inset Formula $\succeq$
24342 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24345 \begin_layout Plain Layout
24353 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24356 \begin_layout Plain Layout
24357 \begin_inset Formula $\supset$
24367 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24370 \begin_layout Plain Layout
24378 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24381 \begin_layout Plain Layout
24382 \begin_inset Formula $\supseteq$
24392 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24395 \begin_layout Plain Layout
24403 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24406 \begin_layout Plain Layout
24407 \begin_inset Formula $\sqsupseteq$
24417 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24420 \begin_layout Plain Layout
24428 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24431 \begin_layout Plain Layout
24432 \begin_inset Formula $\ni$
24442 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24445 \begin_layout Plain Layout
24453 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24456 \begin_layout Plain Layout
24457 \begin_inset Formula $\dashv$
24467 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24470 \begin_layout Plain Layout
24478 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24481 \begin_layout Plain Layout
24482 \begin_inset Formula $\frown$
24492 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24495 \begin_layout Plain Layout
24503 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24506 \begin_layout Plain Layout
24507 \begin_inset Formula $\rhd$
24517 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24520 \begin_layout Plain Layout
24528 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24531 \begin_layout Plain Layout
24532 \begin_inset Formula $\unrhd$
24542 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24545 \begin_layout Plain Layout
24553 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24556 \begin_layout Plain Layout
24557 \begin_inset Formula $\lessgtr$
24567 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24570 \begin_layout Plain Layout
24578 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24581 \begin_layout Plain Layout
24582 \begin_inset Formula $\parallel$
24592 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24595 \begin_layout Plain Layout
24603 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24606 \begin_layout Plain Layout
24607 \begin_inset Formula $\nparallel$
24621 \begin_inset space \hfill{}
24627 \begin_layout Standard
24628 \begin_inset VSpace medskip
24643 are bigger than the equal looking operators
24658 \begin_layout Standard
24659 Relations are, in contrary to symbols, always surrounded by space.
24662 \begin_layout Standard
24663 Relations with labels can be created with the command
24670 \begin_inset Index idx
24673 \begin_layout Plain Layout
24684 \begin_layout Standard
24686 \begin_inset Tabular
24687 <lyxtabular version="3" rows="2" columns="2">
24688 <features tabularvalignment="middle">
24689 <column alignment="center" valignment="top" width="0">
24690 <column alignment="center" valignment="top" width="0">
24692 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24695 \begin_layout Plain Layout
24701 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24704 \begin_layout Plain Layout
24706 \begin_inset Note Note
24709 \begin_layout Plain Layout
24716 is only used as spacer.
24728 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24731 \begin_layout Plain Layout
24738 \begin_layout Plain Layout
24755 \begin_layout Plain Layout
24765 \begin_inset Formula $\downarrow$
24774 \begin_layout Plain Layout
24787 \begin_layout Plain Layout
24801 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24804 \begin_layout Plain Layout
24805 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
24821 \begin_layout Section
24825 \begin_layout Subsection
24826 Predefined Functions
24827 \begin_inset CommandInset label
24829 name "sub:Predefined-Functions"
24834 \begin_inset Index idx
24837 \begin_layout Plain Layout
24838 Functions ! predefined
24846 \begin_layout Standard
24847 In general, variables are set
24851 in mathematical expressions, but not function names, because
24852 \begin_inset Formula $sin$
24855 could be misunderstood as
24856 \begin_inset Formula $s\cdot i\cdot n$
24860 Therefore there are predefined functions, that are additionally a bit separated
24862 They are inserted as commands starting with a backslash before their name.
24865 \begin_layout Standard
24867 \begin_inset Tabular
24868 <lyxtabular version="3" rows="2" columns="4">
24869 <features tabularvalignment="middle">
24870 <column alignment="center" valignment="top" width="0pt">
24871 <column alignment="center" valignment="top" width="0pt">
24872 <column alignment="center" valignment="top" width="0pt">
24873 <column alignment="center" valignment="top" width="0pt">
24875 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24878 \begin_layout Plain Layout
24884 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24887 \begin_layout Plain Layout
24893 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24896 \begin_layout Plain Layout
24902 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24905 \begin_layout Plain Layout
24913 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24916 \begin_layout Plain Layout
24922 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24925 \begin_layout Plain Layout
24926 \begin_inset Formula $Asin(x)+B$
24934 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24937 \begin_layout Plain Layout
24945 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24948 \begin_layout Plain Layout
24949 \begin_inset Formula $A\sin(x)+B$
24965 \begin_layout Standard
24966 The following functions are predefined:
24969 \begin_layout Standard
24970 \begin_inset VSpace -2mm
24976 \begin_layout Standard
24978 \begin_inset Tabular
24979 <lyxtabular version="3" rows="9" columns="4">
24980 <features tabularvalignment="middle">
24981 <column alignment="center" valignment="top" width="0pt">
24982 <column alignment="center" valignment="top" width="0pt">
24983 <column alignment="center" valignment="top" width="0pt">
24984 <column alignment="center" valignment="top" width="0pt">
24986 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24989 \begin_layout Plain Layout
24995 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24998 \begin_layout Plain Layout
25004 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25007 \begin_layout Plain Layout
25013 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25016 \begin_layout Plain Layout
25024 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25027 \begin_layout Plain Layout
25035 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25038 \begin_layout Plain Layout
25046 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25049 \begin_layout Plain Layout
25057 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25060 \begin_layout Plain Layout
25070 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25073 \begin_layout Plain Layout
25081 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25084 \begin_layout Plain Layout
25092 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25095 \begin_layout Plain Layout
25103 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25106 \begin_layout Plain Layout
25116 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25119 \begin_layout Plain Layout
25127 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25130 \begin_layout Plain Layout
25138 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25141 \begin_layout Plain Layout
25149 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25152 \begin_layout Plain Layout
25162 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25165 \begin_layout Plain Layout
25173 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25176 \begin_layout Plain Layout
25184 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25187 \begin_layout Plain Layout
25195 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25198 \begin_layout Plain Layout
25208 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25211 \begin_layout Plain Layout
25219 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25222 \begin_layout Plain Layout
25230 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25233 \begin_layout Plain Layout
25241 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25244 \begin_layout Plain Layout
25254 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25257 \begin_layout Plain Layout
25265 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25268 \begin_layout Plain Layout
25276 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25279 \begin_layout Plain Layout
25287 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25290 \begin_layout Plain Layout
25300 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25303 \begin_layout Plain Layout
25311 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25314 \begin_layout Plain Layout
25322 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25325 \begin_layout Plain Layout
25333 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25336 \begin_layout Plain Layout
25346 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25349 \begin_layout Plain Layout
25357 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25360 \begin_layout Plain Layout
25368 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25371 \begin_layout Plain Layout
25379 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25382 \begin_layout Plain Layout
25398 \begin_layout Standard
25399 They can also be inserted with the math toolbar button
25400 \begin_inset Graphics
25401 filename ../images/math/functions.png
25409 \begin_layout Subsection
25410 Self-defined Functions
25411 \begin_inset Index idx
25414 \begin_layout Plain Layout
25415 Functions ! self-defined
25423 \begin_layout Standard
25424 To use a function that is not predefined, like for example the sign function
25425 sgn(x), there are two possibilities:
25428 \begin_layout Itemize
25429 Define the function by inserting the following line to the LaTeX-preamble
25433 \begin_layout Plain Layout
25438 DeclareMathOperator
25441 \begin_inset CommandInset ref
25443 reference "sub:Self-defined-Operators"
25453 \begin_inset Newline newline
25457 \begin_inset VSpace -3mm
25461 \begin_inset Newline newline
25468 DeclareMathOperator{
25473 \begin_inset Index idx
25476 \begin_layout Plain Layout
25481 DeclareMathOperator
25487 \begin_inset Newline newline
25491 \begin_inset VSpace -2mm
25495 \begin_inset Newline newline
25498 Now the new defined function can be called with the command
25507 \begin_layout Itemize
25508 Write the formula as usual, mark the formula name, in our example the letters
25513 , and change it to mathematical text.
25514 At last a space is inserted between prefactor and function.
25517 \begin_layout Standard
25518 The result is the same with both methods as with a predefined function
25522 \begin_layout Plain Layout
25523 In LyX self-defined functions are displayed red, predefined ones black.
25531 \begin_layout Standard
25533 \begin_inset Tabular
25534 <lyxtabular version="3" rows="3" columns="2">
25535 <features tabularvalignment="middle">
25536 <column alignment="center" valignment="top" width="0pt">
25537 <column alignment="center" valignment="top" width="0pt">
25539 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25542 \begin_layout Plain Layout
25548 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25551 \begin_layout Plain Layout
25559 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25562 \begin_layout Plain Layout
25570 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25573 \begin_layout Plain Layout
25574 \begin_inset Formula $A\sgn(x)+B$
25584 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25587 \begin_layout Plain Layout
25591 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
25599 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25602 \begin_layout Plain Layout
25603 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
25619 \begin_layout Standard
25620 The first method is more suitable when the self-defined function should
25621 be used several times.
25624 \begin_layout Subsection
25626 \begin_inset Index idx
25629 \begin_layout Plain Layout
25638 \begin_layout Standard
25639 For limits there are defined besides
25646 \begin_inset Index idx
25649 \begin_layout Plain Layout
25669 furthermore the following functions:
25672 \begin_layout Standard
25674 \begin_inset Tabular
25675 <lyxtabular version="3" rows="5" columns="2">
25676 <features tabularvalignment="middle">
25677 <column alignment="center" valignment="top" width="0">
25678 <column alignment="center" valignment="top" width="0">
25680 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25683 \begin_layout Plain Layout
25689 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25692 \begin_layout Plain Layout
25694 \begin_inset Note Note
25697 \begin_layout Plain Layout
25704 is only used as spacer.
25716 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25719 \begin_layout Plain Layout
25727 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25730 \begin_layout Plain Layout
25731 \begin_inset Formula $\varliminf$
25741 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25744 \begin_layout Plain Layout
25752 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25755 \begin_layout Plain Layout
25756 \begin_inset Formula $\varlimsup$
25766 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25769 \begin_layout Plain Layout
25777 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25780 \begin_layout Plain Layout
25781 \begin_inset Formula $\varprojlim$
25791 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25794 \begin_layout Plain Layout
25802 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25805 \begin_layout Plain Layout
25806 \begin_inset Formula $\varinjlim$
25810 \begin_inset Formula $\raisebox{-2.5mm}{}$
25826 \begin_layout Standard
25827 \begin_inset VSpace medskip
25830 The limit is created by inserting a subscript.
25831 It is set right beside the function in an inline formula:
25834 \begin_layout Standard
25836 \begin_inset Tabular
25837 <lyxtabular version="3" rows="2" columns="2">
25838 <features tabularvalignment="middle">
25839 <column alignment="center" valignment="top" width="0pt">
25840 <column alignment="center" valignment="top" width="0pt">
25842 <cell alignment="center" valignment="top" usebox="none">
25845 \begin_layout Plain Layout
25851 <cell alignment="center" valignment="top" usebox="none">
25854 \begin_layout Plain Layout
25855 \begin_inset space \hspace{}
25860 \begin_inset Note Note
25863 \begin_layout Plain Layout
25870 are used here as spacer.
25882 <cell alignment="center" valignment="top" usebox="none">
25885 \begin_layout Plain Layout
25894 \begin_layout Plain Layout
25907 \begin_layout Plain Layout
25921 <cell alignment="center" valignment="top" usebox="none">
25924 \begin_layout Plain Layout
25925 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
25941 \begin_layout Standard
25942 In a displayed formula the limit is set below the formula, as usual:
25943 \begin_inset Formula \[
25952 \begin_layout Subsection
25954 \begin_inset Index idx
25957 \begin_layout Plain Layout
25958 Functions ! modulo-
25966 \begin_layout Standard
25967 The modulo-function is special, because it exists in four variants.
25970 \begin_layout Standard
25971 The variants in a displayed formula:
25972 \begin_inset Formula \begin{align*}
25973 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25974 \mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
25975 \mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
25976 \mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
25977 \mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b
25985 \begin_layout Standard
25986 In an inline formula less space is set before the function names for all
25990 \begin_layout Section
25992 \begin_inset Index idx
25995 \begin_layout Plain Layout
26004 \begin_layout Subsection
26005 Special Characters in Mathematical Text
26008 \begin_layout Standard
26009 The following commands can only be used in mathematical text or in TeX-mode:
26012 \begin_layout Standard
26013 \begin_inset space \hfill{}
26017 \begin_inset Tabular
26018 <lyxtabular version="3" rows="8" columns="2">
26019 <features tabularvalignment="middle">
26020 <column alignment="block" valignment="top" width="0">
26021 <column alignment="block" valignment="top" width="0">
26023 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26026 \begin_layout Plain Layout
26032 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26035 \begin_layout Plain Layout
26043 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26046 \begin_layout Plain Layout
26054 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26057 \begin_layout Plain Layout
26058 \begin_inset Formula $\textrm{œ}$
26068 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26071 \begin_layout Plain Layout
26079 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26082 \begin_layout Plain Layout
26083 \begin_inset Formula $\textrm{Œ}$
26093 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26096 \begin_layout Plain Layout
26104 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26107 \begin_layout Plain Layout
26108 \begin_inset Formula $\textrm{æ}$
26118 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26121 \begin_layout Plain Layout
26129 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26132 \begin_layout Plain Layout
26133 \begin_inset Formula $\textrm{Æ}$
26143 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26146 \begin_layout Plain Layout
26154 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26157 \begin_layout Plain Layout
26158 \begin_inset Formula $\textrm{\aa}$
26168 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26171 \begin_layout Plain Layout
26175 \begin_inset Index idx
26178 \begin_layout Plain Layout
26185 \begin_layout Plain Layout
26206 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26209 \begin_layout Plain Layout
26210 \begin_inset Formula $\textrm{Å}$
26220 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26223 \begin_layout Plain Layout
26231 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26234 \begin_layout Plain Layout
26235 \begin_inset Formula $\textrm{ı}$
26249 \begin_inset space \hfill{}
26253 \begin_inset Tabular
26254 <lyxtabular version="3" rows="8" columns="2">
26255 <features tabularvalignment="middle">
26256 <column alignment="block" valignment="top" width="0">
26257 <column alignment="center" valignment="top" width="0">
26259 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26262 \begin_layout Plain Layout
26264 \begin_inset Note Note
26267 \begin_layout Plain Layout
26269 \begin_inset space \thinspace{}
26272 mm is used for separation, because otherwise the output will be ¡ and ¿
26283 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26286 \begin_layout Plain Layout
26294 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26297 \begin_layout Plain Layout
26305 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26308 \begin_layout Plain Layout
26309 \begin_inset Formula $\textrm{ø}$
26319 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26322 \begin_layout Plain Layout
26330 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26333 \begin_layout Plain Layout
26334 \begin_inset Formula $\textrm{Ø}$
26344 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26347 \begin_layout Plain Layout
26355 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26358 \begin_layout Plain Layout
26359 \begin_inset Formula $\textrm{ł}$
26369 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26372 \begin_layout Plain Layout
26380 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26383 \begin_layout Plain Layout
26384 \begin_inset Formula $\textrm{Ł}$
26394 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26397 \begin_layout Plain Layout
26399 \begin_inset space \hspace{}
26407 \begin_layout Plain Layout
26421 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26424 \begin_layout Plain Layout
26425 \begin_inset Formula $\textrm{!`}$
26435 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26438 \begin_layout Plain Layout
26440 \begin_inset space \hspace{}
26448 \begin_layout Plain Layout
26462 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26465 \begin_layout Plain Layout
26466 \begin_inset Formula $\textrm{?`}$
26476 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26479 \begin_layout Plain Layout
26487 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26490 \begin_layout Plain Layout
26491 \begin_inset Formula $\textrm{ȷ}$
26505 \begin_inset space \hfill{}
26511 \begin_layout Standard
26513 \begin_inset Formula $\textrm{\textrm{Å}}$
26517 \begin_inset Formula $\textrm{\textrm{Ø}}$
26520 can also be inserted via the math toolbar button
26521 \begin_inset Graphics
26522 filename ../images/math/digamma.png
26530 \begin_layout Standard
26531 An exception are the commands
26534 \begin_inset space \hspace{}
26543 \begin_inset space \hspace{}
26549 , because they can be inserted in LyX directly to text.
26552 \begin_layout Subsection
26554 \begin_inset CommandInset label
26556 name "sub:Accents-in-Text"
26561 \begin_inset Index idx
26564 \begin_layout Plain Layout
26573 \begin_layout Standard
26574 With the following commands all letters can be accented.
26575 The commands must be inserted in TeX-mode.
26578 \begin_layout Standard
26579 \begin_inset space \hfill{}
26583 \begin_inset Tabular
26584 <lyxtabular version="3" rows="8" columns="2">
26585 <features tabularvalignment="middle">
26586 <column alignment="block" valignment="top" width="0">
26587 <column alignment="block" valignment="top" width="0">
26589 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26592 \begin_layout Plain Layout
26598 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26601 \begin_layout Plain Layout
26609 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26612 \begin_layout Plain Layout
26616 \begin_inset Quotes grd
26624 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26627 \begin_layout Plain Layout
26631 \begin_layout Plain Layout
26647 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26650 \begin_layout Plain Layout
26658 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26661 \begin_layout Plain Layout
26665 \begin_layout Plain Layout
26681 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26684 \begin_layout Plain Layout
26691 \begin_layout Plain Layout
26705 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26708 \begin_layout Plain Layout
26712 \begin_layout Plain Layout
26728 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26731 \begin_layout Plain Layout
26739 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26742 \begin_layout Plain Layout
26746 \begin_layout Plain Layout
26762 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26765 \begin_layout Plain Layout
26772 \begin_layout Plain Layout
26786 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26789 \begin_layout Plain Layout
26793 \begin_layout Plain Layout
26809 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26812 \begin_layout Plain Layout
26819 \begin_layout Plain Layout
26833 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26836 \begin_layout Plain Layout
26840 \begin_layout Plain Layout
26856 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26859 \begin_layout Plain Layout
26866 \begin_layout Plain Layout
26880 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26883 \begin_layout Plain Layout
26887 \begin_layout Plain Layout
26907 \begin_inset space \hfill{}
26911 \begin_inset Tabular
26912 <lyxtabular version="3" rows="8" columns="2">
26913 <features tabularvalignment="middle">
26914 <column alignment="block" valignment="top" width="0">
26915 <column alignment="center" valignment="top" width="0">
26917 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26920 \begin_layout Plain Layout
26926 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26929 \begin_layout Plain Layout
26937 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26940 \begin_layout Plain Layout
26947 \begin_layout Plain Layout
26961 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26964 \begin_layout Plain Layout
26968 \begin_layout Plain Layout
26984 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26987 \begin_layout Plain Layout
26995 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26998 \begin_layout Plain Layout
27002 \begin_layout Plain Layout
27018 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27021 \begin_layout Plain Layout
27025 \begin_inset Index idx
27028 \begin_layout Plain Layout
27039 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27042 \begin_layout Plain Layout
27046 \begin_layout Plain Layout
27062 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27065 \begin_layout Plain Layout
27073 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27076 \begin_layout Plain Layout
27080 \begin_layout Plain Layout
27096 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27099 \begin_layout Plain Layout
27106 \begin_layout Plain Layout
27120 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27123 \begin_layout Plain Layout
27127 \begin_layout Plain Layout
27143 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27146 \begin_layout Plain Layout
27153 \begin_layout Plain Layout
27167 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27170 \begin_layout Plain Layout
27174 \begin_layout Plain Layout
27190 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27193 \begin_layout Plain Layout
27200 \begin_layout Plain Layout
27214 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27217 \begin_layout Plain Layout
27221 \begin_layout Plain Layout
27241 \begin_inset space \hfill{}
27247 \begin_layout Standard
27248 \begin_inset VSpace medskip
27257 also two different characters can be accented.
27266 \begin_layout Plain Layout
27281 \begin_layout Plain Layout
27293 \begin_layout Standard
27306 can in combination with vowels directly be inserted with the keyboard without
27308 The same applies for the tilde
27312 \begin_layout Plain Layout
27313 This only applies for keyboards where the tilde is defined as accent.
27322 in combination with
27337 \begin_layout Standard
27380 and accents that are inserted directly with the keyboard are also available
27381 in mathematical text.
27382 For the other accents there are special math commands to be used in formulas,
27384 \begin_inset CommandInset ref
27386 reference "sub:Accents-for-one"
27393 \begin_layout Standard
27394 \begin_inset VSpace bigskip
27397 Furthermore, with the command
27404 \begin_inset Index idx
27407 \begin_layout Plain Layout
27415 all numbers and letters can be set into a circle, quasi accented with a
27416 circle, similar to the copyright symbol.
27419 \begin_layout Standard
27421 \begin_inset Tabular
27422 <lyxtabular version="3" rows="3" columns="2">
27423 <features tabularvalignment="middle">
27424 <column alignment="center" valignment="top" width="0">
27425 <column alignment="center" valignment="top" width="0">
27427 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27430 \begin_layout Plain Layout
27436 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27439 \begin_layout Plain Layout
27441 \begin_inset Note Note
27444 \begin_layout Plain Layout
27451 is only used as spacer.
27463 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27466 \begin_layout Plain Layout
27474 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27477 \begin_layout Plain Layout
27481 \begin_layout Plain Layout
27497 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27500 \begin_layout Plain Layout
27511 raisebox{-1.5pt}{W}}
27516 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27519 \begin_layout Plain Layout
27520 \begin_inset Formula $\raisebox{4.5mm}{}$
27527 \begin_layout Plain Layout
27545 \begin_inset Formula $\raisebox{-2mm}{}$
27561 \begin_layout Standard
27562 One has to take care that the character fits in the circle.
27573 \begin_layout Plain Layout
27575 \begin_inset CommandInset ref
27577 reference "sub:Font-Sizes"
27586 specifies thereby the size of the circle.
27597 \begin_layout Plain Layout
27599 \begin_inset CommandInset ref
27601 reference "sub:Boxes-without-Frame"
27610 the character can be centered.
27613 \begin_layout Subsection
27615 \begin_inset Index idx
27618 \begin_layout Plain Layout
27627 \begin_layout Standard
27628 Minuscule numbers are created with the command
27635 \begin_inset Index idx
27638 \begin_layout Plain Layout
27647 The command can be used in formulas and in TeX-mode.
27648 The command scheme is:
27651 \begin_layout Standard
27656 oldstylenums{number}
27659 \begin_layout Standard
27664 oldstylenums{0123456789
27667 \begin_inset Formula $\oldstylenums{0123456789}$
27673 \begin_layout Subsection
27674 Miscellaneous special Characters
27675 \begin_inset CommandInset label
27677 name "sub:Miscellaneous-special-Characters"
27682 \begin_inset Index idx
27685 \begin_layout Plain Layout
27686 Special characters ! miscellaneous
27694 \begin_layout Standard
27695 The following characters can only be inserted to formulas by using commands:
27698 \begin_layout Standard
27700 \begin_inset Tabular
27701 <lyxtabular version="3" rows="4" columns="2">
27702 <features tabularvalignment="middle">
27703 <column alignment="center" valignment="top" width="0">
27704 <column alignment="center" valignment="top" width="0">
27706 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27709 \begin_layout Plain Layout
27715 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27718 \begin_layout Plain Layout
27726 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27729 \begin_layout Plain Layout
27736 \begin_layout Plain Layout
27750 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27753 \begin_layout Plain Layout
27754 \begin_inset Formula $\mathcircumflex$
27764 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27767 \begin_layout Plain Layout
27775 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27778 \begin_layout Plain Layout
27779 \begin_inset Formula $\_$
27789 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27792 \begin_layout Plain Layout
27797 \begin_layout Plain Layout
27809 \begin_inset Index idx
27812 \begin_layout Plain Layout
27825 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27828 \begin_layout Plain Layout
27829 \begin_inset Formula $^{\circ}$
27845 \begin_layout Standard
27846 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
27847 contains the following line
27851 \begin_layout Plain Layout
27852 More about this is described in
27853 \begin_inset CommandInset ref
27855 reference "sub:Text-Characters-in"
27867 \begin_layout Standard
27872 DeclareInputtext{176}{
27885 \begin_layout Section
27887 \begin_inset CommandInset label
27889 name "sec:Formula-Styles"
27894 \begin_inset Index idx
27897 \begin_layout Plain Layout
27906 \begin_layout Itemize
27907 There are two different alignment styles:
27911 \begin_layout Description
27912 Centered is the predefined standard
27915 \begin_layout Description
27916 Indented for this the option
27920 must be inserted in the menu
27922 Document\SpecialChar \menuseparator
27928 \begin_inset space ~
27934 \begin_layout Standard
27939 is used, the indentation can be adjusted with the length
27946 \begin_inset Index idx
27949 \begin_layout Plain Layout
27958 Should the distance be 15
27959 \begin_inset space \thinspace{}
27962 mm, the following command line is inserted in the LaTeX-preamble
27965 \begin_layout Standard
27975 \begin_layout Standard
27976 When no length is specified, the predefined value of 30
27977 \begin_inset space \thinspace{}
27984 \begin_layout Itemize
27985 And two different numbering styles:
27989 \begin_layout Description
27990 Right is the predefined standard
27993 \begin_layout Description
27994 Left for this the option
27998 must be inserted in the menu
28000 Document\SpecialChar \menuseparator
28006 \begin_inset space ~
28013 \begin_layout Standard
28022 can also be used together.
28023 In this case both options are inserted, separated by a comma.
28026 \begin_layout Standard
28027 The chosen styles are used for all displayed formulas of the document.
28028 When both, centered and indented formulas should be created in a document,
28034 The indented formulas are then set in a flalign environment, see
28035 \begin_inset CommandInset ref
28037 reference "sub:Flalign-Environment"
28044 \begin_layout Section
28046 \begin_inset CommandInset label
28048 name "sec:Multiline-Formulas"
28053 \begin_inset Index idx
28056 \begin_layout Plain Layout
28057 Formula ! multiline
28065 \begin_layout Subsection
28069 \begin_layout Standard
28070 In LyX multiline formulas are created by pressing
28075 arg "newline-insert newline"
28081 This creates either an
28083 eqnarray environment
28085 that is described in
28086 \begin_inset CommandInset ref
28088 reference "sub:Eqnarray-Environment"
28092 or, when the option
28094 Use AMS math package
28096 in the document settings is selected, an
28100 that is described in
28101 \begin_inset CommandInset ref
28103 reference "sub:Standard-align-Environment"
28110 \begin_layout Standard
28111 There are other multiline formula environments that can be created via the
28114 Insert\SpecialChar \menuseparator
28118 These environments are described in the following sections.
28121 \begin_layout Standard
28122 In all multiline formula environments a new line is created by pressing
28126 arg "newline-insert newline"
28130 To add or delete lines, the math toolbar buttons
28131 \begin_inset Graphics
28132 filename ../images/tabular-feature_append-row.png
28138 \begin_inset Graphics
28139 filename ../images/tabular-feature_delete-row.png
28144 , respectively, or the menu
28146 Edit\SpecialChar \menuseparator
28152 \begin_layout Subsubsection
28154 \begin_inset CommandInset label
28156 name "sub:Line-Separation"
28161 \begin_inset Index idx
28164 \begin_layout Plain Layout
28165 Formula ! multiline ! Line separation
28173 \begin_layout Standard
28174 There is sometimes not enough space in multiline formulas between the lines:
28175 \begin_inset Formula \begin{eqnarray*}
28176 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}\\
28177 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
28185 \begin_layout Standard
28186 In LaTeX additional line space is specified as optional argument of the
28188 This is not yet possible in LyX
28192 \begin_layout Plain Layout
28194 \begin_inset CommandInset href
28196 name "LyX-bug #1505"
28197 target "http://www.lyx.org/trac/ticket/1505"
28206 , therefore the whole formula must be inserted in TeX-mode.
28207 To add in our example space, the command
28215 is inserted at the end of the first line.
28220 \begin_layout Plain Layout
28227 \begin_layout Plain Layout
28229 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
28232 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
28239 \begin_layout Plain Layout
28243 left(B^{2}+x_{0}^{2}
28251 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
28256 \begin_layout Plain Layout
28268 \begin_layout Standard
28269 \begin_inset VSpace bigskip
28272 To set the line separation for all lines in a formula, the length
28279 \begin_inset Index idx
28282 \begin_layout Plain Layout
28292 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
28303 \begin_inset space \thinspace{}
28308 \begin_inset space \thinspace{}
28311 mm additional line separation as in the previous example, the command
28314 \begin_layout Standard
28324 \begin_layout Standard
28325 is inserted in TeX-mode before the formula.
28326 This requires that the LaTeX-package
28334 \begin_layout Plain Layout
28339 is part of every LaTeX standard installation.
28345 \begin_inset Index idx
28348 \begin_layout Plain Layout
28354 was loaded in LaTeX-preamble with the line
28357 \begin_layout Standard
28365 \begin_layout Standard
28370 \begin_layout Plain Layout
28382 \begin_inset Formula \begin{eqnarray*}
28383 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}\\
28384 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
28392 \begin_layout Standard
28396 \begin_layout Plain Layout
28407 To get back to the predefined distance,
28413 is set to the value 3
28414 \begin_inset space \thinspace{}
28420 \begin_layout Subsubsection
28422 \begin_inset CommandInset label
28424 name "sub:Column-Separation"
28429 \begin_inset Index idx
28432 \begin_layout Plain Layout
28433 Formula ! multiline ! Column separation
28441 \begin_layout Standard
28442 Multiline formulas form a matrix.
28443 A formula in the eqnarray environment is for example a matrix with three
28445 By changing the column separation in this environment, the space beside
28446 the relation sign can be changed.
28449 \begin_layout Standard
28450 The column separation is specified with the length
28457 \begin_inset Index idx
28460 \begin_layout Plain Layout
28469 \begin_inset Newline newline
28472 column separation = 2
28473 \begin_inset space \thinspace{}
28483 \begin_inset Newline newline
28489 \begin_layout Standard
28499 \begin_layout Standard
28500 inserted in TeX-mode, sets for all following formulas a column separation
28502 \begin_inset space \thinspace{}
28506 To get back to the predefined distance,
28513 \begin_inset space \thinspace{}
28519 \begin_layout Standard
28521 \begin_inset space \thinspace{}
28524 cm column separation:
28528 \begin_layout Plain Layout
28540 \begin_inset Formula \begin{eqnarray*}
28547 A formula with the predefined column separation for matrices of 10
28548 \begin_inset space \thinspace{}
28555 \begin_layout Plain Layout
28567 \begin_inset Formula \begin{eqnarray*}
28577 \begin_layout Subsubsection
28579 \begin_inset Index idx
28582 \begin_layout Plain Layout
28591 \begin_layout Standard
28592 Long formulas can be typeset using these methods:
28595 \begin_layout Itemize
28596 When one side of the equation is much shorther than the line width, this
28597 one is chosen for the left side and the right side is typeset over two
28599 \begin_inset Formula \begin{eqnarray}
28600 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 \\
28601 & & -\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}
28606 The minus sign at the beginning of the second line does normally not appear
28607 as operator because it is the first character of the line.
28608 Thus it would not be surrounded by space and could not be distinguished
28609 from the fraction bar.
28611 \begin_inset space \thinspace{}
28614 pt space was inserted behind the minus sign with the command
28624 \begin_layout Plain Layout
28632 \begin_inset CommandInset ref
28634 reference "sub:Variable-Space"
28644 \begin_inset Index idx
28647 \begin_layout Plain Layout
28658 \begin_layout Itemize
28659 When both sides of the equation are too long, the command
28666 \begin_inset Index idx
28669 \begin_layout Plain Layout
28678 It is inserted to the first column of the first line and effects that all
28679 further insertions overwrite the following columns:
28680 \begin_inset Formula \begin{eqnarray}
28681 \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 \\
28682 & & -\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 \\
28683 & & =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}
28688 After the insertion of
28694 , the cursor is in a purple box that is a bit shifted to the left from the
28696 In this the formula is inserted.
28697 \begin_inset Newline newline
28700 The content of the further lines is inserted to the second or another formula
28702 The greater the column number where it was inserted, the larger the indentation.
28703 \begin_inset VSpace medskip
28707 \begin_inset Newline newline
28711 \begin_inset Note Greyedout
28714 \begin_layout Plain Layout
28715 Note the following when using
28724 \begin_layout Itemize
28725 The formula doesn't use the full page width.
28727 \begin_inset space \thinspace{}
28731 \begin_inset space \space{}
28735 \begin_inset Formula $-B^{2}$
28738 is added to the first line in the above example, it would have been outside
28740 To better use the width, negative space can be inserted at the beginning
28744 \begin_layout Itemize
28745 Due to a bug in LyX the cursor cannot be set with the mouse into the first
28750 \begin_layout Plain Layout
28751 \begin_inset CommandInset href
28753 name "LyX-bug #1429"
28754 target "http://www.lyx.org/trac/ticket/1429"
28763 One can only set the cursor at the beginning of the line and move it with
28772 \begin_layout Itemize
28773 Other methods to set long formulas are offered by the environments described
28775 \begin_inset CommandInset ref
28777 reference "sub:Multline-Environment"
28782 \begin_inset CommandInset ref
28784 reference "sub:Multiline-Formula-Parts"
28791 \begin_layout Subsubsection
28793 \begin_inset CommandInset label
28795 name "sub:Multiline-Brackets"
28800 \begin_inset Index idx
28803 \begin_layout Plain Layout
28804 Brackets ! for multiline expressions
28812 \begin_layout Standard
28813 For brackets spanning multiple lines the following problem occurs:
28814 \begin_inset Formula \begin{eqnarray*}
28815 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28816 & & \left.\cdots+B-D\right]
28824 \begin_layout Standard
28825 The closing bracket is smaller than the opening bracket because brackets
28826 with variable size may not span multiple lines.
28829 \begin_layout Standard
28830 To set the bracket size for the second line correctly, the first line is
28838 \begin_inset Index idx
28841 \begin_layout Plain Layout
28849 and the second line with
28857 \begin_layout Plain Layout
28871 \begin_inset CommandInset ref
28873 reference "sub:Automatic-Bracket-Size"
28885 \begin_inset Index idx
28888 \begin_layout Plain Layout
28914 \begin_layout Plain Layout
28933 \begin_layout Plain Layout
28952 \begin_layout Plain Layout
28964 \begin_inset Formula $\downarrow$
28970 \begin_inset Index idx
28973 \begin_layout Plain Layout
28981 is inserted, because the multiplication operator with its limits is the
28982 largest symbol in the first line and this should be the size for the bracket
28983 in the second line.
28986 \begin_layout Standard
28987 The result is this:
28988 \begin_inset Formula \begin{eqnarray*}
28989 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28990 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
28998 \begin_layout Subsection
29002 \begin_layout Standard
29003 Align environments can be used for every kind of multiline formulas.
29004 They are specially useful to set several formulas side by side.
29007 \begin_layout Standard
29008 Align environments consist of columns.
29009 The odd columns are right aligned, the even ones left aligned.
29010 Every line in an Align environment can be numbered.
29013 \begin_layout Standard
29014 Align environments are created via the menu
29016 Insert\SpecialChar \menuseparator
29022 Edit\SpecialChar \menuseparator
29023 Math\SpecialChar \menuseparator
29024 Change Formula Type
29026 already existing formulas can be converted to Align environments.
29029 \begin_layout Standard
29030 To add or delete columns, the math toolbar buttons
29031 \begin_inset Graphics
29032 filename ../images/tabular-feature_append-column.png
29038 \begin_inset Graphics
29039 filename ../images/tabular-feature_delete-column.png
29044 , respectively, or the menu
29046 Edit\SpecialChar \menuseparator
29052 \begin_layout Subsubsection
29053 Standard align Environment
29054 \begin_inset CommandInset label
29056 name "sub:Standard-align-Environment"
29061 \begin_inset Index idx
29064 \begin_layout Plain Layout
29065 Formula ! multiline ! align environment
29073 \begin_layout Standard
29074 This Align environment is created by presssing
29077 arg "newline-insert newline"
29080 in a formula or by the menu
29082 Insert\SpecialChar \menuseparator
29083 Math\SpecialChar \menuseparator
29084 AMS align Environment
29089 \begin_layout Standard
29090 An example for two formulas set side by side, that are created with a four
29091 column align environment:
29092 \begin_inset Formula \begin{align*}
29093 A & =\sin(B) & C & =D\\
29094 C & \ne A & B & \ne D
29099 As it can be seen, the formulas in this environment are placed so as if
29108 \begin_layout Plain Layout
29116 \begin_inset CommandInset ref
29118 reference "sub:Variable-Space"
29129 before the first and after every even column.
29130 When the formula style
29136 \begin_layout Plain Layout
29138 \begin_inset CommandInset ref
29140 reference "sec:Formula-Styles"
29151 is used, the formula is set without the
29157 before the first column.
29160 \begin_layout Subsubsection
29161 Alignat Environment
29162 \begin_inset Index idx
29165 \begin_layout Plain Layout
29166 Formula ! multiline ! alignat environment
29174 \begin_layout Standard
29175 The alignat environment has no predefined column separation.
29176 It can be inserted manually with the spaces that are described
29177 \begin_inset CommandInset ref
29179 reference "sub:Space"
29186 \begin_layout Standard
29187 The above example in the alignat environment where 1
29188 \begin_inset space \thinspace{}
29191 cm space was inserted at the beginning of the second formula:
29192 \begin_inset Formula \begin{alignat*}{2}
29193 A & =\sin(B) & \hspace{1cm}C & =D\\
29194 C & \ne A & B & \ne D
29199 Because the column separation can be set separately for every column, this
29200 environment is especially suitable to set three and more formulas side
29204 \begin_layout Subsubsection
29205 Flalign Environment
29206 \begin_inset CommandInset label
29208 name "sub:Flalign-Environment"
29213 \begin_inset Index idx
29216 \begin_layout Plain Layout
29217 Formula ! multiline ! flalign environment
29225 \begin_layout Standard
29226 In this environment the first two columns are always set as much as possible
29227 to the left and the last two ones to the right.
29229 \begin_inset Formula \begin{flalign*}
29230 A & =1 & B & =2 & C & =3\\
29231 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
29239 \begin_layout Standard
29240 By creating a flalign environment with an odd number of columns where an
29241 empty TeX-brace is inserted to the last column, several formulas in a document
29242 can be set to the left, although the formula style
29247 As example the indented formula
29248 \begin_inset CommandInset ref
29250 reference "eq:VolInt"
29255 \begin_inset Formula \begin{flalign}
29256 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}
29261 The first two columns contain the formula.
29262 To indent it as with the formula style
29267 \begin_inset space \thinspace{}
29270 pt space was inserted at the beginning of the first column.
29273 \begin_layout Subsection
29274 Eqnarray Environment
29275 \begin_inset CommandInset label
29277 name "sub:Eqnarray-Environment"
29282 \begin_inset Index idx
29285 \begin_layout Plain Layout
29286 Formula ! multiline ! eqnarray environment
29294 \begin_layout Standard
29295 When this environment has been created, three blue boxes appear.
29296 The content of the first box is right aligned, the content of the last
29298 The content of the middle box appears centered and a bit smaller, because
29299 it is designed to insert there only relation characters.
29300 \begin_inset Formula \begin{eqnarray*}
29301 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
29311 \begin_layout Subsection
29313 \begin_inset Index idx
29316 \begin_layout Plain Layout
29317 Formula ! multiline ! gather environment
29325 \begin_layout Standard
29326 This environment consists of only one centered column.
29327 Every line can be numbered.
29328 \begin_inset Formula \begin{gather}
29338 \begin_layout Subsection
29339 Multline Environment
29340 \begin_inset CommandInset label
29342 name "sub:Multline-Environment"
29347 \begin_inset Index idx
29350 \begin_layout Plain Layout
29351 Formula ! multiline ! multline environment
29359 \begin_layout Standard
29360 The multline environment consists, like the gather environment, of only
29362 But the first line is left aligned, the last one right aligned.
29363 All other lines are centered.
29364 Therefore this environment is suitable for long formulas.
29366 \begin_inset CommandInset ref
29368 reference "eq:lefteqn"
29372 in the multline environment:
29373 \begin_inset Formula \begin{multline}
29374 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}\\
29375 -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}\\
29376 =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}}
29384 \begin_layout Standard
29385 In the output only the last (first) line of a multline environment appears
29386 numbered when the document numbering is right (left).
29390 \begin_layout Plain Layout
29391 numbering styles see
29392 \begin_inset CommandInset ref
29394 reference "sec:Formula-Styles"
29406 \begin_layout Standard
29414 \begin_inset Index idx
29417 \begin_layout Plain Layout
29432 \begin_inset Index idx
29435 \begin_layout Plain Layout
29443 a centered line can be right or left aligned, respectively.
29444 The commands are used as follows:
29447 \begin_layout Standard
29452 shoveright{line content}
29458 shoveleft{line content}
29461 \begin_layout Standard
29462 \begin_inset VSpace medskip
29472 \begin_inset Index idx
29475 \begin_layout Plain Layout
29483 specifies the distance of the first line from the left page margin.
29484 Predefined is the length 0
29485 \begin_inset space \thinspace{}
29491 \begin_layout Standard
29492 As example the above formula where the command
29495 \begin_layout Standard
29505 \begin_layout Standard
29506 was inserted in TeX-mode before:
29510 \begin_layout Plain Layout
29522 \begin_inset Formula \begin{multline}
29523 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}\\
29524 \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}}\\
29525 =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}}
29534 \begin_layout Plain Layout
29545 The second line was left aligned using
29554 \begin_layout Subsection
29555 Multiline Formula Parts
29556 \begin_inset CommandInset label
29558 name "sub:Multiline-Formula-Parts"
29563 \begin_inset Index idx
29566 \begin_layout Plain Layout
29567 Formula ! multiline ! formula parts
29575 \begin_layout Standard
29576 To display only parts of a formula with multiple lines, one of the following
29577 environments are used:
29594 They can be inserted via the menu
29596 Insert\SpecialChar \menuseparator
29599 or by using the commands described in this section.
29602 \begin_layout Standard
29603 The first three have the same properties as the corresponding multiline
29604 formula environments, but it is possible to set further formula parts beside
29607 \begin_inset Formula \[
29608 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29609 \Delta E\Delta t & \ge\frac{\hbar}{2}
29611 \right\} \textrm{Uncertainty relations}
29619 \begin_layout Standard
29620 To get this formula, a displayed formula is created where the command
29627 \begin_inset Index idx
29630 \begin_layout Plain Layout
29639 A purple box appears around the blue formula box where now columns and
29640 lines can be added.
29641 Outside the multiline environment other formula parts can be set, like
29645 \begin_layout Standard
29646 The aligned environment is also suitable for long formulas whose lines are
29647 horizontally aligned.
29648 Using aligned in a displayed formula has the advantage that the formula
29649 number is vertically centered behind the lines.
29651 \begin_inset CommandInset ref
29653 reference "eq:shortlong"
29657 in the aligned environment:
29658 \begin_inset Formula \begin{equation}
29659 \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}|}\\
29660 & -\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}|}
29669 \begin_layout Standard
29670 To use the environments
29689 \begin_inset Index idx
29692 \begin_layout Plain Layout
29707 \begin_inset Index idx
29710 \begin_layout Plain Layout
29725 \begin_inset Index idx
29728 \begin_layout Plain Layout
29736 are inserted, respectively.
29737 The split environment has the same properties as the aligned environment
29738 but it can only have two columns.
29741 \begin_layout Subsection
29742 Text in multiline Formulas
29743 \begin_inset CommandInset label
29745 name "sub:Text-in-multiline"
29750 \begin_inset Index idx
29753 \begin_layout Plain Layout
29760 \begin_inset Index idx
29763 \begin_layout Plain Layout
29764 Formula ! multiline ! text
29772 \begin_layout Standard
29773 In the Align environments, and the multline and gather environment, text
29774 can be inserted that will appear in a separate line and doesn't affect
29775 the column alignment.
29776 To do this, the command
29783 \begin_inset Index idx
29786 \begin_layout Plain Layout
29794 is used in the following scheme:
29797 \begin_layout Standard
29805 \begin_layout Standard
29806 The text should not be longer than a line because it cannot be hyphenated.
29807 As LyX doesn't yet support
29813 directly, the text is written as mathematical text.
29820 must hereby be at the beginning of a line and appears in the output above
29822 An example where the text was inserted at the beginning of the second line:
29823 \begin_inset Formula \begin{align}
29824 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29825 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29833 \begin_layout Section
29835 \begin_inset Index idx
29838 \begin_layout Plain Layout
29845 \begin_inset Index idx
29848 \begin_layout Plain Layout
29849 Formula ! numbering|see
29853 \begin_layout Plain Layout
29864 \begin_layout Plain Layout
29879 \begin_layout Subsection
29883 \begin_layout Standard
29884 Numbered formulas can be created with the menu
29886 Insert\SpecialChar \menuseparator
29887 Math\SpecialChar \menuseparator
29889 \begin_inset space ~
29897 \begin_inset space ~
29903 Existing formulas can be numbered with the menu
29905 Edit\SpecialChar \menuseparator
29906 Math\SpecialChar \menuseparator
29908 \begin_inset space ~
29916 arg "math-number-toggle"
29920 The formula number is displayed in LyX behind the formula as number sign
29922 The number sign is replaced in the output by the formula number.
29925 \begin_layout Standard
29926 When numbering is turned on in multiline formulas, all lines will be numbered.
29927 But the numbering can be controlled with the menu
29929 Edit\SpecialChar \menuseparator
29930 Math\SpecialChar \menuseparator
29932 \begin_inset space ~
29936 \begin_inset space ~
29940 \begin_inset space ~
29948 arg "math-number-line-toggle"
29954 \begin_layout Standard
29955 Except for inline formulas, all formulas can be numbered with two different
29957 \begin_inset CommandInset ref
29959 reference "sec:Formula-Styles"
29966 \begin_layout Subsection
29968 \begin_inset Index idx
29971 \begin_layout Plain Layout
29972 Cross-references ! to formulas
29980 \begin_layout Standard
29981 All labeled formulas can be cross-referenced.
29982 A label is added by the menu
29984 Insert\SpecialChar \menuseparator
29987 or the toolbar button
29988 \begin_inset Graphics
29989 filename ../images/label-insert.png
29995 The cursor must hereby be inside a displayed formula.
29996 A dialog pops up displaying the prefix
30001 The label is inserted there behind the prefix.
30002 The predefined prefix means
30003 \begin_inset Quotes eld
30007 \begin_inset Quotes erd
30010 and makes it easier to find labels in large documents because it marks
30011 it as formula label to divide it from e.
30012 \begin_inset space \thinspace{}
30016 \begin_inset space \space{}
30020 To change a label, the menu
30022 Insert\SpecialChar \menuseparator
30028 \begin_layout Standard
30029 The name of the label is displayed in LyX within two parentheses behind
30031 A formula with a label is always numbered.
30034 \begin_layout Standard
30035 Cross-references are inserted via the menu
30037 Insert\SpecialChar \menuseparator
30040 or with the toolbar button
30041 \begin_inset Graphics
30042 filename ../images/dialog-show-new-inset_ref.png
30048 A formula cross-reference appears in the output as formula number.
30049 When in the cross-reference dialog window the format
30053 is chosen, the cross-reference appears in the output as formula number
30055 \begin_inset Newline newline
30058 By right-clicking on a cross-reference in LyX, one jumps to the formula
30059 that is referenced.
30062 \begin_layout Standard
30063 Here are as examples cross-references to formulas of the following subsections:
30064 \begin_inset Note Note
30067 \begin_layout Plain Layout
30068 Note the different cross-reference types.
30076 \begin_layout Standard
30078 \begin_inset CommandInset ref
30085 \begin_inset CommandInset ref
30093 \begin_inset CommandInset ref
30099 ) big Latin letters are used for the numbering in contrary to (
30100 \begin_inset CommandInset ref
30109 \begin_layout Standard
30110 \begin_inset VSpace medskip
30113 When the argument of
30121 \begin_layout Plain Layout
30129 \begin_inset CommandInset ref
30131 reference "sub:User-defined-Numbering"
30142 contains a box like in
30143 \begin_inset CommandInset ref
30145 reference "sub:Paragraph-Boxes"
30149 , the formula cannot be referenced.
30152 \begin_layout Subsection
30154 \begin_inset Index idx
30157 \begin_layout Plain Layout
30158 Formula numbering ! subnumbering
30166 \begin_layout Standard
30167 With the help of the commands
30171 begin{subequations}
30179 formulas can be subnumbered.
30180 Both commands are inserted in TeX-mode.
30183 \begin_layout Standard
30185 \begin_inset Formula \begin{equation}
30195 \begin_layout Plain Layout
30199 addtocounter{equation}{-1}
30208 \begin_layout Plain Layout
30212 begin{subequations}
30218 \begin_inset VSpace -5mm
30222 \begin_inset Formula \begin{equation}
30229 \begin_inset Formula \begin{equation}
30238 \begin_layout Standard
30242 \begin_layout Plain Layout
30254 \begin_layout Standard
30255 To create the example, the following is done:
30258 \begin_layout Enumerate
30259 first formula is inserted
30262 \begin_layout Enumerate
30267 addtocounter{equation}{-1}
30269 begin{subequations}
30270 \begin_inset Index idx
30273 \begin_layout Plain Layout
30282 \begin_inset Newline newline
30287 is inserted after the first formula
30290 \begin_layout Enumerate
30291 second formula is inserted
30294 \begin_layout Enumerate
30295 third formula is inserted
30298 \begin_layout Enumerate
30305 is inserted after the third formula
30308 \begin_layout Standard
30309 Every formula between the commands
30321 is subnumbered as a, b,
30322 \begin_inset Newline linebreak
30325 c, \SpecialChar \ldots{}
30326 For multiline formulas every line will be subnumbered.
30327 All subnumbered formulas are treated as
30332 But as every numbered formula increases the counter
30336 by one, the command
30342 is needed to decrease it.
30343 Otherwise the formulas
30344 \begin_inset CommandInset ref
30351 \begin_inset CommandInset ref
30358 \begin_inset CommandInset ref
30364 would be numbered as
30365 \begin_inset CommandInset ref
30372 \begin_inset CommandInset ref
30379 \begin_inset CommandInset ref
30388 \begin_layout Standard
30389 By inserting the commands in TeX-mode, a space is created between the first
30392 \begin_inset space \thinspace{}
30395 mm vertical space is inserted after the command
30399 begin{subequations}
30402 When the formula style
30408 \begin_layout Plain Layout
30410 \begin_inset CommandInset ref
30412 reference "sec:Formula-Styles"
30424 \begin_inset space \thinspace{}
30427 mm space is inserted instead.
30430 \begin_layout Standard
30431 Here is an example for a multiline formula where the numbering was turned
30432 off for the second line:
30436 \begin_layout Plain Layout
30440 begin{subequations}
30446 \begin_inset Formula \begin{eqnarray}
30447 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
30448 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
30449 & = & B^{2}-2BZ+Z^{2}\label{eq:f}
30458 \begin_layout Plain Layout
30470 \begin_layout Subsection
30471 User-defined Numbering
30472 \begin_inset CommandInset label
30474 name "sub:User-defined-Numbering"
30479 \begin_inset Index idx
30482 \begin_layout Plain Layout
30483 Formula numbering ! user-defined
30491 \begin_layout Standard
30492 \begin_inset Index idx
30495 \begin_layout Plain Layout
30496 Formula numbering ! self-defined delimiters
30501 With the standard numbering parentheses are set around the formula number.
30502 To replace the parentheses for example by vertical bars, the following
30503 line is added to the LaTeX-preamble:
30506 \begin_layout Standard
30518 \begin_inset Note Note
30521 \begin_layout Plain Layout
30522 This macro is already declared in the LaTeX-preamble for testing.
30523 To activate it, remove the percent sign at the beginning.
30531 \begin_layout Standard
30532 To use other characters, the vertical bars besides the
30536 are replaced by one ore more characters.
30537 To get only the formula number the vertical bars are omitted.
30540 \begin_layout Standard
30541 \begin_inset VSpace bigskip
30544 When there should be an expression of your choice instead of the consecutive
30545 formula number in parentheses behind the formula, the command
30552 \begin_inset Index idx
30555 \begin_layout Plain Layout
30564 \begin_inset Formula \begin{equation}
30565 A+B=C\tag{something}\label{eq:tag}
30570 In this example the command
30578 \begin_layout Plain Layout
30589 was inserted to the formula.
30592 \begin_layout Standard
30601 \begin_layout Plain Layout
30612 is inserted instead, the star prevents the parentheses around the expression:
30613 \begin_inset Formula \[
30614 A+B=C\tag*{something}
30622 \begin_layout Standard
30623 \begin_inset VSpace bigskip
30626 To restart the formula numbering with new document parts or sections, the
30627 following command is used:
30630 \begin_layout Standard
30635 @addtoreset{equation}{part}
30638 \begin_inset Index idx
30641 \begin_layout Plain Layout
30646 \begin_layout Plain Layout
30657 \begin_layout Plain Layout
30670 \begin_layout Plain Layout
30681 \begin_layout Plain Layout
30694 \begin_inset Newline newline
30698 \begin_inset Newline newline
30705 @addtoreset{equation}{section}
30708 \begin_layout Standard
30709 To be able to use these commands in TeX-mode, the
30710 \begin_inset Quotes eld
30714 \begin_inset Quotes erd
30717 character has to be made
30718 \begin_inset Quotes eld
30722 \begin_inset Quotes erd
30725 for LaTeX using the command
30739 So the command sequence in TeX-mode is:
30742 \begin_layout Standard
30748 \begin_inset Newline newline
30753 @addtoreset{equation}{section}
30754 \begin_inset Newline newline
30762 \begin_layout Standard
30763 In the LaTeX-preamble
30775 can be omitted as they are automatically internally inserted by LyX.
30778 \begin_layout Standard
30793 \begin_layout Plain Layout
30798 is part of the LaTeX-package
30803 \begin_inset Index idx
30806 \begin_layout Plain Layout
30807 Packages ! carlisle
30812 that is part of every LaTeX standard installation.
30818 \begin_inset Index idx
30821 \begin_layout Plain Layout
30822 Packages ! remreset
30827 has to be loaded in the LaTeX-preamble with the line
30830 \begin_layout Standard
30835 usepackage{remreset}
30838 \begin_layout Standard
30846 \begin_inset Index idx
30849 \begin_layout Plain Layout
30854 \begin_layout Plain Layout
30865 \begin_layout Plain Layout
30878 \begin_layout Plain Layout
30889 \begin_layout Plain Layout
30901 can be used with the same scheme as
30910 \begin_layout Standard
30911 \begin_inset VSpace bigskip
30914 Sometimes formulas should be numbered in the following form:
30917 \begin_layout Standard
30920 (section number.formula number)
30923 \begin_layout Standard
30924 The formula number should start with every section with
30925 \begin_inset Quotes eld
30929 \begin_inset Quotes erd
30935 \begin_layout Standard
30936 For this case there is the command
30943 \begin_inset Index idx
30946 \begin_layout Plain Layout
30954 , which is used with the following scheme:
30957 \begin_layout Standard
30962 numberwithin{counter}{sectioning}
30965 \begin_layout Standard
30966 Counter denotes what kind of numbering is affected, sectioning denotes what
30967 number is before the dot.
30970 \begin_layout Standard
30971 Thus in our case the following LaTeX-preamble or TeX-Code line is used:
30974 \begin_layout Standard
30979 numberwithin{equation}{section}
30982 \begin_layout Standard
30983 This is the result:
30987 \begin_layout Plain Layout
30991 numberwithin{equation}{section}
30997 \begin_inset Formula \begin{equation}
31006 \begin_layout Standard
31008 \begin_inset space \thinspace{}
31012 \begin_inset space \space{}
31015 tables so that the number of the part is the sectioning,
31016 \begin_inset Newline newline
31023 numberwithin{table}{part}
31028 \begin_layout Standard
31029 To go back to the standard numbering or to prevent this kind of numbering
31030 when it is defined by the document class, the following command is inserted
31031 as TeX-Code or to the LaTeX-preamble:
31034 \begin_layout Standard
31044 \begin_inset Index idx
31047 \begin_layout Plain Layout
31061 \begin_layout Plain Layout
31077 \begin_inset Newline newline
31085 \begin_inset Newline newline
31097 \begin_layout Standard
31104 uses internally the command
31110 , described above, that also needs to be reverted.
31114 \begin_layout Plain Layout
31121 \begin_layout Plain Layout
31125 @removefromreset{equation}{section}
31128 \begin_layout Plain Layout
31140 \begin_layout Subsection
31141 Numbering with Roman Numbers and Letters
31142 \begin_inset Index idx
31145 \begin_layout Plain Layout
31146 Formula numbering ! with letters
31152 \begin_inset Index idx
31155 \begin_layout Plain Layout
31156 Formula numbering ! with Roman numbers
31164 \begin_layout Standard
31165 Formulas can also be numbered with Roman numbers and Latin letters.
31166 To number for example with small Roman numbers, the command
31169 \begin_layout Standard
31181 \begin_layout Standard
31182 is inserted before the formula in TeX-mode.
31190 \begin_inset Index idx
31193 \begin_layout Plain Layout
31201 redefines the predefined command
31217 \begin_layout Plain Layout
31224 has the same scheme like the command
31230 that is described in
31231 \begin_inset CommandInset ref
31233 reference "sub:The-Command-newcommand"
31246 is the formula counter.
31253 is used as prefix for a counter, the value of the counter is output as
31255 When a formula is numbered, LaTeX sets internally the command
31261 behind the formula.
31267 \begin_inset Index idx
31270 \begin_layout Plain Layout
31280 outputs the counter as small Roman number.
31283 \begin_layout Standard
31284 All formulas behind the command
31294 are now numbered Roman.
31295 To switch to numbering with big Roman numbers, the command is inserted
31309 \begin_inset Index idx
31312 \begin_layout Plain Layout
31324 \begin_inset Quotes eld
31328 \begin_inset Quotes erd
31331 with small Latin letters there is the command
31338 \begin_inset Index idx
31341 \begin_layout Plain Layout
31349 , for big ones there is the command
31356 \begin_inset Index idx
31359 \begin_layout Plain Layout
31372 \begin_layout Standard
31373 \begin_inset Note Greyedout
31376 \begin_layout Plain Layout
31381 Only maximal 26 formulas can be numbered with Latin letters in one document.
31389 \begin_layout Standard
31393 \begin_layout Plain Layout
31409 \begin_layout Standard
31410 \begin_inset Formula \begin{equation}
31411 A=\textrm{small roman}
31420 \begin_layout Plain Layout
31434 \begin_inset Formula \begin{equation}
31435 B=\textrm{big Roman}\label{eq:Rom}
31444 \begin_layout Plain Layout
31458 \begin_inset Formula \begin{equation}
31459 C=\textrm{small Latin}
31468 \begin_layout Plain Layout
31482 \begin_inset Formula \begin{equation}
31483 D=\textrm{big Latin}\label{eq:Lat}
31491 \begin_layout Standard
31492 To switch back to the default numbering, insert the command:
31495 \begin_layout Standard
31505 \begin_inset Index idx
31508 \begin_layout Plain Layout
31519 \begin_layout Standard
31523 \begin_layout Plain Layout
31537 \begin_inset Formula \begin{equation}
31546 \begin_layout Standard
31547 \begin_inset VSpace medskip
31550 As you see, formulas are numbered serially independent from the numbering
31552 When then numbering should start with
31553 \begin_inset Quotes eld
31557 \begin_inset Quotes erd
31560 when the style is changed, new equation counters have to be defined.
31561 A description about this can be found in the file
31562 \begin_inset CommandInset href
31564 name "Formula-numbering.lyx"
31565 target "run:Formula-numbering.lyx"
31572 \begin_layout Section
31573 Chemical Symbols and Equations
31574 \begin_inset CommandInset label
31576 name "sub:Chemical-Symbols-and"
31581 \begin_inset Index idx
31584 \begin_layout Plain Layout
31585 Chemical characters ! Symbols
31591 \begin_inset Index idx
31594 \begin_layout Plain Layout
31601 \begin_inset Index idx
31604 \begin_layout Plain Layout
31613 \begin_layout Standard
31614 An example text from chemistry:
31617 \begin_layout Quote
31619 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
31622 -ion reacts with two
31623 \begin_inset Formula $\mathrm{Na^{+}}$
31626 -ions to sodium sulfate
31627 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
31631 The chemical equation for this is:
31632 \begin_inset Formula \begin{equation}
31633 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
31641 \begin_layout Standard
31642 This chemical equation can directly be created as formula.
31643 To avoid that the symbols appear italic, everything is highlighted and
31644 changed by the shortcut
31650 to the upright font style.
31654 \begin_layout Plain Layout
31660 \begin_inset CommandInset ref
31662 reference "sub:Font-Styles"
31674 \begin_layout Standard
31675 A more convenient way to typeset chemical formulas is to use the command
31683 \begin_inset Index idx
31686 \begin_layout Plain Layout
31694 that is available when the LaTeX-package
31699 \begin_inset Index idx
31702 \begin_layout Plain Layout
31715 to a formula a new blue box appears where chemical formulas can be inserted
31716 in an intuitive way.
31719 \begin_layout Standard
31721 \begin_inset Tabular
31722 <lyxtabular version="3" rows="9" columns="2">
31723 <features tabularvalignment="middle">
31724 <column alignment="center" valignment="top" width="0">
31725 <column alignment="center" valignment="top" width="0">
31727 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31730 \begin_layout Plain Layout
31736 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31739 \begin_layout Plain Layout
31741 \begin_inset Note Note
31744 \begin_layout Plain Layout
31751 is only used as spacer.
31763 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31766 \begin_layout Plain Layout
31773 \begin_layout Plain Layout
31787 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31790 \begin_layout Plain Layout
31791 \begin_inset Formula $\raisebox{4.5mm}{}\ce{H2CO3}\raisebox{-2mm}{}$
31801 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31804 \begin_layout Plain Layout
31811 \begin_layout Plain Layout
31825 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31828 \begin_layout Plain Layout
31829 \begin_inset Formula $\raisebox{5mm}{}\ce{SO4^{2-}}\raisebox{-2mm}{}$
31839 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31842 \begin_layout Plain Layout
31849 \begin_layout Plain Layout
31863 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31866 \begin_layout Plain Layout
31867 \begin_inset Formula $\raisebox{4.5mm}{}\ce{(NH4)2S}\raisebox{-2mm}{}$
31877 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31880 \begin_layout Plain Layout
31887 \begin_layout Plain Layout
31901 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31904 \begin_layout Plain Layout
31905 \begin_inset Formula $\raisebox{4.5mm}{}\ce{KCr(SO4)2.12H2O}\raisebox{-2mm}{}$
31915 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31918 \begin_layout Plain Layout
31925 \begin_layout Plain Layout
31940 \begin_layout Plain Layout
31955 \begin_layout Plain Layout
31969 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31972 \begin_layout Plain Layout
31973 \begin_inset Formula $\raisebox{4.5mm}{}\ce{A-B\dbond C\tbond D}\raisebox{-2mm}{}$
31983 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31986 \begin_layout Plain Layout
31993 \begin_layout Plain Layout
32003 \begin_inset Formula $\downarrow$
32007 \begin_inset Formula $\to$
32015 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32018 \begin_layout Plain Layout
32019 \begin_inset Formula $\raisebox{5mm}{}\ce{_{90}^{227}Th+}\raisebox{-2mm}{}$
32029 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32032 \begin_layout Plain Layout
32039 \begin_layout Plain Layout
32052 \begin_layout Plain Layout
32065 \begin_layout Plain Layout
32078 \begin_layout Plain Layout
32091 \begin_layout Plain Layout
32105 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32108 \begin_layout Plain Layout
32109 \begin_inset Formula $\raisebox{4.5mm}{}\ce{CO2 + C <=> 2CO}\raisebox{-2mm}{}$
32119 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32122 \begin_layout Plain Layout
32129 \begin_layout Plain Layout
32142 \begin_layout Plain Layout
32155 \begin_layout Plain Layout
32168 \begin_layout Plain Layout
32185 \begin_layout Plain Layout
32199 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32202 \begin_layout Plain Layout
32203 \begin_inset Formula $\raisebox{5mm}{}\ce{CO2 + C ->[\alpha][\beta] 2CO}\raisebox{-4mm}{}$
32219 \begin_layout Standard
32220 \begin_inset Note Greyedout
32223 \begin_layout Plain Layout
32228 Inserting a formula to a
32234 box will lead to LaTeX errors.
32235 In this case TeX code has to be used like for
32249 \begin_layout Plain Layout
32270 \begin_layout Standard
32277 the command for equation
32278 \begin_inset space ~
32282 \begin_inset CommandInset ref
32284 reference "eq:chem-reaction"
32289 \begin_inset Newline newline
32300 \begin_layout Plain Layout
32313 \begin_layout Plain Layout
32326 \begin_layout Plain Layout
32339 \begin_layout Plain Layout
32352 \begin_layout Plain Layout
32365 \begin_layout Plain Layout
32377 \begin_layout Standard
32378 To create multiline chemical equations first a multiline formula is created
32380 \begin_inset CommandInset ref
32382 reference "sec:Multiline-Formulas"
32387 Afterwards the command
32393 is used in every small blue box of the formula.
32395 \begin_inset CommandInset ref
32397 reference "eq:TEOS-reaction-1"
32402 \begin_inset CommandInset ref
32404 reference "eq:TEOS-reaction-2"
32408 are an example of a multi-stage chemical reaction where every equation
32409 has its own number.
32410 \begin_inset Formula \begin{eqnarray}
32411 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
32412 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
32420 \begin_layout Standard
32431 package provides the command
32438 \begin_inset Index idx
32441 \begin_layout Plain Layout
32449 that has to be used for special cases.
32450 For more information about
32456 and more examples have a look at the documentation of
32461 \begin_inset CommandInset citation
32470 \begin_layout Standard
32471 \begin_inset Newpage newpage
32477 \begin_layout Section
32481 \begin_layout Standard
32482 LyX supports two types of commutative diagrams:
32490 that are explained in the following.
32493 \begin_layout Subsection
32495 \begin_inset Index idx
32498 \begin_layout Plain Layout
32507 \begin_layout Standard
32508 Diagrams of this type visualize relations by vertical and horizontal lines
32510 \begin_inset Formula \[
32511 \begin{CD}A@>>>B@>>>C\\
32522 \begin_layout Standard
32523 To get them, the command
32528 \begin_inset Index idx
32531 \begin_layout Plain Layout
32541 is inserted to a formula.
32542 A blue box appears with two dashed lines where further commands can be
32547 arg "newline-insert newline"
32550 a new line is created.
32551 Horizontal relations are inserted in odd, vertical in even formula lines.
32554 \begin_layout Standard
32555 To create the relations there are the following commands:
32558 \begin_layout Itemize
32563 creates a left arrow,
32574 \begin_layout Itemize
32579 creates an up arrow,
32587 a vertical equal sign
32590 \begin_layout Itemize
32596 is a placeholder for non-existent relations
32599 \begin_layout Standard
32600 All arrows can be labeled as follows:
32603 \begin_layout Itemize
32604 Is text inserted between the first and second < or >, resp., it is placed
32606 When it is inserted between the second and third one, it appears under
32610 \begin_layout Itemize
32611 When text for vertical arrows is inserted between the first and second A
32612 or V, resp., it is placed left beside the arrow.
32613 When it is inserted between the second and third one, it appears right
32615 If the text contains an A or V, these letters must be set into a TeX-brace.
32618 \begin_layout Standard
32619 As example a diagram with all possible relations:
32622 \begin_layout Standard
32623 \begin_inset Formula \[
32624 \begin{CD}A@>j>>B@>>k>C@=F\\
32635 \begin_layout Standard
32636 The command for this is:
32637 \begin_inset Newline newline
32648 \begin_layout Plain Layout
32657 A@>j>>B@>>k>C@=F Ctrl+Return
32658 \begin_inset Newline newline
32662 \begin_inset Phantom HPhantom
32665 \begin_layout Plain Layout
32674 \begin_layout Plain Layout
32693 \begin_inset Formula $\to$
32699 \begin_inset Newline newline
32703 \begin_inset Phantom HPhantom
32706 \begin_layout Plain Layout
32715 \begin_layout Plain Layout
32732 \begin_layout Subsection
32734 \begin_inset Index idx
32737 \begin_layout Plain Layout
32738 Diagrams ! xymatrix
32746 \begin_layout Standard
32747 To be able to use xymatrices, the LaTeX-package
32752 A xymatrix is created by inserting the command
32759 Then you are able to add new matrix columns and rows like for normal matrices,
32761 \begin_inset CommandInset ref
32763 reference "sec:Matrices"
32770 \begin_layout Standard
32771 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
32773 All possibilities to create commutative diagrams and decorations are explained
32778 that you find in the menu
32780 Help\SpecialChar \menuseparator
32782 \begin_inset space ~
32790 \begin_layout Subsection
32796 \begin_inset Index idx
32799 \begin_layout Plain Layout
32808 \begin_layout Standard
32813 -diagrams, the LaTeX-package
32822 -diagram is created by inserting the command
32829 Then you are able to add new matrix columns and rows like for normal matrices,
32831 \begin_inset CommandInset ref
32833 reference "sec:Matrices"
32840 \begin_layout Standard
32841 Examples how to create
32845 diagrams in LyX is given in the
32847 Feynman-diagram manual
32849 that you find in the menu
32851 Help\SpecialChar \menuseparator
32853 \begin_inset space ~
32861 \begin_layout Section
32862 User-defined Commands
32863 \begin_inset Index idx
32866 \begin_layout Plain Layout
32867 User-defined commands
32875 \begin_layout Standard
32876 \begin_inset Note Greyedout
32879 \begin_layout Plain Layout
32884 The names of user-defined commands and macros may only consist of Latin
32893 \begin_layout Subsection
32897 \begin_inset CommandInset label
32899 name "sub:The-Command-newcommand"
32904 \begin_inset Index idx
32907 \begin_layout Plain Layout
32908 User-defined commands !
32916 \begin_inset Index idx
32919 \begin_layout Plain Layout
32930 \begin_layout Standard
32931 Many LaTeX-commands are too long to be used frequently.
32932 But it is possible to define with the command
32938 new shorter commands.
32941 \begin_layout Standard
32942 The command scheme of
32951 \begin_layout Standard
32956 newcommand{new command name}[number of arguments][optional
32961 \begin_inset Newline newline
32965 \begin_inset Phantom HPhantom
32968 \begin_layout Plain Layout
32978 {command definition}
32981 \begin_layout Standard
32982 \begin_inset Note Greyedout
32985 \begin_layout Plain Layout
32990 Assure that the name of the new command is not already used in your document
32991 or by LaTeX-packages that you use.
32992 When you for example define the command
33004 , you get an error message because
33010 is already defined as command for
33011 \begin_inset Quotes eld
33015 \begin_inset Formula $\le$
33019 \begin_inset Quotes erd
33030 \begin_layout Standard
33031 The number of arguments is an integer in the range 0
33032 \begin_inset space \thinspace{}
33036 \begin_inset space \thinspace{}
33039 9 and specifies how many arguments the new command should have.
33040 With the optional value a value for an optional argument can be predefined.
33041 When this is done, the
33049 rgument of the new command is automatically an optional one.
33052 \begin_layout Standard
33053 Here are some examples:
33056 \begin_layout Itemize
33057 To define the command
33069 , the LaTeX-preamble line is:
33070 \begin_inset VSpace medskip
33074 \begin_inset Newline newline
33088 \begin_layout Itemize
33089 To define the command
33101 , the argument (that should be underlined) must be taken into account.
33102 For this the preamble line is:
33103 \begin_inset VSpace medskip
33107 \begin_inset Newline newline
33121 \begin_inset VSpace medskip
33125 \begin_inset Newline newline
33132 acts as argument placeholder, the
33136 behind it denotes that it is the placeholder for the first argument.
33139 \begin_layout Itemize
33147 \begin_inset space \thinspace{}
33151 \begin_inset space \space{}
33161 \begin_inset VSpace medskip
33165 \begin_inset Newline newline
33176 framebox#1#2{$#3$}}
33179 \begin_inset VSpace medskip
33183 \begin_inset Newline newline
33186 The two Dollar signs creates the extra formula needed for
33193 \begin_inset CommandInset ref
33195 reference "sub:Boxes-with-Frame"
33202 \begin_layout Itemize
33203 To create a new command for
33209 where the color for the box needn't to be specified, the argument for the
33210 color is defined optional:
33211 \begin_inset VSpace medskip
33215 \begin_inset Newline newline
33226 fcolorbox{#2}{#1}{$#3$}}
33229 \begin_inset VSpace medskip
33233 \begin_inset Newline newline
33236 When the color is not specified when using
33242 , the predefined color
33249 \begin_layout Standard
33250 A test of the new defined commands:
33253 \begin_layout Standard
33255 \begin_inset Tabular
33256 <lyxtabular version="3" rows="6" columns="2">
33257 <features tabularvalignment="middle">
33258 <column alignment="center" valignment="top" width="0">
33259 <column alignment="center" valignment="top" width="0">
33261 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33264 \begin_layout Plain Layout
33270 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33273 \begin_layout Plain Layout
33275 \begin_inset Note Note
33278 \begin_layout Plain Layout
33285 is only used as spacer.
33297 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33300 \begin_layout Plain Layout
33307 \begin_layout Plain Layout
33321 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33324 \begin_layout Plain Layout
33325 \begin_inset Formula $A\gr B$
33335 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33338 \begin_layout Plain Layout
33346 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33349 \begin_layout Plain Layout
33350 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
33360 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33363 \begin_layout Plain Layout
33367 \begin_inset Formula $\to$
33373 \begin_inset Formula $\to$
33384 \begin_layout Plain Layout
33398 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33401 \begin_layout Plain Layout
33402 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
33412 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33415 \begin_layout Plain Layout
33419 \begin_inset Formula $\to$
33430 \begin_layout Plain Layout
33444 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33447 \begin_layout Plain Layout
33448 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
33458 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33461 \begin_layout Plain Layout
33467 \begin_inset Formula $\to$
33478 \begin_layout Plain Layout
33492 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33495 \begin_layout Plain Layout
33496 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
33512 \begin_layout Subsection
33514 \begin_inset Index idx
33517 \begin_layout Plain Layout
33518 User-defined commands! Math macros
33524 \begin_inset Index idx
33527 \begin_layout Plain Layout
33536 \begin_layout Standard
33537 User-defined commands are especially convenient for complex expressions.
33538 When you are for example dealing in a document with quadratic equations,
33539 the same solution type occurs several times.
33540 The general form of a quadratic equation is
33541 \begin_inset Formula \[
33542 0=\lambda^{2}+p\lambda+q
33547 The general form of the solution is
33548 \begin_inset Formula \[
33549 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
33557 \begin_layout Standard
33558 To define a command for the solution formula where only the three parameters
33560 \begin_inset Formula $\lambda$
33564 \begin_inset Formula $p$
33568 \begin_inset Formula $q$
33571 need to be specified and the index of
33572 \begin_inset Formula $\lambda$
33575 can be given optionally, the LaTeX-preamble line is
33576 \begin_inset Newline newline
33592 \begin_inset Newline newline
33596 \begin_inset Phantom HPhantom
33599 \begin_layout Plain Layout
33613 frac{#3^{2}}{4}-#4}}
33616 \begin_layout Standard
33617 To create with this the solution formula, the command
33618 \begin_inset Newline newline
33628 \begin_inset Formula $\to$
33634 \begin_inset Formula $\to$
33641 is inserted to a formula
33646 \begin_layout Standard
33647 The definition of the new command is unintuitive because one has to know
33648 the schemes of all used LaTeX commands, e.
33649 \begin_inset space \thinspace{}
33653 \begin_inset space \space{}
33656 that a fraction is inserted in LaTeX as
33660 frac{numerator}{denominator}
33663 Furthermore one can easily forget a brace in the definition and cannot
33664 see in LyX what the new command is doing.
33665 To avoid these problems LyX offers the possibility to use math macros instead
33675 \begin_layout Standard
33676 A math macro is created by using the menu
33678 Insert\SpecialChar \menuseparator
33679 Math\SpecialChar \menuseparator
33682 or the toolbar button
33683 \begin_inset Graphics
33684 filename ../images/math-macro_newmacroname_newcommand.png
33690 The math macro toolbar appears together with the following box where the
33692 \begin_inset Newline newline
33696 \begin_inset space \hspace*{\fill}
33700 \begin_inset Graphics
33701 filename clipart/macrobox.png
33706 \begin_inset space \hspace*{\fill}
33710 \begin_inset Newline newline
33714 \begin_inset FormulaMacro
33715 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
33720 newmacroname is the default name of the macro that should be changed to
33721 something sensible.
33722 The wanted formula is inserted in the first blue box.
33723 An argument placeholder is inserted with the command
33730 \begin_inset space \thinspace{}
33734 \begin_inset space \space{}
33743 or by using the macro toolbar button
33744 \begin_inset Graphics
33745 filename ../images/math-macro-add-param.png
33751 Argument placeholders are displayed red.
33752 Maximum 9 arguments are possible.
33753 Optional arguments are created with the toolbar button
33754 \begin_inset Graphics
33755 filename ../images/math-macro-add-optional-param.png
33761 The first non-optional argument can be transformed to an optional one with
33763 \begin_inset Graphics
33764 filename ../images/math-macro-make-optional.png
33770 In the second blue box the appearance of the macro in LyX can be defined.
33771 Normally you want to see it as it is defined, so the box is kept empty.
33772 But when you have created a macro that needs lot of space on the screen,
33773 you can insert in the box for example
33774 \begin_inset Newline newline
33804 \begin_inset Newline newline
33809 For the macro only the arguments with the macro name in front of them will
33810 then be displayed in LyX, leading to a better overview.
33811 The formula appears in the output as defined in the first box.
33812 \begin_inset Newline newline
33815 The appearance of macros in formulas can furthermore be changed for single
33816 macros by setting the cursor in the macro and using the menu
33818 View\SpecialChar \menuseparator
33820 \begin_inset space ~
33824 \begin_inset space ~
33832 \begin_layout Standard
33833 To use a macro, the macro name is inserted as command to a formula, in our
33841 Our macro looks in LyX like this:
33842 \begin_inset Newline newline
33846 \begin_inset space \hspace*{\fill}
33850 \begin_inset Graphics
33851 filename clipart/macrouse.png
33856 \begin_inset space \hspace*{\fill}
33860 \begin_inset Newline newline
33863 Here is our macro example with the arguments
33864 \begin_inset Formula $x$
33868 \begin_inset Formula $\ln(x)$
33872 \begin_inset Formula $B$
33878 \begin_layout Standard
33879 \begin_inset Formula \[
33888 \begin_layout Standard
33889 LyX offers in the menu
33891 Tools\SpecialChar \menuseparator
33892 Preferences\SpecialChar \menuseparator
33893 Editing\SpecialChar \menuseparator
33896 different styles to edit macros.
33897 To find the style that suits you the most, choose a style and set the cursor
33898 in a macro formula to see the difference.
33901 \begin_layout Standard
33902 A math macro is transformed internally to a
33908 command when exporting the document.
33915 command is not placed in the LaTeX-preamble, therefore macros can only
33916 be used in formulas that are in the document below the macro definition
33920 \begin_layout Standard
33921 Math macros can also be directly be created from a
33928 When writing for example the command
33931 \begin_inset Newline newline
33940 xleftarrow[#2]{#1}}
33941 \begin_inset Newline newline
33946 in LyX as normal text, highlighting it completely and using then the shortcut
33951 , the command will be transformed to a math macro.
33952 Using this method you need to be careful that the
33958 command is typed correctly, otherwise you get a faulty macro leading to
33962 \begin_layout Standard
33963 Math macros currently yet have the problem that further formulas in macro
33964 definitions are handled wrongly.
33965 Therefore the example
33972 \begin_inset CommandInset ref
33974 reference "sub:The-Command-newcommand"
33978 cannot be created as macro.
33981 \begin_layout Standard
33982 When the cursor is in a macro definition box, you will see the macro toolbar
33986 \begin_layout Standard
33987 \begin_inset VSpace defskip
33993 \begin_layout Standard
33994 \begin_inset Graphics
33995 filename clipart/MacroToolbar.png
34000 \begin_inset Index idx
34003 \begin_layout Plain Layout
34012 \begin_layout Standard
34013 \begin_inset VSpace defskip
34019 \begin_layout Standard
34020 The macro toolbar contains from left to right the following buttons:
34023 \begin_layout Standard
34024 \begin_inset VSpace defskip
34030 \begin_layout Standard
34031 \begin_inset Tabular
34032 <lyxtabular version="3" rows="9" columns="2">
34033 <features islongtable="true" longtabularalignment="center">
34034 <column alignment="left" valignment="top" width="0">
34035 <column alignment="left" valignment="top" width="85col%">
34036 <row interlinespace="2.5mm">
34037 <cell alignment="center" valignment="top" usebox="none">
34040 \begin_layout Plain Layout
34041 \begin_inset Graphics
34042 filename ../images/math-macro-remove-param.png
34043 rotateOrigin center
34052 <cell alignment="center" valignment="top" usebox="none">
34055 \begin_layout Plain Layout
34058 Edit\SpecialChar \menuseparator
34059 Math\SpecialChar \menuseparator
34061 \begin_inset space ~
34064 Definition\SpecialChar \menuseparator
34065 Remove Last Argument
34071 <row interlinespace="2.5mm">
34072 <cell alignment="center" valignment="top" usebox="none">
34075 \begin_layout Plain Layout
34076 \begin_inset Graphics
34077 filename ../images/math-macro-add-param.png
34078 rotateOrigin center
34087 <cell alignment="center" valignment="top" usebox="none">
34090 \begin_layout Plain Layout
34093 Edit\SpecialChar \menuseparator
34094 Math\SpecialChar \menuseparator
34096 \begin_inset space ~
34099 Definition\SpecialChar \menuseparator
34106 <row interlinespace="2.5mm">
34107 <cell alignment="center" valignment="top" usebox="none">
34110 \begin_layout Plain Layout
34111 \begin_inset Graphics
34112 filename ../images/math-macro-make-optional.png
34113 rotateOrigin center
34122 <cell alignment="center" valignment="top" usebox="none">
34125 \begin_layout Plain Layout
34128 Edit\SpecialChar \menuseparator
34129 Math\SpecialChar \menuseparator
34131 \begin_inset space ~
34134 Definition\SpecialChar \menuseparator
34135 Make First Non-Optional into
34136 \begin_inset Newline newline
34140 \begin_inset Phantom HPhantom
34143 \begin_layout Plain Layout
34146 Edit\SpecialChar \menuseparator
34147 Math\SpecialChar \menuseparator
34149 \begin_inset space ~
34152 Definition\SpecialChar \menuseparator
34164 <row interlinespace="2.5mm">
34165 <cell alignment="center" valignment="top" usebox="none">
34168 \begin_layout Plain Layout
34169 \begin_inset Graphics
34170 filename ../images/math-macro-make-nonoptional.png
34171 rotateOrigin center
34180 <cell alignment="center" valignment="top" usebox="none">
34183 \begin_layout Plain Layout
34186 Edit\SpecialChar \menuseparator
34187 Math\SpecialChar \menuseparator
34189 \begin_inset space ~
34192 Definition\SpecialChar \menuseparator
34193 Make Last Optional into
34194 \begin_inset Newline newline
34198 \begin_inset Phantom HPhantom
34201 \begin_layout Plain Layout
34204 Edit\SpecialChar \menuseparator
34205 Math\SpecialChar \menuseparator
34207 \begin_inset space ~
34210 Definition\SpecialChar \menuseparator
34216 Non-Optional Argument
34222 <row interlinespace="2.5mm">
34223 <cell alignment="center" valignment="top" usebox="none">
34226 \begin_layout Plain Layout
34227 \begin_inset Graphics
34228 filename ../images/math-macro-remove-optional-param.png
34229 rotateOrigin center
34238 <cell alignment="center" valignment="top" usebox="none">
34241 \begin_layout Plain Layout
34244 Edit\SpecialChar \menuseparator
34245 Math\SpecialChar \menuseparator
34247 \begin_inset space ~
34250 Definition\SpecialChar \menuseparator
34251 Remove Optional Argument
34257 <row interlinespace="2.5mm">
34258 <cell alignment="center" valignment="top" usebox="none">
34261 \begin_layout Plain Layout
34262 \begin_inset Graphics
34263 filename ../images/math-macro-add-optional-param.png
34264 rotateOrigin center
34273 <cell alignment="center" valignment="top" usebox="none">
34276 \begin_layout Plain Layout
34279 Edit\SpecialChar \menuseparator
34280 Math\SpecialChar \menuseparator
34282 \begin_inset space ~
34285 Definition\SpecialChar \menuseparator
34286 Insert Optional Argument
34292 <row interlinespace="2.5mm">
34293 <cell alignment="center" valignment="top" usebox="none">
34296 \begin_layout Plain Layout
34297 \begin_inset Graphics
34298 filename ../images/math-macro-remove-greedy-param.png
34299 rotateOrigin center
34308 <cell alignment="center" valignment="top" usebox="none">
34311 \begin_layout Plain Layout
34314 Edit\SpecialChar \menuseparator
34315 Math\SpecialChar \menuseparator
34317 \begin_inset space ~
34320 Definition\SpecialChar \menuseparator
34321 Remove Last Argument
34322 \begin_inset Newline newline
34326 \begin_inset Phantom HPhantom
34329 \begin_layout Plain Layout
34332 Edit\SpecialChar \menuseparator
34333 Math\SpecialChar \menuseparator
34335 \begin_inset space ~
34338 Definition\SpecialChar \menuseparator
34344 Spitting Out To The Right
34350 <row interlinespace="2.5mm">
34351 <cell alignment="center" valignment="top" usebox="none">
34354 \begin_layout Plain Layout
34355 \begin_inset Graphics
34356 filename ../images/math-macro-append-greedy-param.png
34357 rotateOrigin center
34366 <cell alignment="center" valignment="top" usebox="none">
34369 \begin_layout Plain Layout
34372 Edit\SpecialChar \menuseparator
34373 Math\SpecialChar \menuseparator
34375 \begin_inset space ~
34378 Definition\SpecialChar \menuseparator
34380 \begin_inset Newline newline
34384 \begin_inset Phantom HPhantom
34387 \begin_layout Plain Layout
34390 Edit\SpecialChar \menuseparator
34391 Math\SpecialChar \menuseparator
34393 \begin_inset space ~
34396 Definition\SpecialChar \menuseparator
34402 Eating From The Right
34408 <row interlinespace="2.5mm">
34409 <cell alignment="center" valignment="top" usebox="none">
34412 \begin_layout Plain Layout
34413 \begin_inset Graphics
34414 filename ../images/math-macro-add-greedy-optional-param.png
34415 rotateOrigin center
34424 <cell alignment="center" valignment="top" usebox="none">
34427 \begin_layout Plain Layout
34430 Edit\SpecialChar \menuseparator
34431 Math\SpecialChar \menuseparator
34433 \begin_inset space ~
34436 Definition\SpecialChar \menuseparator
34437 Append Optional Argument
34438 \begin_inset Newline newline
34442 \begin_inset Phantom HPhantom
34445 \begin_layout Plain Layout
34448 Edit\SpecialChar \menuseparator
34449 Math\SpecialChar \menuseparator
34451 \begin_inset space ~
34454 Definition\SpecialChar \menuseparator
34460 Eating From The Right
34473 \begin_layout Standard
34474 \begin_inset Newpage newpage
34480 \begin_layout Section
34482 \begin_inset Index idx
34485 \begin_layout Plain Layout
34494 \begin_layout Subsection
34496 \begin_inset Index idx
34499 \begin_layout Plain Layout
34508 \begin_layout Standard
34509 Negative numbers often look ugly in formulas because the minus sign before
34510 the number is set with the same length as the minus operator sign.
34511 When writing the negative number in normal text, the minus sign appears
34515 \begin_layout Standard
34516 Thus, the problem disappears when converting the minus sign to mathematical
34520 \begin_layout Standard
34521 An example to visualize the problem:
34524 \begin_layout Standard
34526 \begin_inset Tabular
34527 <lyxtabular version="3" rows="3" columns="2">
34528 <features tabularvalignment="middle">
34529 <column alignment="right" valignment="top" width="0">
34530 <column alignment="left" valignment="top" width="0">
34532 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34535 \begin_layout Plain Layout
34541 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
34544 \begin_layout Plain Layout
34552 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34555 \begin_layout Plain Layout
34561 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34564 \begin_layout Plain Layout
34565 \begin_inset Formula $x=-2$
34575 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34578 \begin_layout Plain Layout
34584 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34587 \begin_layout Plain Layout
34588 \begin_inset Formula $x=\textrm{-}2$
34604 \begin_layout Subsection
34605 Comma as decimal Separator
34606 \begin_inset Index idx
34609 \begin_layout Plain Layout
34618 \begin_layout Standard
34619 In LaTeX a comma inside a formula is used, according to the English convention,
34620 as number group separator.
34621 So there will be space added behind all commas in formulas.
34624 \begin_layout Standard
34625 To avoid this, the comma is highlighted and changed to mathematical text
34635 \begin_layout Standard
34636 To use all formula commas in the document as decimal separator, the file
34645 \begin_layout Plain Layout
34650 is part of the LaTeX-package
34655 \begin_inset Index idx
34658 \begin_layout Plain Layout
34663 \begin_layout Plain Layout
34683 \begin_inset Index idx
34686 \begin_layout Plain Layout
34692 is loaded with the LaTeX-preamble line
34695 \begin_layout Standard
34703 \begin_layout Subsection
34705 \begin_inset CommandInset label
34707 name "sub:Physical-Vectors"
34712 \begin_inset Index idx
34715 \begin_layout Plain Layout
34724 \begin_layout Standard
34725 Predefined vectors are offered by the LaTeX-package
34730 \begin_inset Index idx
34733 \begin_layout Plain Layout
34739 that is loaded with the LaTeX-preamble line
34742 \begin_layout Standard
34750 \begin_layout Standard
34754 \begin_layout Plain Layout
34764 \begin_inset Note Note
34767 \begin_layout Plain Layout
34768 The following table will only be displayed when the LaTeX-package
34780 \begin_layout Standard
34781 The following commands are defined:
34784 \begin_layout Standard
34786 \begin_inset Tabular
34787 <lyxtabular version="3" rows="4" columns="2">
34788 <features tabularvalignment="middle">
34789 <column alignment="center" valignment="top" width="0">
34790 <column alignment="center" valignment="top" width="0">
34792 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34795 \begin_layout Plain Layout
34801 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34804 \begin_layout Plain Layout
34812 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34815 \begin_layout Plain Layout
34825 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34828 \begin_layout Plain Layout
34829 \begin_inset Formula $\Bra{\psi}$
34839 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34842 \begin_layout Plain Layout
34852 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34855 \begin_layout Plain Layout
34856 \begin_inset Formula $\Ket{\psi}$
34866 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34869 \begin_layout Plain Layout
34881 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34884 \begin_layout Plain Layout
34885 \begin_inset Formula $\Braket{\psi|\phi}$
34901 \begin_layout Standard
34908 assures that all vertical bars are set in the size of the surrounding brackets:
34909 \begin_inset Formula \[
34910 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}
34919 \begin_layout Plain Layout
34929 \begin_inset Note Note
34932 \begin_layout Plain Layout
34933 The following will be displayed when the LaTeX-package
34945 \begin_layout Standard
34946 You need to install the LaTeX-package
34950 to see the rest of this subsection in the output.
34953 \begin_layout Standard
34957 \begin_layout Plain Layout
34969 \begin_layout Standard
34976 can also be achieved using the command
34982 , that is described in
34983 \begin_inset CommandInset ref
34985 reference "sub:Automatic-Bracket-Size"
34992 \begin_layout Subsection
34993 Self-defined Fractions
34994 \begin_inset CommandInset label
34996 name "sub:Self-defined-Fractions"
35001 \begin_inset Index idx
35004 \begin_layout Plain Layout
35005 Fractions ! self-defined
35013 \begin_layout Standard
35014 To define custom commands for fractions, the command
35021 \begin_inset Index idx
35024 \begin_layout Plain Layout
35032 is used in the following scheme:
35035 \begin_layout Standard
35048 bracket}{fraction bar thickness}{style}
35049 \begin_inset Newline newline
35053 \begin_inset Phantom HPhantom
35056 \begin_layout Plain Layout
35066 {numerator}{denominator}
35069 \begin_layout Standard
35070 The style is a number in the range of 0
35071 \begin_inset space \thinspace{}
35075 \begin_inset space \thinspace{}
35081 \begin_layout Standard
35083 \begin_inset Tabular
35084 <lyxtabular version="3" rows="5" columns="2">
35085 <features tabularvalignment="middle">
35086 <column alignment="center" valignment="top" width="0">
35087 <column alignment="center" valignment="top" width="0">
35089 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35092 \begin_layout Plain Layout
35098 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35101 \begin_layout Plain Layout
35109 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35112 \begin_layout Plain Layout
35118 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35121 \begin_layout Plain Layout
35122 display style formula
35129 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35132 \begin_layout Plain Layout
35138 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35141 \begin_layout Plain Layout
35149 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35152 \begin_layout Plain Layout
35158 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35161 \begin_layout Plain Layout
35169 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35172 \begin_layout Plain Layout
35178 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35181 \begin_layout Plain Layout
35195 \begin_layout Standard
35196 When no style is given, the size is adjusted to the surrounding environment
35197 like for the command
35206 \begin_layout Standard
35207 When no fraction bar thickness is given, the predefined value of 0.4
35208 \begin_inset space \thinspace{}
35214 \begin_layout Standard
35215 \begin_inset VSpace medskip
35218 For example, the commands
35231 \begin_inset CommandInset ref
35233 reference "sub:Fractions"
35237 are defined with the commands
35240 \begin_layout Standard
35249 genfrac{}{}{}{0}{#1}{#2}}
35252 \begin_layout Standard
35256 \begin_layout Standard
35265 genfrac{(}{)}{0pt}{1}{#1}{#2}}
35268 \begin_layout Standard
35269 \begin_inset VSpace medskip
35272 To define a fraction where the fraction bar thickness can be given as optional
35273 argument, the following line is inserted to the LaTeX-preamble:
35276 \begin_layout Standard
35285 genfrac{}{}{#1}{}{#2}{#3}}
35288 \begin_layout Standard
35290 \begin_inset Formula \begin{align*}
35291 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
35292 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
35297 As one can see, the distance of the numerator and the denominator to the
35298 fraction bar is round about three times the bar thickness.
35301 \begin_layout Subsection
35303 \begin_inset Index idx
35306 \begin_layout Plain Layout
35315 \begin_layout Standard
35316 To cancel formulas or formula parts, the LaTeX-package
35321 \begin_inset Index idx
35324 \begin_layout Plain Layout
35330 has to be loaded with the LaTeX-preamble line
35333 \begin_layout Standard
35338 usepackage[samesize]{cancel}
35341 \begin_layout Standard
35345 \begin_layout Plain Layout
35355 \begin_inset Note Note
35358 \begin_layout Plain Layout
35359 The following table will only be displayed when the LaTeX-package
35371 \begin_layout Standard
35372 There are four ways to cancel formulas:
35375 \begin_layout Standard
35377 \begin_inset Tabular
35378 <lyxtabular version="3" rows="5" columns="2">
35379 <features tabularvalignment="middle">
35380 <column alignment="center" valignment="top" width="0">
35381 <column alignment="center" valignment="top" width="0">
35383 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35386 \begin_layout Plain Layout
35392 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35395 \begin_layout Plain Layout
35397 \begin_inset Note Note
35400 \begin_layout Plain Layout
35407 are used here as spacer.
35419 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35422 \begin_layout Plain Layout
35431 \begin_layout Plain Layout
35445 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35448 \begin_layout Plain Layout
35449 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
35459 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35462 \begin_layout Plain Layout
35471 \begin_layout Plain Layout
35485 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35488 \begin_layout Plain Layout
35489 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
35499 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35502 \begin_layout Plain Layout
35511 \begin_layout Plain Layout
35525 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35528 \begin_layout Plain Layout
35529 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
35539 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35542 \begin_layout Plain Layout
35546 \begin_inset Formula $\to$
35557 \begin_layout Plain Layout
35571 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35574 \begin_layout Plain Layout
35575 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
35591 \begin_layout Standard
35598 is especially suitable to visualize the reduction of fractions within formulas:
35599 \begin_inset Formula \[
35600 \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}}}
35608 \begin_layout Standard
35612 \begin_layout Plain Layout
35622 \begin_inset Note Note
35625 \begin_layout Plain Layout
35626 The following will be displayed when the LaTeX-package
35638 \begin_layout Standard
35639 You need to install the LaTeX-package
35643 to see the rest of this subsection in the output.
35646 \begin_layout Standard
35650 \begin_layout Plain Layout
35662 \begin_layout Subsection
35663 Formulas in Section Headings
35664 \begin_inset CommandInset label
35666 name "sub:Formulas-in-Section"
35671 \begin_inset Index idx
35674 \begin_layout Plain Layout
35675 Formula ! in section headings
35683 \begin_layout Standard
35684 When formulas are used in section headings, the following has to be taken
35688 \begin_layout Standard
35689 \begin_inset Note Greyedout
35692 \begin_layout Plain Layout
35698 \begin_inset Index idx
35701 \begin_layout Plain Layout
35702 Packages ! hyperref
35707 support is enabled in the document settings dialog under
35710 \begin_inset space ~
35715 , PDF-bookmarks are created for every section heading in the table of contents.
35716 If a section heading contains formulas, they are incorrectly displayed
35717 in the bookmark text, because formulas in bookmarks infringe the PDF convention
35726 \begin_layout Standard
35727 Both problems can be solved by inserting at the end of the section heading
35728 a short title with the menu
35730 Insert\SpecialChar \menuseparator
35732 \begin_inset space ~
35738 Short titles are used as alternative for multiline section headings to
35739 keep the table of contents clearly arranged.
35740 Only the short title appears in the table of contents and therefore also
35741 in the PDF-bookmark.
35744 \begin_layout Standard
35745 When formulas should be used in the table of contents but
35749 is used, one can use the following command in TeX-mode:
35752 \begin_layout Standard
35757 texorpdfstring{part}{alternative}
35758 \begin_inset Index idx
35761 \begin_layout Plain Layout
35772 \begin_layout Standard
35773 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
35774 This can be characters, formulas, footnotes, but also cross-references.
35775 The alternative is used instead of the part for the bookmark.
35778 \begin_layout Standard
35779 Here are two example headings:
35780 \begin_inset VSpace -3mm
35787 \begin_layout Plain Layout
35799 \begin_layout Subsubsection
35800 Heading without formula in table of contents
35801 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35805 \begin_inset Argument
35808 \begin_layout Plain Layout
35809 Heading without formula in table of contents
35817 \begin_layout Subsubsection
35818 Heading with formula in table of contents
35822 \begin_layout Plain Layout
35832 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35839 \begin_layout Plain Layout
35849 \begin_layout Standard
35853 \begin_layout Plain Layout
35862 In the first heading a short title was used, in the second one
35871 \begin_layout Standard
35872 To get the same formatting as for the other headings, the complete heading
35881 \begin_layout Plain Layout
35883 \begin_inset CommandInset ref
35885 reference "sub:Bold-Formulas"
35897 \begin_layout Subsection
35898 Formulas in multi-column Text
35899 \begin_inset Index idx
35902 \begin_layout Plain Layout
35903 Formula ! in multi-column text
35911 \begin_layout Standard
35912 Formulas in multi-column text are often too wide to fit into a column and
35913 thus need to be set over the whole page width.
35914 This is done by using the LaTeX-package
35922 \begin_layout Plain Layout
35927 is part of every LaTeX standard installation.
35933 \begin_inset Index idx
35936 \begin_layout Plain Layout
35937 Packages ! multicol
35942 , that is loaded with the LaTeX-preamble line
35945 \begin_layout Standard
35950 usepackage{multicol}
35953 \begin_layout Standard
35954 \begin_inset Note Greyedout
35957 \begin_layout Plain Layout
35958 Note herby that the setting
35961 \begin_inset space ~
35968 Document\SpecialChar \menuseparator
35974 \begin_inset space ~
35994 \begin_layout Standard
35995 Before the multi-column text the command
35998 \begin_layout Standard
36003 begin{multicols}{column number}
36006 \begin_layout Standard
36007 is written in TeX-mode.
36008 The column number is a number in the range of 2
36009 \begin_inset space \thinspace{}
36013 \begin_inset space \thinspace{}
36017 Before the formula the multi-column text is ended by inserting the command
36020 \begin_layout Standard
36028 \begin_layout Standard
36032 \begin_layout Standard
36033 Due to the command some space is automatically added before the formula.
36035 \begin_inset space \thinspace{}
36038 mm vertical space is inserted before the formula.
36039 When the formula style
36045 \begin_layout Plain Layout
36047 \begin_inset CommandInset ref
36049 reference "sec:Formula-Styles"
36061 \begin_inset space \thinspace{}
36064 mm space is inserted instead.
36067 \begin_layout Standard
36068 As example a multi-column text with a displayed formula:
36071 \begin_layout Standard
36077 \begin_layout Plain Layout
36081 begin{multicols}{2}
36086 Das Spektrum wird fouriertransformiert.
36087 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
36088 , Lösungsmittel) zu trennen.
36089 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
36090 nun das Aussehen des Ausgangssignals.
36091 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
36092 über alle Phasen integrieren muss.
36094 \begin_inset Formula $S$
36097 unser normiertes Ausgangssignal und
36098 \begin_inset Formula $P$
36101 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
36105 \begin_layout Plain Layout
36115 \begin_inset VSpace -6mm
36119 \begin_inset Formula \begin{equation}
36120 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
36129 \begin_layout Plain Layout
36133 begin{multicols}{2}
36139 \begin_inset Formula $S_{0}$
36142 das Signal ohne Gradient ist und die Normierungsbedingung
36143 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
36147 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
36149 \begin_inset Formula $\nicefrac{\pi}{2}$
36153 \begin_inset space \thinspace{}
36156 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
36157 das Signal zusätzlich abschwächt.
36158 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
36160 \begin_inset Formula $T_{2}$
36166 \begin_layout Standard
36172 \begin_layout Plain Layout
36184 \begin_layout Subsection
36185 Formulas with Description of Variables
36186 \begin_inset Index idx
36189 \begin_layout Plain Layout
36190 Formula ! with description of variables
36198 \begin_layout Standard
36199 To describe variables within a formula, like in formula
36200 \begin_inset CommandInset ref
36202 reference "eq:within"
36211 \begin_inset Formula $n$
36215 \begin_inset space ~
36218 matrix is used with left aligned columns for the
36219 \begin_inset Formula $n$
36226 \begin_layout Plain Layout
36228 \begin_inset CommandInset ref
36230 reference "sec:Matrices"
36239 To set the description in a smaller size, before the matrix e.
36240 \begin_inset space \thinspace{}
36244 \begin_inset space \space{}
36257 \begin_layout Plain Layout
36259 \begin_inset CommandInset ref
36261 reference "sub:Font-Sizes"
36273 \begin_layout Standard
36274 When the formula style
36280 \begin_layout Plain Layout
36282 \begin_inset CommandInset ref
36284 reference "sec:Formula-Styles"
36305 \begin_layout Plain Layout
36312 only works in formulas with the style
36317 \begin_inset CommandInset ref
36319 reference "sub:Variable-Space"
36328 is inserted before and after the matrix to have the same separation of
36329 the matrix from the equation and the side margin.
36332 \begin_layout Standard
36333 When the formula style
36337 is used, the method described in
36338 \begin_inset CommandInset ref
36340 reference "sub:Flalign-Environment"
36344 is used to indent formulas.
36346 \begin_inset CommandInset ref
36348 reference "eq:within"
36352 consists of five columns whereas in the first two columns contain the equation,
36353 the third the matrix and the last one an empty TeX-brace.
36354 \begin_inset Formula \begin{flalign}
36355 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
36356 \rho & \textrm{density}\\
36357 V & \textrm{volume}\\
36358 g & \textrm{gravitational acceleration}
36359 \end{array} & & {}\label{eq:within}
36367 \begin_layout Subsection
36368 Upright small Greek Letters
36369 \begin_inset CommandInset label
36371 name "sub:Upright-small-Greek"
36376 \begin_inset Index idx
36379 \begin_layout Plain Layout
36380 Greek letters ! upright
36388 \begin_layout Standard
36389 Most of the math fonts only provide italic small Greek letters.
36390 But for symbols of elementary particles like pions and neutrinos, upright
36391 Greek letters are needed.
36400 \begin_layout Plain Layout
36405 is part of the LaTeX-package
36410 \begin_inset Index idx
36413 \begin_layout Plain Layout
36418 \begin_layout Plain Layout
36438 \begin_inset Index idx
36441 \begin_layout Plain Layout
36447 that is loaded with the LaTeX-preamble line
36450 \begin_layout Standard
36455 usepackage{upgreek}
36458 \begin_layout Standard
36464 \begin_layout Plain Layout
36474 \begin_inset Note Note
36477 \begin_layout Plain Layout
36478 The following table will only be displayed when the LaTeX-package
36487 They are created when the command for a small Greek letters is started
36493 For example the command
36500 \begin_inset Formula $\uptau$
36506 \begin_layout Standard
36507 With these commands reactions of elementary particles can be typeset:
36508 \begin_inset Formula \[
36509 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
36517 \begin_layout Standard
36518 The upright letters are more bold and wider than the italic ones.
36519 They should therefore not be used for units like
36520 \begin_inset Quotes eld
36524 \begin_inset Quotes erd
36530 \begin_layout Standard
36534 \begin_layout Plain Layout
36544 \begin_inset Note Note
36547 \begin_layout Plain Layout
36548 The following will be displayed when the LaTeX-package
36560 \begin_layout Standard
36561 You need to install the LaTeX-package
36565 to see the rest of this subsection in the output.
36568 \begin_layout Standard
36572 \begin_layout Plain Layout
36584 \begin_layout Subsection
36585 Text Characters in Formulas
36586 \begin_inset CommandInset label
36588 name "sub:Text-Characters-in"
36593 \begin_inset Index idx
36596 \begin_layout Plain Layout
36605 \begin_layout Standard
36606 In some cases you might want to insert text characters directly into formulas.
36607 When for example the centered dot · is often used in formulas like
36608 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
36611 , one would have to insert the command
36621 \begin_layout Plain Layout
36623 \begin_inset CommandInset ref
36625 reference "sub:Binary-Operators"
36634 all the time, because this character is defined in all encodings as text
36636 But the encoding can be changed by this LaTeX-preamble line:
36639 \begin_layout Standard
36644 Declare Inputtext{183}{
36654 f\SpecialChar \textcompwordmark{}
36658 \begin_layout Standard
36659 The character encoding (menu
36661 Document\SpecialChar \menuseparator
36662 Settings\SpecialChar \menuseparator
36665 ) specifies what character appears when a keyboard key is pressed.
36666 When the key for the character '·' is pressed, internally the command
36673 But this command is not available in a formula so that you would get LaTeX-erro
36675 With the changed encoding the right command is chosen automatically, depending
36676 on if the character was inserted into a formula or not.
36679 \begin_layout Standard
36680 The encoding of several characters is saved in definition files.
36681 Fore example the encoding
36685 is defined in the file
36689 that is in the installation folder of LaTeX.
36690 Encodings should only be changed via the LaTeX-preamble and not in the
36692 Otherwise own documents could not be edited by other LyX users working
36693 on other computers.
36696 \begin_layout Standard
36697 \begin_inset VSpace medskip
36700 Besides the centered dot, in this document the degree sign ° is defined
36701 with the following LaTeX-preamble line so that it can directly be inserted
36705 \begin_layout Standard
36710 DeclareInputtext{176}{
36720 f\SpecialChar \textcompwordmark{}
36724 \begin_layout Standard
36725 \begin_inset Newpage newpage
36731 \begin_layout Section
36734 \begin_inset Index idx
36737 \begin_layout Plain Layout
36746 \begin_layout Standard
36747 This section is a summary of the most important typographic rules, listed
36752 \begin_layout Plain Layout
36753 This collection was partly taken from the German semi-official dictionary
36755 \begin_inset Quotes eld
36759 \begin_inset Quotes erd
36763 \begin_inset CommandInset citation
36769 that lists some of the ISO rules.
36770 More rules are listed in
36771 \begin_inset CommandInset citation
36785 \begin_layout Itemize
36794 \begin_layout Plain Layout
36795 done with font styles, see
36796 \begin_inset CommandInset ref
36798 reference "sub:Font-Styles"
36807 , no matter if they appear in italic text: 30
36808 \begin_inset space \thinspace{}
36812 \begin_inset Newline newline
36815 Between the value and the unit is the smallest space, see
36816 \begin_inset CommandInset ref
36818 reference "sub:Predefined-Space"
36823 \begin_inset Newline newline
36826 This convention is automatically fulfilled when the command
36833 When it is entered to a formula, two boxes appear.
36834 In the first one the value is inserted, in the second one the unit, and
36836 \begin_inset Formula $\unit[30]{km/h}$
36840 \begin_inset space \thinspace{}
36850 is not a real LaTeX command but the command
36856 , therefore you cannot use it in TeX code.
36859 \begin_layout Itemize
36860 Percent and perthousand signs are set like physical units:
36861 \begin_inset Newline newline
36865 \begin_inset space \thinspace{}
36871 \begin_layout Itemize
36872 The degree sign follows directly on the value: 15°, but not when it is used
36874 \begin_inset space \thinspace{}
36880 \begin_layout Itemize
36881 In numbers with more than four digits the smallest space is inserted before
36882 every third digit to group them:
36892 \begin_inset space \thinspace{}
36896 \begin_inset space \thinspace{}
36902 \begin_layout Itemize
36903 For dimensions like 120×90×40
36904 \begin_inset space \thinspace{}
36907 cm the multiplication sign
36908 \begin_inset Quotes eld
36912 \begin_inset Quotes erd
36916 It is available either via the command
36924 Insert\SpecialChar \menuseparator
36925 Special Character\SpecialChar \menuseparator
36931 \begin_layout Itemize
36932 Functions with names consisting of several letters are set upright to avoid
36934 \begin_inset CommandInset ref
36936 reference "sub:Predefined-Functions"
36943 \begin_layout Itemize
36944 Indices consisting of several letters, are set upright:
36945 \begin_inset Formula $E_{\mathrm{kin}}$
36949 \begin_inset Newline newline
36952 Components of matrices are set italic:
36953 \begin_inset Formula $\hat{H}_{kl}$
36959 \begin_layout Itemize
36960 The differentiation/integration operator 'd', the Euler's number 'e' and
36961 the imaginary unit 'i' should be set upright, to avoid mixing them up with
36965 \begin_layout Itemize
36966 The character that denotes a
36970 transformation is inserted either by the command
36978 \begin_layout Plain Layout
36991 Insert\SpecialChar \menuseparator
36992 Special Character\SpecialChar \menuseparator
36993 Symbols\SpecialChar \menuseparator
36995 \begin_inset space ~
37001 \begin_inset Formula $\mathscr{F}$
37007 \begin_layout Standard
37008 \begin_inset Newpage newpage
37014 \begin_layout Section
37016 \begin_inset Index idx
37019 \begin_layout Plain Layout
37028 \begin_layout Standard
37029 Some characters and symbols can be created with several commands.
37030 Here is a list of the synonym commands:
37033 \begin_layout Standard
37034 \begin_inset VSpace bigskip
37038 \begin_inset space \hfill{}
37042 \begin_inset Tabular
37043 <lyxtabular version="3" rows="12" columns="2">
37044 <features tabularvalignment="middle">
37045 <column alignment="center" valignment="top" width="0pt">
37046 <column alignment="center" valignment="top" width="0pt">
37048 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37051 \begin_layout Plain Layout
37057 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37060 \begin_layout Plain Layout
37062 \begin_inset Note Note
37065 \begin_layout Plain Layout
37072 is only used as spacer.
37084 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37087 \begin_layout Plain Layout
37095 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37098 \begin_layout Plain Layout
37102 \begin_layout Plain Layout
37115 \begin_layout Plain Layout
37129 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37132 \begin_layout Plain Layout
37140 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37143 \begin_layout Plain Layout
37153 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37156 \begin_layout Plain Layout
37164 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37167 \begin_layout Plain Layout
37177 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37180 \begin_layout Plain Layout
37188 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37191 \begin_layout Plain Layout
37199 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37202 \begin_layout Plain Layout
37210 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37213 \begin_layout Plain Layout
37221 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37224 \begin_layout Plain Layout
37232 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37235 \begin_layout Plain Layout
37245 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37248 \begin_layout Plain Layout
37256 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37259 \begin_layout Plain Layout
37269 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37272 \begin_layout Plain Layout
37280 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37283 \begin_layout Plain Layout
37293 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37296 \begin_layout Plain Layout
37304 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37307 \begin_layout Plain Layout
37317 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37320 \begin_layout Plain Layout
37328 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37331 \begin_layout Plain Layout
37339 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37342 \begin_layout Plain Layout
37350 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37353 \begin_layout Plain Layout
37365 \begin_inset space \hfill{}
37369 \begin_inset Tabular
37370 <lyxtabular version="3" rows="12" columns="2">
37371 <features tabularvalignment="middle">
37372 <column alignment="center" valignment="top" width="0pt">
37373 <column alignment="center" valignment="top" width="0pt">
37375 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37378 \begin_layout Plain Layout
37384 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37387 \begin_layout Plain Layout
37395 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37398 \begin_layout Plain Layout
37406 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37409 \begin_layout Plain Layout
37421 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37424 \begin_layout Plain Layout
37432 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37435 \begin_layout Plain Layout
37445 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37448 \begin_layout Plain Layout
37456 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37459 \begin_layout Plain Layout
37469 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37472 \begin_layout Plain Layout
37480 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37483 \begin_layout Plain Layout
37491 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37494 \begin_layout Plain Layout
37502 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37505 \begin_layout Plain Layout
37513 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37516 \begin_layout Plain Layout
37524 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37527 \begin_layout Plain Layout
37537 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37540 \begin_layout Plain Layout
37548 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37551 \begin_layout Plain Layout
37561 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37564 \begin_layout Plain Layout
37572 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37575 \begin_layout Plain Layout
37585 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37588 \begin_layout Plain Layout
37596 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37599 \begin_layout Plain Layout
37609 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37612 \begin_layout Plain Layout
37620 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37623 \begin_layout Plain Layout
37633 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37636 \begin_layout Plain Layout
37644 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37647 \begin_layout Plain Layout
37661 \begin_inset space \hfill{}
37667 \begin_layout Standard
37668 \begin_inset Newpage newpage
37674 \begin_layout Bibliography
37675 \labelwidthstring References
37676 \begin_inset CommandInset bibitem
37677 LatexCommand bibitem
37689 The LaTeX Companion
37692 Addison Wesley, 2004
37695 \begin_layout Bibliography
37696 \labelwidthstring References
37697 \begin_inset CommandInset bibitem
37698 LatexCommand bibitem
37704 \begin_inset CommandInset href
37707 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
37711 of LaTeX's math abilities
37714 \begin_layout Bibliography
37715 \labelwidthstring References
37716 \begin_inset CommandInset bibitem
37717 LatexCommand bibitem
37723 \begin_inset CommandInset href
37726 target "ftp://ftp.ams.org/pub/tex/doc/amsmath/amsldoc.pdf"
37734 \begin_layout Plain Layout
37746 \begin_layout Bibliography
37747 \labelwidthstring References
37748 \begin_inset CommandInset bibitem
37749 LatexCommand bibitem
37755 \begin_inset CommandInset href
37758 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
37762 of all symbols available with LaTeX-packages
37765 \begin_layout Bibliography
37766 \labelwidthstring References
37767 \begin_inset CommandInset bibitem
37768 LatexCommand bibitem
37774 \begin_inset CommandInset href
37776 name "Documentation"
37777 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
37781 of the LaTeX-package
37786 \begin_inset Index idx
37789 \begin_layout Plain Layout
37790 Packages ! hyperref
37798 \begin_layout Bibliography
37799 \labelwidthstring References
37800 \begin_inset CommandInset bibitem
37801 LatexCommand bibitem
37807 \begin_inset CommandInset href
37809 name "Documentation"
37810 target "http://www.ctan.org/tex-archive/macros/latex/contrib/mhchem/mhchem.pdf"
37814 of the LaTeX-package
37819 \begin_inset Index idx
37822 \begin_layout Plain Layout
37831 \begin_layout Bibliography
37832 \labelwidthstring References
37833 \begin_inset CommandInset bibitem
37834 LatexCommand bibitem
37840 \begin_inset CommandInset href
37843 target "http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf"
37854 \begin_inset CommandInset ref
37856 reference "sub:Operator-Limits"
37861 \begin_inset Index idx
37864 \begin_layout Plain Layout
37875 \begin_layout Bibliography
37876 \labelwidthstring References
37877 \begin_inset CommandInset bibitem
37878 LatexCommand bibitem
37889 Auflage, Duden 2001
37892 \begin_layout Bibliography
37893 \labelwidthstring References
37894 \begin_inset CommandInset bibitem
37895 LatexCommand bibitem
37901 \begin_inset CommandInset href
37904 target "http://physics.nist.gov/Document/checklist.pdf"
37908 for reviewing manuscripts
37911 \begin_layout Standard
37912 \begin_inset CommandInset index_print
37913 LatexCommand printindex