1 #LyX 2.0 created this file. For more info see http://www.lyx.org/
7 % DO NOT ALTER THIS PREAMBLE!!!
9 % This preamble is designed to ensure that the file prints
10 % out as advertised. If you mess with this preamble,
11 % parts of this document may not print out as expected. If you
12 % have problems LaTeXing this file, please contact
13 % the documentation team
14 % email: lyx-docs@lists.lyx.org
20 % set fonts for nicer pdf view
21 \IfFileExists{lmodern.sty}
22 {\usepackage{lmodern}}{}
24 \fi % end if pdflatex is used
26 % Folgendes Problem lösen:
27 % Besteht die Kapitelnummer aus zu vielen Ziffern, wird die
28 % Kapitelüberschrift im Inhaltsverzeichnis direkt an oder über
29 % die Kapitelnummer geschrieben.
30 % Als Lösung wird mehr Platz zwischen Nummer und
31 % Überschrift eingefügt.
32 \renewcommand{\l@subsection}{\@dottedtocline{2}{1.5em}{2.8em}}
33 \renewcommand{\l@subsubsection}{\@dottedtocline{3}{4.3em}{3.6em}}
35 % To be able to enter the character ° and · directly in LyX,
37 \DeclareInputText{176}{\ifmmode^\circ\else\textdegree\fi}
38 \DeclareInputText{183}{\ifmmode\cdot\else\textperiodcentered\fi}
40 % increase link area for cross-references and autoname them,
41 \AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}}
43 \settowidth{\abc}{\space}
46 \renewcommand{\equationautorefname}{\hspace{-\abc}}
47 \renewcommand{\sectionautorefname}{sec.\negthinspace}
48 \renewcommand{\subsectionautorefname}{sec.\negthinspace}
49 \renewcommand{\subsubsectionautorefname}{sec.\negthinspace}}
52 % don't load packages twice
53 % see first footnote in sec. 9.3
54 \@ifundefined{textcolor}{\usepackage{color}}{}
56 % the pages of the TOC are numbered roman
57 % and a PDF-bookmark for the TOC is added
59 \let\myTOC\tableofcontents
60 \renewcommand{\tableofcontents}{%
62 \pdfbookmark[1]{\contentsname}{}
65 \pagenumbering{arabic}}
67 % insert additional vertical space of 1.5 mm between footnotes,
69 \renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
71 % provides caption formatting
72 \setkomafont{captionlabel}{\bfseries}
75 \usepackage[samesize]{cancel}
77 % enables calculation of values
80 % for multiple columns used in sec. 23.7
86 % for the Fourier transformation symbol
89 % define a color, used in sec.9.3
90 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
92 % declare operators (see sec. 10.4 and sec. 15.2)
93 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
94 \DeclareMathOperator{\sgn}{sgn}
96 \newcommand{\spce}{\textvisiblespace}
98 % example definitions for sec. 20.1
99 \newcommand{\gr}{\Longrightarrow}
100 \newcommand{\us}[1]{\underline{#1}}
101 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
102 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
103 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
105 % example macro from sec. 19.4
106 %\def\tagform@#1{\maketag@@@{|#1|}}
108 % macro from sec. 10.2
109 \def\clap#1{\hbox to 0pt{\hss #1\hss}}
110 \def\mathclap {\mathpalette \mathclapinternal}
111 \def\mathclapinternal #1#2{\clap{$\mathsurround =0pt #1{#2}$}}
114 % ------------------------------------
115 % used to check for needed LaTeX packages
118 % check for package eurosym
119 % used for the Euro symbol
121 \IfFileExists{eurosym.sty}
122 {\usepackage[gennarrow]{eurosym}
123 \setboolean{eurosym}{true}}
124 {\setboolean{eurosym}{false}}
126 % check for package braket
127 % used for physical vectors
129 \IfFileExists{braket.sty}
131 \setboolean{braket}{true}}
132 {\setboolean{braket}{false}}
134 % check for package cancel
136 \IfFileExists{cancel.sty}
138 \setboolean{cancel}{true}}
139 {\setboolean{cancel}{false}}
141 % check for package upgreek
143 \IfFileExists{upgreek.sty}
144 {\usepackage{upgreek}
145 \setboolean{upgreek}{true}}
146 {\setboolean{upgreek}{false}}
148 \options bibliography=totoc,index=totoc,BCOR7.5mm,titlepage,captions=tableheading
149 \use_default_options false
150 \maintain_unincluded_children false
152 \language_package default
157 \font_typewriter default
158 \font_default_family default
159 \use_non_tex_fonts false
166 \default_output_format default
168 \bibtex_command default
169 \index_command default
173 \pdf_title "LyX's Math Manual"
174 \pdf_author "LyX Team, Uwe Stöhr"
175 \pdf_subject "LyX-documentation about math"
176 \pdf_keywords "LyX, Mathed"
178 \pdf_bookmarksnumbered true
179 \pdf_bookmarksopen true
180 \pdf_bookmarksopenlevel 1
181 \pdf_breaklinks false
185 \pdf_pdfusetitle false
186 \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false"
196 \paperorientation portrait
199 \notefontcolor #0000ff
206 \paragraph_separation skip
208 \quotes_language english
211 \paperpagestyle plain
215 \tracking_changes false
216 \output_changes false
219 \html_be_strict false
225 LyX's detailed Math manual
233 \begin_layout Plain Layout
235 If you have comments or error corrections, please send them to the LyX Documenta
239 \begin_inset CommandInset href
241 name "lyx-docs@lists.lyx.org"
242 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
253 \begin_inset Note Note
256 \begin_layout Plain Layout
263 \begin_inset Newline newline
267 \begin_inset Newline newline
275 \begin_layout Standard
276 \begin_inset CommandInset toc
277 LatexCommand tableofcontents
284 \begin_layout Standard
285 \begin_inset Note Note
288 \begin_layout Plain Layout
289 To export this document to PDF, PS or DVI the LaTeX-packages
291 braket, cancel, eurosym,
302 If they are not installed the document can be export anyway but the sections
303 where the packages are required will not appear in the output.
308 ; if it is not installed, this file cannot be exported.
311 \begin_layout Plain Layout
312 The latest PDF-version of this document can be found here:
313 \begin_inset Newline newline
318 http://wiki.lyx.org/LyX/DocumentationDevelopment#Math
326 \begin_layout Standard
327 \begin_inset Newpage newpage
333 \begin_layout Section
337 \begin_layout Standard
338 This document explains LyX's math features and is furthermore a collection
339 of LaTeX-commands used for mathematical characters and constructs.
340 The explanations are designed for the usage of commands.
341 It is therefore required that you have read the section
352 \begin_layout Standard
353 Most of the characters and many constructs explained in this manual are
354 also accessible via the menu
358 \SpecialChar \menuseparator
374 But everybody who has to write lots of formulas will notice that it is
375 much faster to use commands instead of the math toolbar.
376 Therefore this manual is focused on commands but also mentions the correspondin
377 g toolbar buttons when available.
380 \begin_layout Standard
381 If not specially mentioned the commands are only available within formulas.
382 To be able to use all commands explained in this document, the option
386 must be used in the document settings (menu
388 Document\SpecialChar \menuseparator
389 Settings\SpecialChar \menuseparator
400 \begin_layout Plain Layout
403 Use AMS math package automatically
409 \begin_layout Plain Layout
418 -math when math constructs are found that are supported by LyX.
426 \begin_layout Standard
427 This document doesn't list all
431 \begin_layout Plain Layout
444 \begin_layout Plain Layout
449 \begin_layout Plain Layout
458 -math commands is in the file
461 \begin_inset CommandInset href
464 target "ftp://ctan.tug.org/tex-archive/macros/amstex/doc/amsguide.ps"
470 , which is part of every LaTeX standard installation.
475 for lucidity reasons.
478 \begin_layout Section
482 \begin_layout Standard
483 To create an inline formula
484 \begin_inset Index idx
487 \begin_layout Plain Layout
493 that is embedded into a text line, use one of the shortcuts
499 or the toolbar button
500 \begin_inset Graphics
501 filename ../images/math-mode.png
507 \begin_inset Newline newline
510 To create a display style formula
511 \begin_inset Index idx
514 \begin_layout Plain Layout
515 Formula ! display style
520 that will appear bigger and in an own paragraph, use one of these shortcuts:
530 \begin_layout Standard
531 To change a display style formula to an inline formula, set the cursor into
532 the formula and use one of the shortcuts
540 Edit\SpecialChar \menuseparator
541 Math\SpecialChar \menuseparator
545 The same way is used to change an inline formula to a display style formula.
548 \begin_layout Standard
549 To display parts of an inline formula in the size of a display style formula,
557 \begin_inset Index idx
560 \begin_layout Plain Layout
569 Then a new blue box appears in which the desired formula part is inserted.
572 \begin_layout Standard
573 Only inline formulas are allowed inside tables.
576 \begin_layout Standard
581 can be turned on in the menu
583 View\SpecialChar \menuseparator
587 When you click there on
588 \begin_inset Quotes eld
592 \begin_inset Quotes erd
595 the toolbar will be shown permanently at the bottom; this state is visualized
600 menu with a checkmark.
601 When you click in this state again on
602 \begin_inset Quotes eld
606 \begin_inset Quotes erd
617 is only shown when the cursor is within a formula; this state is visualized
618 by the renaming of the menu entry from
619 \begin_inset Quotes eld
623 \begin_inset Quotes erd
627 \begin_inset Quotes eld
635 \begin_inset Quotes erd
641 \begin_layout Standard
643 \begin_inset Index idx
646 \begin_layout Plain Layout
652 is invoked by pressing the toolbar button
653 \begin_inset Graphics
654 filename ../images/ert-insert.png
661 Insert\SpecialChar \menuseparator
666 \begin_layout Plain Layout
682 \begin_inset Note Note
685 \begin_layout Plain Layout
686 In LyX there are three
687 \begin_inset Quotes eld
691 \begin_inset Quotes erd
694 that appear in the output with sub- and superscript letters: TeX, LaTeX
698 \begin_layout Plain Layout
699 To avoid that these names are recognized as proper names, a TeX-brace pair
708 \begin_layout Standard
709 To change the LaTeX-preamble
710 \begin_inset Index idx
713 \begin_layout Plain Layout
721 Document\SpecialChar \menuseparator
722 Settings\SpecialChar \menuseparator
727 \begin_layout Plain Layout
743 \begin_layout Standard
744 To edit matrices, case differentiations and multiline formulas subsequently,
747 Edit\SpecialChar \menuseparator
752 Edit\SpecialChar \menuseparator
754 \begin_inset space \thinspace{}
758 \begin_inset space \thinspace{}
768 When lines and columns are swapped via the menu, the column or line where
769 the cursor is in is exchanged with the column to the right or the line
771 Is the cursor in the last column or row, the exchange is done with the
772 column to the left or the line above.
775 \begin_layout Standard
776 To write text in formulas
780 \begin_layout Plain Layout
781 For multiline formulas the command
788 \begin_inset CommandInset ref
790 reference "sub:Text-in-multiline"
804 \begin_inset Index idx
807 \begin_layout Plain Layout
814 \begin_inset Index idx
817 \begin_layout Plain Layout
824 This mode is invoked with the shortcut
830 or by the insertion of the command
837 \begin_inset Index idx
840 \begin_layout Plain Layout
849 The text appears black in LyX and can therefore be distinguished from the
850 other formula parts that appear blue.
851 In the output mathematical text is set upright, in contrary to other formula
855 \begin_layout Subsection*
859 \begin_layout Standard
860 Most of the LaTeX-commands for math constructs have the following scheme:
863 \begin_layout Standard
879 \begin_layout Standard
880 A command starts always with a backslash
881 \begin_inset Quotes gld
891 \begin_inset Quotes grd
895 To omit optional arguments, also omit the associated brackets.
896 The braces around the required arguments are named in this document as
898 \begin_inset Index idx
901 \begin_layout Plain Layout
908 If you add in a formula a left brace to a command name, LyX creates automatical
910 In all other cases TeX-braces are created in formulas with the command
918 TeX-braces appear red in LyX, in contrary to normal braces that appear
920 In TeX-mode no command is needed to get TeX-braces.
921 TeX-braces don't appear in the output.
924 \begin_layout Standard
925 When commands without arguments, like commands for symbols are entered in
926 TeX-mode, a space character must
930 be behind the command to end it.
931 This space doesn't appear in the output.
932 When the space should appear in the output, the space must be followed
933 by a protected space in normal text.
936 \begin_layout Standard
937 A protected space is inserted with
940 arg "space-insert protected"
946 \begin_layout Subsection*
947 \begin_inset Newpage newpage
953 \begin_layout Itemize
958 \begin_layout Plain Layout
959 This visible space character can be created with the command
966 \begin_inset Index idx
969 \begin_layout Plain Layout
977 , inserted in TeX-mode.
986 \begin_layout Plain Layout
999 denotes a space character to be input.
1002 \begin_layout Itemize
1004 \begin_inset Formula $\to$
1007 denotes the usage of the corresponding arrow key on the keyboard.
1010 \begin_layout Subsection*
1014 \begin_layout Standard
1016 \begin_inset Float table
1022 \begin_layout Plain Layout
1024 \begin_inset Caption
1026 \begin_layout Plain Layout
1027 \begin_inset CommandInset label
1029 name "tab:Available-units"
1041 \begin_layout Plain Layout
1043 \begin_inset Tabular
1044 <lyxtabular version="3" rows="13" columns="2">
1045 <features tabularvalignment="middle">
1046 <column alignment="center" valignment="top" width="0">
1047 <column alignment="center" valignment="top" width="0">
1049 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1052 \begin_layout Plain Layout
1058 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1061 \begin_layout Plain Layout
1069 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1072 \begin_layout Plain Layout
1078 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1081 \begin_layout Plain Layout
1089 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1092 \begin_layout Plain Layout
1098 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1101 \begin_layout Plain Layout
1109 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1112 \begin_layout Plain Layout
1118 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1121 \begin_layout Plain Layout
1123 \begin_inset space \thinspace{}
1127 \begin_inset space \thinspace{}
1137 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1140 \begin_layout Plain Layout
1146 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1149 \begin_layout Plain Layout
1151 \begin_inset space \thinspace{}
1155 \begin_inset space \thinspace{}
1165 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1168 \begin_layout Plain Layout
1174 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1177 \begin_layout Plain Layout
1179 \begin_inset space \thinspace{}
1183 \begin_inset space \thinspace{}
1193 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1196 \begin_layout Plain Layout
1202 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1205 \begin_layout Plain Layout
1207 \begin_inset space \thinspace{}
1211 \begin_inset space \thinspace{}
1221 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1224 \begin_layout Plain Layout
1230 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1233 \begin_layout Plain Layout
1235 \begin_inset space \thinspace{}
1239 \begin_inset space \thinspace{}
1249 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1252 \begin_layout Plain Layout
1258 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1261 \begin_layout Plain Layout
1263 \begin_inset space \thinspace{}
1267 \begin_inset Formula $\approx$
1271 \begin_inset space \thinspace{}
1281 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1284 \begin_layout Plain Layout
1290 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1293 \begin_layout Plain Layout
1295 \begin_inset space \thinspace{}
1299 \begin_inset space \thinspace{}
1309 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1312 \begin_layout Plain Layout
1318 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1321 \begin_layout Plain Layout
1325 \begin_inset Quotes eld
1331 \begin_inset Quotes erd
1341 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1344 \begin_layout Plain Layout
1350 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1353 \begin_layout Plain Layout
1355 \begin_inset Quotes eld
1363 \begin_inset Quotes erd
1373 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1376 \begin_layout Plain Layout
1382 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1385 \begin_layout Plain Layout
1387 \begin_inset space \thinspace{}
1391 \begin_inset Formula $\nicefrac{1}{18}$
1395 \begin_inset space \thinspace{}
1416 \begin_layout Standard
1417 \begin_inset Newpage newpage
1423 \begin_layout Section
1427 \begin_layout Subsection
1429 \begin_inset Index idx
1432 \begin_layout Plain Layout
1439 \begin_inset Index idx
1442 \begin_layout Plain Layout
1449 \begin_inset Index idx
1452 \begin_layout Plain Layout
1457 \begin_layout Plain Layout
1468 \begin_layout Plain Layout
1481 \begin_inset Index idx
1484 \begin_layout Plain Layout
1489 \begin_layout Plain Layout
1500 \begin_layout Plain Layout
1515 \begin_layout Standard
1516 Indices are created with an underscore
1517 \begin_inset Quotes eld
1521 \begin_inset Quotes erd
1524 or via the math toolbar button
1525 \begin_inset Graphics
1526 filename ../images/math-subscript.png
1531 , exponents with a caret
1532 \begin_inset Quotes eld
1536 \begin_inset Quotes erd
1539 or via the math toolbar button
1540 \begin_inset Graphics
1541 filename ../images/math-superscript.png
1549 \begin_layout Standard
1551 \begin_inset Tabular
1552 <lyxtabular version="3" rows="4" columns="2">
1553 <features tabularvalignment="middle">
1554 <column alignment="center" valignment="top" width="0pt">
1555 <column alignment="center" valignment="top" width="0pt">
1557 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1560 \begin_layout Plain Layout
1566 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1569 \begin_layout Plain Layout
1571 \begin_inset Note Note
1574 \begin_layout Plain Layout
1581 is only used as spacer.
1593 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1596 \begin_layout Plain Layout
1602 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1605 \begin_layout Plain Layout
1606 \begin_inset Formula $B_{V}$
1616 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1619 \begin_layout Plain Layout
1625 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1628 \begin_layout Plain Layout
1629 \begin_inset Formula $\raisebox{5mm}{}B^{V}$
1639 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1642 \begin_layout Plain Layout
1647 \begin_layout Plain Layout
1661 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1664 \begin_layout Plain Layout
1665 \begin_inset Formula $\raisebox{5mm}{}B^{A}$
1681 \begin_layout Standard
1682 As the caret is in some languages an accent, vowels will be accentuated
1683 in this case and not set as exponents
1687 \begin_layout Plain Layout
1688 Depending on the used keyboard settings this can also happen for other character
1695 To get in this case exponents, press
1699 after the caret as in the last example.
1702 \begin_layout Subsection
1704 \begin_inset CommandInset label
1706 name "sub:Fractions"
1711 \begin_inset Index idx
1714 \begin_layout Plain Layout
1723 \begin_layout Standard
1724 Fractions are generated with the command
1731 \begin_inset Index idx
1734 \begin_layout Plain Layout
1742 or via the math toolbar button
1743 \begin_inset Graphics
1744 filename ../images/math/frac.png
1750 The font size is adjusted automatically, depending on whether the fraction
1751 is in an inline or display style formula.
1752 With the math toolbar button
1753 \begin_inset Graphics
1754 filename ../images/math/frac-square.png
1759 you can select different fraction types.
1762 \begin_layout Standard
1770 \begin_inset Index idx
1773 \begin_layout Plain Layout
1781 a fraction can be created that has in any case the size of a display style
1790 \begin_inset Index idx
1793 \begin_layout Plain Layout
1801 the fraction appears always with the size of an inline formula.
1805 \begin_layout Standard
1806 A line with the fraction
1807 \begin_inset Formula $\frac{1}{2}$
1810 that was created with the command
1819 \begin_layout Standard
1820 A line with the fraction
1821 \begin_inset Formula $\dfrac{1}{2}$
1824 that was created with the command
1833 \begin_layout Standard
1835 \begin_inset Tabular
1836 <lyxtabular version="3" rows="4" columns="2">
1837 <features tabularvalignment="middle">
1838 <column alignment="center" valignment="top" width="0pt">
1839 <column alignment="center" valignment="top" width="0pt">
1841 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1844 \begin_layout Plain Layout
1850 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1853 \begin_layout Plain Layout
1855 \begin_inset Note Note
1858 \begin_layout Plain Layout
1865 is only used as spacer.
1877 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1880 \begin_layout Plain Layout
1887 \begin_layout Plain Layout
1897 \begin_inset Formula $\downarrow$
1905 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1908 \begin_layout Plain Layout
1909 \begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$
1919 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1922 \begin_layout Plain Layout
1929 \begin_layout Plain Layout
1939 \begin_inset Formula $\downarrow$
1947 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1950 \begin_layout Plain Layout
1951 \begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$
1961 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1964 \begin_layout Plain Layout
1971 \begin_layout Plain Layout
1984 \begin_layout Plain Layout
1999 \begin_layout Plain Layout
2009 \begin_inset Formula $\downarrow$
2013 \begin_inset Formula $\downarrow\downarrow$
2021 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2024 \begin_layout Plain Layout
2025 \begin_inset Formula $\raisebox{8mm}{}\dfrac{e^{\frac{1}{2}}}{3}\raisebox{-4mm}{}$
2041 \begin_layout Standard
2042 \begin_inset VSpace bigskip
2046 \begin_inset Newpage newpage
2049 For nested fractions the command
2056 \begin_inset Index idx
2059 \begin_layout Plain Layout
2069 \begin_inset VSpace -3mm
2075 \begin_layout Standard
2076 \begin_inset Formula
2078 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
2079 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}
2087 \begin_layout Standard
2088 The command for the example above is:
2091 \begin_layout Standard
2100 \begin_layout Plain Layout
2110 \begin_inset Formula $\downarrow$
2119 \begin_layout Plain Layout
2134 \begin_layout Plain Layout
2144 \begin_inset Formula $\downarrow$
2148 \begin_inset Formula $\downarrow$
2154 \begin_layout Standard
2155 \begin_inset VSpace medskip
2161 \begin_layout Standard
2168 sets the fraction always in the size of a displayed formula, also when
2169 it is part of another fraction.
2172 \begin_layout Standard
2173 It is possible to specify the alignment of the numerator.
2180 is used to left align it, the command
2193 centers the numerator.
2194 These fractions demonstrate the different alignments:
2197 \begin_layout Standard
2198 \begin_inset Formula $\cfrac[l]{A}{B+C}$
2202 \begin_inset Formula $\cfrac{A}{B+C}$
2206 \begin_inset Formula $\cfrac[r]{A}{B+C}$
2212 \begin_layout Standard
2213 \begin_inset Note Greyedout
2216 \begin_layout Plain Layout
2233 are no real LaTeX commands but represent the command
2237 cfrac[alignment]{numerator}{denominator}
2240 Therefore you cannot use them in TeX code.
2248 \begin_layout Standard
2249 \begin_inset VSpace medskip
2252 It is often advantageous to combine
2265 \begin_inset Formula
2267 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}
2275 \begin_layout Standard
2276 For inline fractions with a sloped fraction stroke you can use the command
2284 \begin_inset Index idx
2287 \begin_layout Plain Layout
2296 \begin_inset Formula $\nicefrac{5}{31}$
2306 \begin_inset Index idx
2309 \begin_layout Plain Layout
2318 \begin_inset Formula $\unitfrac{5}{31}$
2321 There is furthermore the command
2327 that offers to write a fraction in combination with a number:
2328 \begin_inset Formula $\unitfrac[2]{1}{3}$
2334 \begin_layout Standard
2335 \begin_inset Note Greyedout
2338 \begin_layout Plain Layout
2349 is not a real LaTeX command but the command
2350 \begin_inset Newline newline
2357 unitfrac[number]{numerator}{denominator}
2360 Therefore you cannot use it in TeX code.
2368 \begin_layout Standard
2369 How to define own fractions where the fraction stroke can be changed, is
2371 \begin_inset CommandInset ref
2373 reference "sub:Self-defined-Fractions"
2380 \begin_layout Subsection
2382 \begin_inset Index idx
2385 \begin_layout Plain Layout
2394 \begin_layout Standard
2395 Square roots are created with
2402 \begin_inset Index idx
2405 \begin_layout Plain Layout
2413 or the math toolbar button
2414 \begin_inset Graphics
2415 filename ../images/math/sqrt.png
2420 , all other roots with the command
2427 \begin_inset Index idx
2430 \begin_layout Plain Layout
2438 or with the math toolbar button
2439 \begin_inset Graphics
2440 filename ../images/math/root.png
2448 \begin_layout Standard
2450 \begin_inset Tabular
2451 <lyxtabular version="3" rows="3" columns="2">
2452 <features tabularvalignment="middle">
2453 <column alignment="center" valignment="top" width="0pt">
2454 <column alignment="center" valignment="top" width="0pt">
2456 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2459 \begin_layout Plain Layout
2465 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2468 \begin_layout Plain Layout
2470 \begin_inset Note Note
2473 \begin_layout Plain Layout
2480 is only used as spacer.
2492 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2495 \begin_layout Plain Layout
2502 \begin_layout Plain Layout
2516 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2519 \begin_layout Plain Layout
2520 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$
2530 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
2533 \begin_layout Plain Layout
2540 \begin_layout Plain Layout
2550 \begin_inset Formula $\downarrow$
2558 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
2561 \begin_layout Plain Layout
2562 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$
2578 \begin_layout Standard
2579 A square root can also be created with
2585 when the root index field is left empty.
2588 \begin_layout Standard
2589 With certain indices the distance to the root is too small, like in this
2591 \begin_inset Formula $\sqrt[\beta]{B}$
2595 \begin_inset Newline newline
2599 \begin_inset Formula $\beta$
2603 To avoid this, the commands
2610 \begin_inset Index idx
2613 \begin_layout Plain Layout
2628 \begin_inset Index idx
2631 \begin_layout Plain Layout
2639 are used with the following scheme:
2642 \begin_layout Standard
2656 \begin_layout Standard
2657 Distance is the number of Big Points (unit bp;
2658 \begin_inset Formula $\mathrm{72\, bp=1\, inch}$
2661 ), that the index should be moved to the left or top, resp..
2662 The commands are written to the index.
2663 This way the command
2664 \begin_inset Newline newline
2674 \begin_inset Formula $\to$
2680 \begin_inset Formula $\to$
2689 \begin_layout Plain Layout
2699 \begin_inset Formula $\to$
2703 \begin_inset Newline newline
2708 produces a correct typeset formula:
2709 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2715 \begin_layout Subsection
2716 Binomial Coefficients
2717 \begin_inset Index idx
2720 \begin_layout Plain Layout
2721 Binomial coefficients
2729 \begin_layout Standard
2730 Binomial coefficients are inserted with the command
2737 \begin_inset Index idx
2740 \begin_layout Plain Layout
2748 or with the submenu of the math toolbar button
2749 \begin_inset Graphics
2750 filename ../images/math/frac-square.png
2756 Analog to fractions (
2775 \begin_inset Index idx
2778 \begin_layout Plain Layout
2793 \begin_inset Index idx
2796 \begin_layout Plain Layout
2805 For other brackets around binomial coeficients there are the commands
2812 \begin_inset Index idx
2815 \begin_layout Plain Layout
2830 \begin_inset Index idx
2833 \begin_layout Plain Layout
2844 \begin_layout Standard
2846 \begin_inset Tabular
2847 <lyxtabular version="3" rows="6" columns="2">
2848 <features tabularvalignment="middle">
2849 <column alignment="center" valignment="top" width="0pt">
2850 <column alignment="center" valignment="top" width="0pt">
2852 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2855 \begin_layout Plain Layout
2861 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2864 \begin_layout Plain Layout
2866 \begin_inset Note Note
2869 \begin_layout Plain Layout
2876 is only used as spacer.
2888 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2891 \begin_layout Plain Layout
2898 \begin_layout Plain Layout
2908 \begin_inset Formula $\downarrow$
2916 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2919 \begin_layout Plain Layout
2920 \begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$
2930 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2933 \begin_layout Plain Layout
2940 \begin_layout Plain Layout
2950 \begin_inset Formula $\downarrow$
2958 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2961 \begin_layout Plain Layout
2962 \begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$
2972 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2975 \begin_layout Plain Layout
2982 \begin_layout Plain Layout
2992 \begin_inset Formula $\downarrow$
3000 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3003 \begin_layout Plain Layout
3004 \begin_inset Formula $\raisebox{5mm}{}\tbinom{A}{B}\raisebox{-2.5mm}{}$
3014 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3017 \begin_layout Plain Layout
3024 \begin_layout Plain Layout
3034 \begin_inset Formula $\downarrow$
3042 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3045 \begin_layout Plain Layout
3046 \begin_inset Formula $\raisebox{5mm}{}{A \brack B}\raisebox{-2.5mm}{}$
3056 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3059 \begin_layout Plain Layout
3066 \begin_layout Plain Layout
3076 \begin_inset Formula $\downarrow$
3084 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3087 \begin_layout Plain Layout
3088 \begin_inset Formula $\raisebox{5mm}{}{A \brace B}\raisebox{-2.5mm}{}$
3104 \begin_layout Subsection
3105 Case Differentiations
3106 \begin_inset Index idx
3109 \begin_layout Plain Layout
3110 Case differentiations
3118 \begin_layout Standard
3120 \begin_inset Tabular
3121 <lyxtabular version="3" rows="3" columns="2">
3122 <features tabularvalignment="middle">
3123 <column alignment="center" valignment="top" width="0pt">
3124 <column alignment="center" valignment="top" width="0pt">
3126 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3129 \begin_layout Plain Layout
3135 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3138 \begin_layout Plain Layout
3146 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3149 \begin_layout Plain Layout
3156 \begin_layout Plain Layout
3166 \begin_inset Formula $\to$
3170 \begin_inset Index idx
3173 \begin_layout Plain Layout
3186 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3189 \begin_layout Plain Layout
3190 \begin_inset Formula $\begin{cases}
3201 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3204 \begin_layout Plain Layout
3211 \begin_layout Plain Layout
3223 arg "newline-insert newline"
3231 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3234 \begin_layout Plain Layout
3235 \begin_inset Formula $\begin{cases}
3236 A & \textrm{for }x>0\\
3237 B & \textrm{for }x=0
3254 \begin_layout Standard
3261 or the usage of the math toolbar button
3262 \begin_inset Graphics
3263 filename ../images/math/cases.png
3268 you can create new lines with the shortcut
3271 arg "newline-insert newline"
3274 or the table toolbar button
3275 \begin_inset Graphics
3276 filename ../images/tabular-feature_append-row.png
3284 \begin_layout Standard
3291 is also available via the menu
3293 Insert\SpecialChar \menuseparator
3294 Math\SpecialChar \menuseparator
3300 \begin_layout Subsection
3302 \begin_inset Index idx
3305 \begin_layout Plain Layout
3314 \begin_layout Standard
3322 \begin_inset Index idx
3325 \begin_layout Plain Layout
3333 every character can be displayed canceled.
3334 The characters are quasi accentuated by a slash.
3337 \begin_layout Standard
3339 \begin_inset Tabular
3340 <lyxtabular version="3" rows="4" columns="2">
3341 <features tabularvalignment="middle">
3342 <column alignment="center" valignment="top" width="0pt">
3343 <column alignment="center" valignment="top" width="0pt">
3345 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3348 \begin_layout Plain Layout
3354 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3357 \begin_layout Plain Layout
3365 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3368 \begin_layout Plain Layout
3376 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3379 \begin_layout Plain Layout
3380 \begin_inset Formula $\not=$
3390 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3393 \begin_layout Plain Layout
3403 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3406 \begin_layout Plain Layout
3407 \begin_inset Formula $\not\le$
3417 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3420 \begin_layout Plain Layout
3430 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3433 \begin_layout Plain Layout
3434 \begin_inset Formula $\not\parallel$
3450 \begin_layout Standard
3451 The last example shows, that not all negations look good.
3452 Therefore there are for some negations special commands (see
3453 \begin_inset CommandInset ref
3455 reference "sub:Mathematical-Symbols"
3460 \begin_inset CommandInset ref
3462 reference "sec:Relations"
3469 \begin_layout Subsection
3471 \begin_inset CommandInset label
3473 name "sub:Placeholders"
3478 \begin_inset Index idx
3481 \begin_layout Plain Layout
3488 \begin_inset Index idx
3491 \begin_layout Plain Layout
3492 Chemical characters ! Isotopes
3498 \begin_inset Index idx
3501 \begin_layout Plain Layout
3506 \begin_layout Plain Layout
3517 \begin_layout Plain Layout
3532 \begin_layout Standard
3534 \begin_inset space \thinspace{}
3538 \begin_inset space \space{}
3545 \begin_layout Plain Layout
3546 Typesetting isotopes and chemical symbols is described in
3547 \begin_inset CommandInset ref
3549 reference "sub:Chemical-Symbols-and"
3558 the following problem occurs:
3561 \begin_layout Standard
3563 \begin_inset Tabular
3564 <lyxtabular version="3" rows="2" columns="2">
3565 <features tabularvalignment="middle">
3566 <column alignment="center" valignment="top" width="0pt">
3567 <column alignment="center" valignment="top" width="0pt">
3569 <cell alignment="center" valignment="top" usebox="none">
3572 \begin_layout Plain Layout
3573 Indices created with sub- and superscripts:
3578 <cell alignment="center" valignment="top" usebox="none">
3581 \begin_layout Plain Layout
3582 \begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
3592 <cell alignment="center" valignment="top" usebox="none">
3595 \begin_layout Plain Layout
3601 <cell alignment="center" valignment="top" usebox="none">
3604 \begin_layout Plain Layout
3605 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3619 \begin_inset Note Note
3622 \begin_layout Plain Layout
3629 is only used as spacer.
3637 \begin_layout Standard
3638 The shorter index is by default placed below or above the first character
3639 of the longer index.
3640 To avoid this there is the command
3647 \begin_inset Index idx
3650 \begin_layout Plain Layout
3658 or the math toolbar button
3659 \begin_inset space \thinspace{}
3666 \begin_layout Plain Layout
3667 can be found in the submenu of the toolbar button
3668 \begin_inset Graphics
3669 filename ../images/math/space.png
3680 \begin_inset Graphics
3681 filename ../images/math/phantom.png
3686 that creates one or more phantom characters.
3693 a small blue box appears that is superposed with two red arrows.
3694 The arrows indicate that the complete width and height of the box content
3695 will be created as placeholder.
3696 Phantom characters are accordingly placeholders with the size of the characters.
3699 \begin_layout Standard
3701 \begin_inset Tabular
3702 <lyxtabular version="3" rows="4" columns="2">
3703 <features tabularvalignment="middle">
3704 <column alignment="center" valignment="top" width="0">
3705 <column alignment="center" valignment="top" width="0">
3707 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3710 \begin_layout Plain Layout
3716 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3719 \begin_layout Plain Layout
3721 \begin_inset Note Note
3724 \begin_layout Plain Layout
3731 is only used as spacer.
3743 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3746 \begin_layout Plain Layout
3751 \begin_layout Plain Layout
3766 \begin_layout Plain Layout
3776 \begin_inset Formula $\to$
3783 \begin_layout Plain Layout
3797 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3800 \begin_layout Plain Layout
3801 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
3811 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3814 \begin_layout Plain Layout
3819 \begin_layout Plain Layout
3834 \begin_layout Plain Layout
3844 \begin_inset Formula $\to$
3851 \begin_layout Plain Layout
3865 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3868 \begin_layout Plain Layout
3869 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
3879 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3882 \begin_layout Plain Layout
3889 \begin_layout Plain Layout
3904 \begin_layout Plain Layout
3914 \begin_inset Formula $\to$
3921 \begin_layout Plain Layout
3935 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3938 \begin_layout Plain Layout
3939 \begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
3955 \begin_layout Standard
3956 Furthermore there are the commands
3963 \begin_inset Index idx
3966 \begin_layout Plain Layout
3975 \begin_inset space ~
3979 \begin_inset Graphics
3980 filename ../images/math/vphantom.png
3992 \begin_inset Index idx
3995 \begin_layout Plain Layout
4004 \begin_inset space ~
4008 \begin_inset Graphics
4009 filename ../images/math/hphantom.png
4021 creates only space for the maximal height of the characters in the box
4022 but not for its width.
4029 creates only space for the width of the box content.
4030 Therefore the boxes of both commands have only one red arrow.
4033 \begin_layout Standard
4044 \begin_layout Plain Layout
4059 space for the height of the integral sign,
4063 \begin_layout Plain Layout
4070 creates an integral sign, see
4071 \begin_inset CommandInset ref
4073 reference "sub:Big-Operators"
4082 because this is the larger character.
4083 An example application is in
4084 \begin_inset CommandInset ref
4086 reference "sub:Multiline-Brackets"
4093 \begin_layout Standard
4094 Placeholders can also be used for text when it is inserted via the menu
4097 Insert\SpecialChar \menuseparator
4098 Formatting\SpecialChar \menuseparator
4104 \begin_layout Standard
4106 \begin_inset Newline newline
4110 \begin_inset Phantom Phantom
4113 \begin_layout Plain Layout
4122 \begin_layout Subsection
4124 \begin_inset Index idx
4127 \begin_layout Plain Layout
4134 \begin_inset Index idx
4137 \begin_layout Plain Layout
4138 Formula ! underlined
4146 \begin_layout Standard
4148 \begin_inset Tabular
4149 <lyxtabular version="3" rows="4" columns="2">
4150 <features tabularvalignment="middle">
4151 <column alignment="center" valignment="top" width="0pt">
4152 <column alignment="center" valignment="top" width="0pt">
4154 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4157 \begin_layout Plain Layout
4163 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4166 \begin_layout Plain Layout
4168 \begin_inset Note Note
4171 \begin_layout Plain Layout
4178 is only used as spacer.
4190 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4193 \begin_layout Plain Layout
4200 \begin_layout Plain Layout
4210 \begin_inset Index idx
4213 \begin_layout Plain Layout
4226 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4229 \begin_layout Plain Layout
4230 \begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
4240 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
4243 \begin_layout Plain Layout
4250 \begin_layout Plain Layout
4260 \begin_inset Index idx
4263 \begin_layout Plain Layout
4276 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
4279 \begin_layout Plain Layout
4280 \begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
4290 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4293 \begin_layout Plain Layout
4300 \begin_layout Plain Layout
4315 \begin_layout Plain Layout
4329 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4332 \begin_layout Plain Layout
4333 \begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
4349 \begin_layout Standard
4350 In the last example it doesn't matter if first
4365 \begin_layout Standard
4366 To double underline e.
4367 \begin_inset space \thinspace{}
4371 \begin_inset space \space{}
4383 \begin_layout Standard
4384 It is possible to place up to 6 lines above or below characters.
4387 \begin_layout Standard
4388 \begin_inset VSpace bigskip
4391 Custom lines can be created using the command
4398 \begin_inset Index idx
4401 \begin_layout Plain Layout
4409 which has the following scheme:
4412 \begin_layout Standard
4417 rule[vertical offset]{length}{thickness}
4420 \begin_layout Standard
4421 The optional vertical offset shifts the line upwards (or downwards, when
4422 the value is negative).
4424 \begin_inset CommandInset ref
4426 reference "tab:Available-units"
4430 can be used for the values.
4431 Here are two example lines created with the commands
4432 \begin_inset Newline newline
4439 rule[-2ex]{3cm}{2pt}
4450 \begin_layout Standard
4452 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4458 \begin_layout Standard
4465 can also be used for text when a line is inserted via the menu
4467 Insert\SpecialChar \menuseparator
4468 Formatting\SpecialChar \menuseparator
4470 \begin_inset space ~
4478 \begin_layout Standard
4480 \begin_inset CommandInset line
4491 \begin_layout Subsection
4493 \begin_inset CommandInset label
4500 \begin_inset Index idx
4503 \begin_layout Plain Layout
4512 \begin_layout Standard
4513 There are different types of ellipses available.
4517 \begin_layout Plain Layout
4518 In the math toolbar in the submenu of the button
4519 \begin_inset Graphics
4520 filename ../images/math/ldots.png
4530 For listings dots at the baseline are used (
4537 \begin_inset Index idx
4540 \begin_layout Plain Layout
4548 ), while for operations dots are needed that are on the same height as the
4556 \begin_inset Index idx
4559 \begin_layout Plain Layout
4568 When using the command
4575 \begin_inset Index idx
4578 \begin_layout Plain Layout
4586 , LaTeX decides on the basis of the next character what type is used.
4589 \begin_layout Standard
4591 \begin_inset Tabular
4592 <lyxtabular version="3" rows="9" columns="2">
4593 <features tabularvalignment="middle">
4594 <column alignment="center" valignment="top" width="0pt">
4595 <column alignment="center" valignment="top" width="0pt">
4597 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4600 \begin_layout Plain Layout
4606 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4609 \begin_layout Plain Layout
4617 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4620 \begin_layout Plain Layout
4625 \begin_layout Plain Layout
4640 \begin_layout Plain Layout
4654 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4657 \begin_layout Plain Layout
4658 \begin_inset Formula $A_{1},\dots,A_{n}$
4668 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4671 \begin_layout Plain Layout
4676 \begin_layout Plain Layout
4691 \begin_layout Plain Layout
4705 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4708 \begin_layout Plain Layout
4709 \begin_inset Formula $A_{1}+\dots+A_{n}$
4719 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4722 \begin_layout Plain Layout
4727 \begin_layout Plain Layout
4742 \begin_layout Plain Layout
4756 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4759 \begin_layout Plain Layout
4760 \begin_inset Formula $A_{1},\ldots,A_{n}$
4770 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4773 \begin_layout Plain Layout
4778 \begin_layout Plain Layout
4793 \begin_layout Plain Layout
4807 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4810 \begin_layout Plain Layout
4811 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4821 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4824 \begin_layout Plain Layout
4832 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4835 \begin_layout Plain Layout
4836 \begin_inset Formula $\vdots$
4846 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4849 \begin_layout Plain Layout
4857 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4860 \begin_layout Plain Layout
4861 \begin_inset Formula $\ddots$
4871 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4874 \begin_layout Plain Layout
4882 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4885 \begin_layout Plain Layout
4886 \begin_inset Formula $\iddots$
4896 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4899 \begin_layout Plain Layout
4901 \begin_inset space \thinspace{}
4904 matrix with the different dots
4909 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4912 \begin_layout Plain Layout
4913 \begin_inset Formula $\begin{array}{ccc}
4914 A_{11} & \cdots & A_{1m}\\
4915 \vdots & \ddots & \vdots\\
4916 A_{n1} & \cdots & A_{nm}
4933 \begin_layout Standard
4934 The ellipses available in menu
4936 Insert\SpecialChar \menuseparator
4938 \begin_inset space ~
4952 \begin_layout Standard
4953 \begin_inset VSpace medskip
4962 , one of the options
4964 Use mathdots package (automatically)
4966 must be set in the document settings under
4969 \begin_inset space ~
4975 \begin_inset Newline newline
4980 Use mathdots package
4982 will improve the appearance of all dots in the documents if their font
4983 style or size is not the default.
4986 \begin_layout Standard
4987 \begin_inset VSpace medskip
4990 Specially for matrices there are ellipses that span over several columns.
4991 They are created with the command
4998 \begin_inset Index idx
5001 \begin_layout Plain Layout
5009 , that has the following scheme:
5012 \begin_layout Standard
5017 hdotsfor[distance]{number of columns}
5020 \begin_layout Standard
5021 The number of columns specifies how many columns should be spanned.
5022 Distance is a factor for the distance between the dots.
5025 \begin_layout Standard
5026 In the following matrix the command
5032 was inserted in the first box of the second line, to get an ellipsis with
5033 a dot distance twice as long as with the command
5040 \begin_inset Formula
5042 \left(\begin{array}{cccc}
5051 Note that the matrix fields that should be spanned must be empty, otherwise
5052 you get LaTeX-errors.
5055 \begin_layout Standard
5056 \begin_inset VSpace bigskip
5059 Furthermore you can fill with the command
5066 \begin_inset Index idx
5069 \begin_layout Plain Layout
5077 the rest of a line with dots.
5078 The effect of these commands is the same like with
5085 \begin_inset CommandInset ref
5087 reference "sub:Variable-Space"
5094 \begin_layout Standard
5095 For example the command
5103 \begin_layout Plain Layout
5117 \begin_layout Standard
5118 \begin_inset Formula $A\dotfill B$
5124 \begin_layout Standard
5131 there is for a line the command
5138 \begin_inset Index idx
5141 \begin_layout Plain Layout
5152 \begin_layout Standard
5153 \begin_inset Formula $A\hrulefill B$
5159 \begin_layout Standard
5160 To use the commands for text, they have to be inserted in TeX-mode.
5163 \begin_layout Section
5165 \begin_inset CommandInset label
5172 \begin_inset Index idx
5175 \begin_layout Plain Layout
5184 \begin_layout Standard
5185 Matrices can be inserted via the math toolbar button
5186 \begin_inset Graphics
5187 filename ../images/dialog-show_mathmatrix.png
5194 Insert\SpecialChar \menuseparator
5195 Math\SpecialChar \menuseparator
5199 In the matrix dialog you can specify the number of columns and rows, the
5200 alignment and the decoration.
5201 The vertical alignment is hereby only of importance for matrices in inline
5205 \begin_layout Standard
5206 The first matrix is top
5207 \begin_inset Formula $\begin{array}[t]{cccc}
5215 \begin_inset Formula $\begin{array}{cccc}
5222 and the third bottom
5223 \begin_inset Formula $\begin{array}[b]{cccc}
5233 \begin_layout Standard
5234 The horizontal alignment specifies how the column entries should be aligned.
5235 It is set by entering a letter for every column.
5240 denotes left aligned,
5249 To create for example a 4
5254 \begin_inset space ~
5257 matrix where the first column is left aligned, the second and third are
5258 centered and the last one is right aligned, one enters for the horizontal
5264 Normally are in a matrix all columns centered, therefore the default is
5265 for every column is a
5272 \begin_layout Standard
5273 Horizontal alignment:
5276 \begin_layout Standard
5282 \begin_inset Formula $\begin{array}{lll}
5294 \begin_inset Formula $\begin{array}{ccc}
5306 \begin_inset Formula $\begin{array}{rrr}
5316 \begin_layout Standard
5317 To add or delete rows and columns subsequently, the math toolbar buttons
5319 \begin_inset Graphics
5320 filename ../images/tabular-feature_append-row.png
5326 \begin_inset Graphics
5327 filename ../images/tabular-feature_delete-row.png
5333 \begin_inset space \thinspace{}
5338 Edit\SpecialChar \menuseparator
5342 New rows can also be created with
5345 arg "newline-insert newline"
5351 \begin_layout Standard
5352 \begin_inset VSpace bigskip
5359 adds parentheses in the selected style around the matrix.
5360 Alternatively, parentheses can can either be created with the commands
5368 \begin_inset Index idx
5371 \begin_layout Plain Layout
5386 \begin_inset Index idx
5389 \begin_layout Plain Layout
5400 \begin_inset space ~
5406 \begin_inset CommandInset ref
5408 reference "sub:Automatic-Bracket-Size"
5412 , or by using the following commands:
5413 \begin_inset VSpace medskip
5419 \begin_layout Standard
5420 \begin_inset space \hfill{}
5424 \begin_inset Tabular
5425 <lyxtabular version="3" rows="4" columns="2">
5426 <features tabularvalignment="middle">
5427 <column alignment="center" valignment="top" width="0">
5428 <column alignment="center" valignment="top" width="0">
5430 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5433 \begin_layout Plain Layout
5439 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5442 \begin_layout Plain Layout
5444 \begin_inset Note Note
5447 \begin_layout Plain Layout
5454 is only used as spacer.
5466 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5469 \begin_layout Plain Layout
5476 \begin_layout Plain Layout
5490 \begin_inset space \thinspace{}
5498 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5501 \begin_layout Plain Layout
5502 \begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
5503 0 & \textrm{-}\mathrm{i}\\
5505 \end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
5515 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5518 \begin_layout Plain Layout
5525 \begin_layout Plain Layout
5539 \begin_inset space \thinspace{}
5547 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5550 \begin_layout Plain Layout
5551 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
5552 0 & \textrm{-}\mathrm{i}\\
5554 \end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
5564 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5567 \begin_layout Plain Layout
5574 \begin_layout Plain Layout
5588 \begin_inset space \thinspace{}
5596 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5599 \begin_layout Plain Layout
5600 \begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
5601 0 & \textrm{-}\mathrm{i}\\
5603 \end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
5617 \begin_inset space \hfill{}
5621 \begin_inset Tabular
5622 <lyxtabular version="3" rows="4" columns="2">
5623 <features tabularvalignment="middle">
5624 <column alignment="center" valignment="top" width="0">
5625 <column alignment="center" valignment="top" width="0">
5627 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5630 \begin_layout Plain Layout
5636 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5639 \begin_layout Plain Layout
5647 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5650 \begin_layout Plain Layout
5657 \begin_layout Plain Layout
5671 \begin_inset space \thinspace{}
5679 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5682 \begin_layout Plain Layout
5683 \begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
5684 0 & \textrm{-}\mathrm{i}\\
5686 \end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
5696 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5699 \begin_layout Plain Layout
5706 \begin_layout Plain Layout
5720 \begin_inset space \thinspace{}
5728 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5731 \begin_layout Plain Layout
5732 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
5733 0 & \textrm{-}\mathrm{i}\\
5735 \end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
5745 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5748 \begin_layout Plain Layout
5755 \begin_layout Plain Layout
5769 \begin_inset space \thinspace{}
5777 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5780 \begin_layout Plain Layout
5781 \begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
5782 0 & \textrm{-}\mathrm{i}\\
5784 \end{array}\end{matrix}\raisebox{-5.3mm}{}$
5798 \begin_inset space \hfill{}
5804 \begin_layout Standard
5805 \begin_inset VSpace medskip
5809 \begin_inset space \thinspace{}
5813 \begin_inset space \space{}
5822 is inserted, a blue box appears between two vertical lines where the matrix
5824 \begin_inset Newline newline
5827 Note that decorated matrices ignore the vertical alignment.
5830 \begin_layout Standard
5831 \begin_inset VSpace bigskip
5834 As all multiline formulas are matrices, the length
5841 \begin_inset Index idx
5844 \begin_layout Plain Layout
5852 that is described in
5853 \begin_inset CommandInset ref
5855 reference "sub:Column-Separation"
5859 can also be used to change the column separation of matrices.
5862 \begin_layout Standard
5863 To change the row separation, the command
5870 \begin_inset Index idx
5873 \begin_layout Plain Layout
5882 It is used as follows:
5885 \begin_layout Standard
5892 arraystretch}{stretch factor}
5893 \begin_inset Index idx
5896 \begin_layout Plain Layout
5907 \begin_layout Standard
5914 assigns the stretch factor to the predefined command
5922 \begin_inset space \thinspace{}
5926 \begin_inset space \space{}
5929 the row separation, use the factor 2.
5930 This is then used for all following matrices.
5931 To go back to the original separation, assign the factor 1 to
5940 \begin_layout Standard
5941 To set matrices into a text line, the command
5948 \begin_inset Index idx
5951 \begin_layout Plain Layout
5960 When it is inserted a blue box with two dashed lines appears.
5961 In this box the matrix is inserted.
5964 \begin_layout Standard
5966 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5968 \end{smallmatrix}\right)$
5974 \begin_layout Section
5975 Brackets and Delimiters
5976 \begin_inset Index idx
5979 \begin_layout Plain Layout
5986 \begin_inset Index idx
5989 \begin_layout Plain Layout
5998 \begin_layout Subsection
5999 Vertical Brackets and Delimiters
6000 \begin_inset Index idx
6003 \begin_layout Plain Layout
6012 \begin_layout Standard
6013 \begin_inset space \hfill{}
6017 \begin_inset Tabular
6018 <lyxtabular version="3" rows="9" columns="2">
6019 <features tabularvalignment="middle">
6020 <column alignment="center" valignment="top" width="0pt">
6021 <column alignment="center" valignment="top" width="0pt">
6023 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6026 \begin_layout Plain Layout
6032 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6035 \begin_layout Plain Layout
6043 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6046 \begin_layout Plain Layout
6052 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6055 \begin_layout Plain Layout
6056 \begin_inset Formula $($
6066 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6069 \begin_layout Plain Layout
6075 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6078 \begin_layout Plain Layout
6079 \begin_inset Formula $\{$
6089 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6092 \begin_layout Plain Layout
6098 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6101 \begin_layout Plain Layout
6102 \begin_inset Formula $[$
6112 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6115 \begin_layout Plain Layout
6123 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6126 \begin_layout Plain Layout
6127 \begin_inset Formula $\langle$
6137 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6140 \begin_layout Plain Layout
6148 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6151 \begin_layout Plain Layout
6152 \begin_inset Formula $\lceil$
6162 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6165 \begin_layout Plain Layout
6173 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6176 \begin_layout Plain Layout
6177 \begin_inset Formula $\lfloor$
6187 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6190 \begin_layout Plain Layout
6196 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6199 \begin_layout Plain Layout
6200 \begin_inset Formula $/$
6210 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6213 \begin_layout Plain Layout
6219 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6222 \begin_layout Plain Layout
6223 \begin_inset Formula $|$
6237 \begin_inset space \hfill{}
6241 \begin_inset Tabular
6242 <lyxtabular version="3" rows="9" columns="2">
6243 <features tabularvalignment="middle">
6244 <column alignment="center" valignment="top" width="0pt">
6245 <column alignment="center" valignment="top" width="0pt">
6247 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6250 \begin_layout Plain Layout
6256 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6259 \begin_layout Plain Layout
6267 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6270 \begin_layout Plain Layout
6276 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6279 \begin_layout Plain Layout
6280 \begin_inset Formula $)$
6290 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6293 \begin_layout Plain Layout
6299 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6302 \begin_layout Plain Layout
6303 \begin_inset Formula $\}$
6313 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6316 \begin_layout Plain Layout
6322 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6325 \begin_layout Plain Layout
6326 \begin_inset Formula $]$
6336 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6339 \begin_layout Plain Layout
6347 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6350 \begin_layout Plain Layout
6351 \begin_inset Formula $\rangle$
6361 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6364 \begin_layout Plain Layout
6372 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6375 \begin_layout Plain Layout
6376 \begin_inset Formula $\rceil$
6386 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6389 \begin_layout Plain Layout
6397 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6400 \begin_layout Plain Layout
6401 \begin_inset Formula $\rfloor$
6411 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6414 \begin_layout Plain Layout
6424 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6427 \begin_layout Plain Layout
6428 \begin_inset Formula $\backslash$
6438 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6441 \begin_layout Plain Layout
6449 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6452 \begin_layout Plain Layout
6453 \begin_inset Formula $\|$
6467 \begin_inset space \hfill{}
6473 \begin_layout Standard
6476 \begin_inset Note Greyedout
6479 \begin_layout Plain Layout
6484 In TeX-mode the command
6491 \begin_inset Index idx
6494 \begin_layout Plain Layout
6502 must be used for the backslash, because the command
6510 produces there a line break.
6518 \begin_layout Standard
6519 For all characters listed above the size can be adjusted with the commands
6520 described in the following two subsections.
6521 When using these commands, the characters < and > can directly be used
6522 instead of the commands
6537 \begin_layout Subsubsection
6539 \begin_inset CommandInset label
6541 name "sub:Manual-Bracket-Size"
6546 \begin_inset Index idx
6549 \begin_layout Plain Layout
6550 Bracket size ! manual
6558 \begin_layout Standard
6559 The bracket size can be specified manually by the LaTeX-commands
6566 \begin_inset Index idx
6569 \begin_layout Plain Layout
6602 denotes the smallest and
6608 the largest bracket size.
6611 \begin_layout Standard
6612 These commands are used to emphasize levels of brackets:
6615 \begin_layout Standard
6617 \begin_inset Tabular
6618 <lyxtabular version="3" rows="2" columns="2">
6619 <features tabularvalignment="middle">
6620 <column alignment="center" valignment="top" width="0pt">
6621 <column alignment="center" valignment="top" width="0pt">
6623 <cell alignment="center" valignment="top" usebox="none">
6626 \begin_layout Plain Layout
6627 all brackets in the same size:
6632 <cell alignment="center" valignment="top" usebox="none">
6635 \begin_layout Plain Layout
6636 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
6646 <cell alignment="center" valignment="top" usebox="none">
6649 \begin_layout Plain Layout
6655 <cell alignment="center" valignment="top" usebox="none">
6658 \begin_layout Plain Layout
6659 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6673 \begin_inset Note Note
6676 \begin_layout Plain Layout
6683 is only used as spacer.
6691 \begin_layout Standard
6692 For the second formula the command
6702 \begin_layout Plain Layout
6716 \begin_layout Standard
6717 Here is an overview about all bracket sizes:
6720 \begin_layout Standard
6740 \begin_layout Plain Layout
6757 \begin_layout Plain Layout
6770 \begin_layout Plain Layout
6786 \begin_layout Standard
6788 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6794 \begin_layout Standard
6801 -commands there is the variant
6808 \begin_inset Index idx
6811 \begin_layout Plain Layout
6819 that adds a bit more space between the bracket and its content, and the
6833 \begin_inset Index idx
6836 \begin_layout Plain Layout
6846 , that don't add additional space.
6851 at the end of the command
6857 is for a left bracket; for a right bracket this will be replaced by an
6863 A left or right bracket can each be an opening or closing bracket.
6866 \begin_layout Standard
6867 In the following table is a comparison of the variants:
6870 \begin_layout Standard
6872 \begin_inset Tabular
6873 <lyxtabular version="3" rows="5" columns="2">
6874 <features tabularvalignment="middle">
6875 <column alignment="center" valignment="middle" width="0">
6876 <column alignment="center" valignment="middle" width="0">
6878 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6881 \begin_layout Plain Layout
6887 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6890 \begin_layout Plain Layout
6892 \begin_inset Note Note
6895 \begin_layout Plain Layout
6902 is only used as spacer.
6914 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6917 \begin_layout Plain Layout
6932 \begin_layout Plain Layout
6950 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6953 \begin_layout Plain Layout
6954 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
6964 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6967 \begin_layout Plain Layout
6982 \begin_layout Plain Layout
7000 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7003 \begin_layout Plain Layout
7004 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
7014 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7017 \begin_layout Plain Layout
7032 \begin_layout Plain Layout
7050 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7053 \begin_layout Plain Layout
7054 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
7064 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7067 \begin_layout Plain Layout
7079 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7082 \begin_layout Plain Layout
7083 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
7099 \begin_layout Subsubsection
7100 Automatic Bracket Size
7101 \begin_inset CommandInset label
7103 name "sub:Automatic-Bracket-Size"
7108 \begin_inset Index idx
7111 \begin_layout Plain Layout
7112 Bracket size ! automatic
7120 \begin_layout Standard
7121 Brackets with variable size can be inserted with the commands
7128 \begin_inset Index idx
7131 \begin_layout Plain Layout
7146 \begin_inset Index idx
7149 \begin_layout Plain Layout
7157 or via the math toolbar button
7158 \begin_inset Graphics
7159 filename ../images/dialog-show_mathdelimiter.png
7177 the wanted bracket must be inserted.
7178 The bracket size will then automatically be calculated for the output.
7181 \begin_layout Standard
7183 normal bracket: The command
7193 \begin_layout Plain Layout
7203 \begin_inset Formula $\downarrow$
7210 \begin_layout Plain Layout
7222 \begin_inset Formula
7232 \begin_layout Standard
7234 multiline bracket: The command
7246 \begin_layout Plain Layout
7256 \begin_inset Formula $\downarrow$
7263 \begin_layout Plain Layout
7277 \begin_inset Formula
7279 \ln\left(\frac{A}{C}\right)
7287 \begin_layout Standard
7303 \begin_inset space ~
7309 This has the advantage that you can see in LyX immediately the real bracket
7310 size and that the matching right bracket will be created too.
7311 \begin_inset Newline newline
7314 The command for the last example would then be:
7328 \begin_layout Plain Layout
7338 \begin_inset Formula $\downarrow$
7344 \begin_layout Standard
7345 To omit a left or right bracket, a dot is inserted for the omitted bracket.
7346 For example the command
7356 \begin_layout Plain Layout
7366 \begin_inset Formula $\downarrow$
7373 \begin_layout Plain Layout
7389 \begin_inset Formula
7391 \left.\frac{A}{B}\right\}
7410 will be converted by LyX to brackets in the right size when the document
7411 is reloaded and an omitted bracket will appear as dashed line.
7414 \begin_layout Standard
7415 \begin_inset VSpace bigskip
7418 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
7426 \begin_inset Index idx
7429 \begin_layout Plain Layout
7437 is additionally available for all brackets and limits.
7438 With this command the height of the following character is adapted to the
7439 one of the surrounding brackets, what is e.
7440 \begin_inset space \thinspace{}
7444 \begin_inset space \space{}
7447 needed for physical vectors:
7448 \begin_inset Formula
7450 \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle
7455 For physical vectors there is a special LaTeX-package, described in
7456 \begin_inset CommandInset ref
7458 reference "sub:Physical-Vectors"
7465 \begin_layout Subsection
7467 \begin_inset Index idx
7470 \begin_layout Plain Layout
7471 Brackets ! horizontal
7479 \begin_layout Standard
7481 \begin_inset Tabular
7482 <lyxtabular version="3" rows="4" columns="2">
7483 <features tabularvalignment="middle">
7484 <column alignment="center" valignment="top" width="0pt">
7485 <column alignment="center" valignment="top" width="0pt">
7487 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7490 \begin_layout Plain Layout
7492 \begin_inset Note Note
7495 \begin_layout Plain Layout
7502 is only used as spacer.
7512 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7515 \begin_layout Plain Layout
7523 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7526 \begin_layout Plain Layout
7530 \begin_layout Plain Layout
7545 \begin_layout Plain Layout
7558 \begin_layout Plain Layout
7571 \begin_layout Plain Layout
7584 \begin_layout Plain Layout
7592 \begin_inset Index idx
7595 \begin_layout Plain Layout
7608 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7611 \begin_layout Plain Layout
7612 \begin_inset Formula $\overbrace{A+B}^{3}$
7622 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7625 \begin_layout Plain Layout
7629 \begin_layout Plain Layout
7644 \begin_layout Plain Layout
7657 \begin_layout Plain Layout
7670 \begin_layout Plain Layout
7678 \begin_inset Index idx
7681 \begin_layout Plain Layout
7694 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7697 \begin_layout Plain Layout
7698 \begin_inset Formula $\underbrace{A+B}_{5}$
7708 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7711 \begin_layout Plain Layout
7718 \begin_layout Plain Layout
7733 \begin_layout Plain Layout
7746 \begin_layout Plain Layout
7759 \begin_layout Plain Layout
7772 \begin_layout Plain Layout
7785 \begin_layout Plain Layout
7798 \begin_layout Plain Layout
7812 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7815 \begin_layout Plain Layout
7816 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
7832 \begin_layout Standard
7833 In the last example it doesn't matter if
7845 is inserted at first.
7848 \begin_layout Standard
7849 \begin_inset VSpace bigskip
7852 When brackets are needed that overlap each other, multiline formulas, as
7854 \begin_inset CommandInset ref
7856 reference "sec:Multiline-Formulas"
7861 \begin_inset Formula
7863 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
7864 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
7869 In the first row the formula is inserted together with the first brace.
7870 It is hereby important that the space command
7874 \begin_layout Plain Layout
7875 Space commands are explained in
7876 \begin_inset CommandInset ref
7878 reference "sub:Predefined-Space"
7893 is inserted before the first
7894 \begin_inset Formula $d$
7897 , because the brace that ends behind the
7898 \begin_inset Formula $q$
7901 prevents that the following
7902 \begin_inset Quotes eld
7906 \begin_inset Quotes erd
7909 is surrounded by space.
7913 \begin_layout Plain Layout
7914 because a bracket is not handled as character, see
7915 \begin_inset CommandInset ref
7917 reference "sub:Binary-Operators"
7926 In the second row the second brace is inserted.
7927 As it should begin before the
7928 \begin_inset Formula $b$
7943 \begin_layout Plain Layout
7951 \begin_inset CommandInset ref
7953 reference "sub:Placeholders"
7962 This space is needed because the
7963 \begin_inset Quotes eld
7967 \begin_inset Quotes erd
7970 is also surrounded by space in the formula.
7971 The brace is placed under the command
7980 \begin_layout Standard
7981 It gets more complicated when brackets overlap each other, like in the following
7986 \begin_layout Plain Layout
7998 \begin_inset Formula
8000 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
8001 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd
8010 \begin_layout Plain Layout
8021 The first formula row is the same as the second row of the previous example,
8022 with the difference that the brace is above.
8023 The second row contains the formula together with the second brace.
8024 To avoid that there is space between the upper brace in the first row and
8025 the formula, the row spacing need to be reduced.
8026 This is not easily possible due to a bug in LyX
8030 \begin_layout Plain Layout
8031 \begin_inset CommandInset href
8033 name "LyX-bug #1505"
8034 target "http://www.lyx.org/trac/ticket/1505"
8044 As solution for the problem, the global formula row separation
8051 \begin_inset Index idx
8054 \begin_layout Plain Layout
8062 must be changed to -6
8063 \begin_inset space \thinspace{}
8066 pt before the formula with the command
8081 is set back after the formula to the standard value of 3
8082 \begin_inset space \thinspace{}
8085 pt using the same command.
8086 More about the row separation in formulas is explained in
8087 \begin_inset CommandInset ref
8089 reference "sub:Line-Separation"
8096 \begin_layout Section
8098 \begin_inset Index idx
8101 \begin_layout Plain Layout
8110 \begin_layout Standard
8111 Arrows can be inserted via the math toolbar button
8112 \begin_inset Graphics
8113 filename ../images/math/leftarrow.png
8118 or the commands listed in the following subsections.
8121 \begin_layout Standard
8122 \begin_inset Newpage newpage
8128 \begin_layout Subsection
8130 \begin_inset Index idx
8133 \begin_layout Plain Layout
8142 \begin_layout Standard
8143 \begin_inset space \hfill{}
8147 \begin_inset Tabular
8148 <lyxtabular version="3" rows="8" columns="2">
8149 <features tabularvalignment="middle">
8150 <column alignment="center" valignment="top" width="0pt">
8151 <column alignment="center" valignment="top" width="0pt">
8153 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8156 \begin_layout Plain Layout
8162 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8165 \begin_layout Plain Layout
8173 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8176 \begin_layout Plain Layout
8184 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8187 \begin_layout Plain Layout
8188 \begin_inset Formula $\gets$
8198 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8201 \begin_layout Plain Layout
8209 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8212 \begin_layout Plain Layout
8213 \begin_inset Formula $\Leftarrow$
8223 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8226 \begin_layout Plain Layout
8234 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8237 \begin_layout Plain Layout
8238 \begin_inset Formula $\longleftarrow$
8248 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8251 \begin_layout Plain Layout
8259 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8262 \begin_layout Plain Layout
8263 \begin_inset Formula $\Longleftarrow$
8273 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8276 \begin_layout Plain Layout
8284 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8287 \begin_layout Plain Layout
8288 \begin_inset Formula $\leftharpoonup$
8298 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8301 \begin_layout Plain Layout
8309 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8312 \begin_layout Plain Layout
8313 \begin_inset Formula $\leftharpoondown$
8323 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8326 \begin_layout Plain Layout
8334 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8337 \begin_layout Plain Layout
8338 \begin_inset Formula $\hookleftarrow$
8352 \begin_inset space \hfill{}
8356 \begin_inset Tabular
8357 <lyxtabular version="3" rows="8" columns="2">
8358 <features tabularvalignment="middle">
8359 <column alignment="center" valignment="top" width="0pt">
8360 <column alignment="center" valignment="top" width="0pt">
8362 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8365 \begin_layout Plain Layout
8371 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8374 \begin_layout Plain Layout
8382 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8385 \begin_layout Plain Layout
8393 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8396 \begin_layout Plain Layout
8397 \begin_inset Formula $\to$
8407 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8410 \begin_layout Plain Layout
8418 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8421 \begin_layout Plain Layout
8422 \begin_inset Formula $\Rightarrow$
8432 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8435 \begin_layout Plain Layout
8443 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8446 \begin_layout Plain Layout
8447 \begin_inset Formula $\longrightarrow$
8457 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8460 \begin_layout Plain Layout
8468 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8471 \begin_layout Plain Layout
8472 \begin_inset Formula $\Longrightarrow$
8482 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8485 \begin_layout Plain Layout
8493 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8496 \begin_layout Plain Layout
8497 \begin_inset Formula $\rightharpoonup$
8507 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8510 \begin_layout Plain Layout
8518 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8521 \begin_layout Plain Layout
8522 \begin_inset Formula $\rightharpoondown$
8532 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8535 \begin_layout Plain Layout
8543 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8546 \begin_layout Plain Layout
8547 \begin_inset Formula $\hookrightarrow$
8561 \begin_inset space \hfill{}
8567 \begin_layout Standard
8568 \begin_inset space \hfill{}
8572 \begin_inset Tabular
8573 <lyxtabular version="3" rows="6" columns="2">
8574 <features tabularvalignment="middle">
8575 <column alignment="center" valignment="top" width="0pt">
8576 <column alignment="center" valignment="top" width="0pt">
8578 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8581 \begin_layout Plain Layout
8587 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8590 \begin_layout Plain Layout
8598 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8601 \begin_layout Plain Layout
8609 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8612 \begin_layout Plain Layout
8613 \begin_inset Formula $\leftrightarrow$
8623 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8626 \begin_layout Plain Layout
8634 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8637 \begin_layout Plain Layout
8638 \begin_inset Formula $\Leftrightarrow$
8648 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8651 \begin_layout Plain Layout
8659 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8662 \begin_layout Plain Layout
8663 \begin_inset Formula $\longleftrightarrow$
8673 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8676 \begin_layout Plain Layout
8684 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8687 \begin_layout Plain Layout
8688 \begin_inset Formula $\Longleftrightarrow$
8698 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8701 \begin_layout Plain Layout
8709 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8712 \begin_layout Plain Layout
8713 \begin_inset Formula $\rightleftharpoons$
8727 \begin_inset space \hspace{}
8732 \begin_inset space \hfill{}
8736 \begin_inset Tabular
8737 <lyxtabular version="3" rows="5" columns="2">
8738 <features tabularvalignment="middle">
8739 <column alignment="center" valignment="top" width="0pt">
8740 <column alignment="center" valignment="top" width="0pt">
8742 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8745 \begin_layout Plain Layout
8751 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8754 \begin_layout Plain Layout
8762 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8765 \begin_layout Plain Layout
8773 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8776 \begin_layout Plain Layout
8777 \begin_inset Formula $\mapsto$
8787 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8790 \begin_layout Plain Layout
8798 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8801 \begin_layout Plain Layout
8802 \begin_inset Formula $\longmapsto$
8812 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8815 \begin_layout Plain Layout
8823 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8826 \begin_layout Plain Layout
8827 \begin_inset Formula $\leadsto$
8837 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8840 \begin_layout Plain Layout
8848 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8851 \begin_layout Plain Layout
8852 \begin_inset Formula $\dasharrow$
8866 \begin_inset space \hfill{}
8872 \begin_layout Standard
8873 \begin_inset VSpace medskip
8876 Arrows used as accent like e.
8877 \begin_inset space \thinspace{}
8881 \begin_inset space \space{}
8884 vector arrows are listed in
8885 \begin_inset CommandInset ref
8887 reference "sec:Accents"
8894 \begin_layout Standard
8895 \begin_inset VSpace bigskip
8898 Furthermore there are the labeled arrows
8899 \begin_inset Index idx
8902 \begin_layout Plain Layout
8915 \begin_inset Index idx
8918 \begin_layout Plain Layout
8933 \begin_inset Index idx
8936 \begin_layout Plain Layout
8943 \begin_layout Plain Layout
8958 When inserting one of these commands in a formula, an arrow with two blue
8959 boxes appear where the label can be inserted.
8960 The length of the arrow adapts to the label width.
8963 \begin_layout Standard
8965 \begin_inset Tabular
8966 <lyxtabular version="3" rows="3" columns="2">
8967 <features tabularvalignment="middle">
8968 <column alignment="center" valignment="top" width="0pt">
8969 <column alignment="center" valignment="top" width="0pt">
8971 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8974 \begin_layout Plain Layout
8980 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8983 \begin_layout Plain Layout
8985 \begin_inset Note Note
8988 \begin_layout Plain Layout
8995 is only used as spacer.
9007 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9010 \begin_layout Plain Layout
9017 \begin_layout Plain Layout
9027 \begin_inset Formula $\downarrow$
9031 \begin_inset Formula $\to$
9039 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9042 \begin_layout Plain Layout
9043 \begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
9053 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9056 \begin_layout Plain Layout
9063 \begin_layout Plain Layout
9073 \begin_inset Formula $\downarrow$
9077 \begin_inset Formula $\to$
9085 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9088 \begin_layout Plain Layout
9089 \begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
9105 \begin_layout Subsection
9106 Vertical and diagonal Arrows
9107 \begin_inset Index idx
9110 \begin_layout Plain Layout
9117 \begin_inset Index idx
9120 \begin_layout Plain Layout
9129 \begin_layout Standard
9130 \begin_inset space \hfill{}
9134 \begin_inset Tabular
9135 <lyxtabular version="3" rows="7" columns="2">
9136 <features tabularvalignment="middle">
9137 <column alignment="center" valignment="top" width="0pt">
9138 <column alignment="center" valignment="top" width="0pt">
9140 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9143 \begin_layout Plain Layout
9149 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9152 \begin_layout Plain Layout
9160 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9163 \begin_layout Plain Layout
9171 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9174 \begin_layout Plain Layout
9175 \begin_inset Formula $\uparrow$
9185 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9188 \begin_layout Plain Layout
9196 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9199 \begin_layout Plain Layout
9200 \begin_inset Formula $\Uparrow$
9210 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9213 \begin_layout Plain Layout
9221 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9224 \begin_layout Plain Layout
9225 \begin_inset Formula $\updownarrow$
9235 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9238 \begin_layout Plain Layout
9246 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9249 \begin_layout Plain Layout
9250 \begin_inset Formula $\Updownarrow$
9260 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9263 \begin_layout Plain Layout
9271 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9274 \begin_layout Plain Layout
9275 \begin_inset Formula $\Downarrow$
9285 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9288 \begin_layout Plain Layout
9296 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9299 \begin_layout Plain Layout
9300 \begin_inset Formula $\downarrow$
9314 \begin_inset space \hfill{}
9318 \begin_inset Tabular
9319 <lyxtabular version="3" rows="5" columns="2">
9320 <features tabularvalignment="middle">
9321 <column alignment="center" valignment="top" width="0pt">
9322 <column alignment="center" valignment="top" width="0pt">
9324 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9327 \begin_layout Plain Layout
9333 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9336 \begin_layout Plain Layout
9344 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9347 \begin_layout Plain Layout
9355 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9358 \begin_layout Plain Layout
9359 \begin_inset Formula $\nearrow$
9369 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9372 \begin_layout Plain Layout
9380 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9383 \begin_layout Plain Layout
9384 \begin_inset Formula $\searrow$
9394 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9397 \begin_layout Plain Layout
9405 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9408 \begin_layout Plain Layout
9409 \begin_inset Formula $\swarrow$
9419 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9422 \begin_layout Plain Layout
9430 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9433 \begin_layout Plain Layout
9434 \begin_inset Formula $\nwarrow$
9448 \begin_inset space \hfill{}
9454 \begin_layout Standard
9455 \begin_inset VSpace medskip
9458 Vertical arrows can be used also as delimiter together with the commands
9460 \begin_inset CommandInset ref
9462 reference "sub:Manual-Bracket-Size"
9467 \begin_inset CommandInset ref
9469 reference "sub:Automatic-Bracket-Size"
9476 \begin_layout Standard
9477 \begin_inset Newpage newpage
9483 \begin_layout Section
9485 \begin_inset CommandInset label
9492 \begin_inset Index idx
9495 \begin_layout Plain Layout
9504 \begin_layout Standard
9505 Accents can be inserted via the math toolbar button
9506 \begin_inset Graphics
9507 filename ../images/math/hat.png
9512 or the commands listed in the following subsections.
9515 \begin_layout Subsection
9516 Accents for one Character
9520 \begin_layout Plain Layout
9533 \begin_layout Plain Layout
9535 \begin_inset CommandInset ref
9537 reference "sub:Accents-in-Text"
9550 \begin_layout Plain Layout
9558 \begin_inset Note Note
9561 \begin_layout Plain Layout
9568 is used to avoid that the footnote appears in the PDF-bookmark.
9571 \begin_layout Plain Layout
9579 \begin_inset CommandInset ref
9581 reference "sub:Formulas-in-Section"
9591 \begin_inset CommandInset label
9593 name "sub:Accents-for-one"
9598 \begin_inset Index idx
9601 \begin_layout Plain Layout
9602 Accents ! for one character
9610 \begin_layout Standard
9611 \begin_inset space \hfill{}
9615 \begin_inset Tabular
9616 <lyxtabular version="3" rows="8" columns="2">
9617 <features tabularvalignment="middle">
9618 <column alignment="center" valignment="top" width="0pt">
9619 <column alignment="center" valignment="top" width="0pt">
9621 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9624 \begin_layout Plain Layout
9630 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9633 \begin_layout Plain Layout
9635 \begin_inset Note Note
9638 \begin_layout Plain Layout
9645 is only used as spacer.
9657 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9660 \begin_layout Plain Layout
9667 \begin_layout Plain Layout
9681 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9684 \begin_layout Plain Layout
9685 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
9695 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9698 \begin_layout Plain Layout
9705 \begin_layout Plain Layout
9719 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9722 \begin_layout Plain Layout
9723 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
9733 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9736 \begin_layout Plain Layout
9743 \begin_layout Plain Layout
9757 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9760 \begin_layout Plain Layout
9761 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
9771 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9774 \begin_layout Plain Layout
9781 \begin_layout Plain Layout
9795 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9798 \begin_layout Plain Layout
9799 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
9809 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9812 \begin_layout Plain Layout
9819 \begin_layout Plain Layout
9829 \begin_inset Index idx
9832 \begin_layout Plain Layout
9843 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9846 \begin_layout Plain Layout
9847 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
9857 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9860 \begin_layout Plain Layout
9867 \begin_layout Plain Layout
9881 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9884 \begin_layout Plain Layout
9885 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
9895 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9898 \begin_layout Plain Layout
9905 \begin_layout Plain Layout
9919 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9922 \begin_layout Plain Layout
9923 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
9937 \begin_inset space \hfill{}
9941 \begin_inset Tabular
9942 <lyxtabular version="3" rows="7" columns="2">
9943 <features tabularvalignment="middle">
9944 <column alignment="center" valignment="top" width="0pt">
9945 <column alignment="center" valignment="top" width="0pt">
9947 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9950 \begin_layout Plain Layout
9956 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9959 \begin_layout Plain Layout
9967 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9970 \begin_layout Plain Layout
9977 \begin_layout Plain Layout
9991 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9994 \begin_layout Plain Layout
9995 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
10005 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10008 \begin_layout Plain Layout
10015 \begin_layout Plain Layout
10029 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10032 \begin_layout Plain Layout
10033 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
10043 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10046 \begin_layout Plain Layout
10053 \begin_layout Plain Layout
10067 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10070 \begin_layout Plain Layout
10071 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
10081 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10084 \begin_layout Plain Layout
10091 \begin_layout Plain Layout
10105 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10108 \begin_layout Plain Layout
10109 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
10119 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10122 \begin_layout Plain Layout
10129 \begin_layout Plain Layout
10143 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10146 \begin_layout Plain Layout
10147 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
10157 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10160 \begin_layout Plain Layout
10167 \begin_layout Plain Layout
10181 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10184 \begin_layout Plain Layout
10185 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
10199 \begin_inset space \hfill{}
10205 \begin_layout Standard
10206 \begin_inset VSpace bigskip
10212 \begin_layout Standard
10213 You can directly insert accents like é to formulas.
10214 LyX will transform them to the corresponding accent command.
10216 \begin_inset Index idx
10219 \begin_layout Plain Layout
10225 it is better to insert a quotation mark before the vowel.
10226 These two characters are then treated by LaTeX as
10230 character when the formula part with the umlaut is marked as German.
10238 \begin_inset Quotes eld
10242 \begin_inset Quotes erd
10245 umlauts are created as demonstrated in the following example:
10248 \begin_layout Standard
10249 \begin_inset VSpace -2mm
10255 \begin_layout Standard
10257 \begin_inset Tabular
10258 <lyxtabular version="3" rows="3" columns="2">
10259 <features tabularvalignment="middle">
10260 <column alignment="center" valignment="top" width="0">
10261 <column alignment="center" valignment="top" width="0">
10263 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10266 \begin_layout Plain Layout
10272 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10275 \begin_layout Plain Layout
10277 \begin_inset Note Note
10280 \begin_layout Plain Layout
10288 \begin_inset space \thinspace{}
10291 pt space are only used as spacer.
10303 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10306 \begin_layout Plain Layout
10309 \begin_inset Quotes grd
10317 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10320 \begin_layout Plain Layout
10321 \begin_inset space \hspace{}
10328 \begin_inset Formula $"i$
10338 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10341 \begin_layout Plain Layout
10348 \begin_layout Plain Layout
10362 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10365 \begin_layout Plain Layout
10366 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
10382 \begin_layout Standard
10383 Another advantage to
10389 is that umlauts can directly be converted to mathematical text because
10390 the accent commands above are
10396 in mathematical text
10399 To convert an accented character to mathematical text, only the character
10400 under the accent may be converted.
10401 This applies also for all other conversions, e.
10402 \begin_inset space \thinspace{}
10406 \begin_inset space \space{}
10412 \begin_layout Standard
10413 In mathematical text, umlauts and other accented characters can directly
10417 \begin_layout Subsection
10418 Accents for Operators
10419 \begin_inset Index idx
10422 \begin_layout Plain Layout
10423 Accents ! for operators
10431 \begin_layout Standard
10439 \begin_inset Index idx
10442 \begin_layout Plain Layout
10457 \begin_inset Index idx
10460 \begin_layout Plain Layout
10468 characters can be placed above or below an operator, respectively, to accent
10477 \begin_inset Index idx
10480 \begin_layout Plain Layout
10488 characters can be set before and behind an operator.
10489 The command scheme is:
10492 \begin_layout Standard
10508 \begin_layout Standard
10515 must always be before the operator that should be accented.
10516 You can accent with several characters and even with other operators and
10524 for example only characters behind an operator, write nothing between the
10525 first braces but don't omit the braces.
10528 \begin_layout Standard
10529 For example the command
10534 \begin_inset Formula $\to$
10544 \begin_inset Formula $\to$
10553 \begin_layout Plain Layout
10569 \begin_inset Formula
10571 \sideset{}{'}\sum_{k=1}^{n}
10579 \begin_layout Standard
10588 \begin_layout Plain Layout
10603 \begin_layout Plain Layout
10615 \begin_inset Formula $\uparrow$
10623 \begin_inset Formula
10625 \overset{a}{\maltese}
10630 As seen in the last example, with
10642 also symbols and characters can be accented; with
10648 this is not possible.
10651 \begin_layout Subsection
10652 Accents for several Characters
10653 \begin_inset Index idx
10656 \begin_layout Plain Layout
10657 Accents ! for several characters
10665 \begin_layout Standard
10666 \begin_inset space \hfill{}
10670 \begin_inset Tabular
10671 <lyxtabular version="3" rows="5" columns="2">
10672 <features tabularvalignment="middle">
10673 <column alignment="center" valignment="top" width="0pt">
10674 <column alignment="center" valignment="top" width="0pt">
10676 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10679 \begin_layout Plain Layout
10685 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10688 \begin_layout Plain Layout
10690 \begin_inset Note Note
10693 \begin_layout Plain Layout
10700 is only used as spacer.
10712 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10715 \begin_layout Plain Layout
10722 \begin_layout Plain Layout
10736 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10739 \begin_layout Plain Layout
10740 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
10750 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10753 \begin_layout Plain Layout
10760 \begin_layout Plain Layout
10774 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10777 \begin_layout Plain Layout
10778 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
10788 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10791 \begin_layout Plain Layout
10798 \begin_layout Plain Layout
10812 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10815 \begin_layout Plain Layout
10816 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
10826 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10829 \begin_layout Plain Layout
10832 underleftrightarrow
10836 \begin_layout Plain Layout
10850 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10853 \begin_layout Plain Layout
10854 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
10868 \begin_inset space \hfill{}
10872 \begin_inset Tabular
10873 <lyxtabular version="3" rows="5" columns="2">
10874 <features tabularvalignment="middle">
10875 <column alignment="center" valignment="top" width="0pt">
10876 <column alignment="center" valignment="top" width="0pt">
10878 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10881 \begin_layout Plain Layout
10887 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10890 \begin_layout Plain Layout
10898 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10901 \begin_layout Plain Layout
10908 \begin_layout Plain Layout
10922 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10925 \begin_layout Plain Layout
10926 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
10936 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10939 \begin_layout Plain Layout
10946 \begin_layout Plain Layout
10960 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10963 \begin_layout Plain Layout
10964 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
10974 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10977 \begin_layout Plain Layout
10984 \begin_layout Plain Layout
10998 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11001 \begin_layout Plain Layout
11002 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
11012 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11015 \begin_layout Plain Layout
11022 \begin_layout Plain Layout
11036 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11039 \begin_layout Plain Layout
11040 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
11054 \begin_inset space \hfill{}
11060 \begin_layout Standard
11061 \begin_inset VSpace medskip
11064 With these commands as many characters as you like can be accented.
11077 will only be set in the output with a length of three characters, as shown
11078 in the following example:
11079 \begin_inset Formula
11081 \widetilde{A+B=C-D}
11089 \begin_layout Standard
11097 \begin_inset Index idx
11100 \begin_layout Plain Layout
11115 \begin_inset Index idx
11118 \begin_layout Plain Layout
11126 described in the previous subsection it is also possible to accent several
11136 \begin_layout Plain Layout
11146 \begin_inset Formula $\downarrow$
11152 \begin_inset Formula
11154 \underset{***}{A=B}
11162 \begin_layout Section
11164 \begin_inset CommandInset label
11171 \begin_inset Index idx
11174 \begin_layout Plain Layout
11183 \begin_layout Subsection
11185 \begin_inset CommandInset label
11187 name "sub:Predefined-Space"
11192 \begin_inset Index idx
11195 \begin_layout Plain Layout
11196 Space ! horizontal ! predefined
11204 \begin_layout Standard
11205 Sometimes it is necessary to insert horizontal space to a formula.
11206 This is done by inserting a protected space (shortcut
11209 arg "space-insert protected"
11214 \begin_inset Quotes eld
11223 \begin_layout Plain Layout
11235 \begin_inset Quotes erd
11238 appears and by pressing
11242 several times one can select one of eight different space sizes.
11243 The spaces can also be inserted using the math toolbar button
11244 \begin_inset Graphics
11245 filename ../images/math/space.png
11250 or special commands.
11251 Independent from the inserted command, one can select the size again by
11259 \begin_layout Standard
11262 \begin_inset VSpace -5mm
11266 \begin_inset Tabular
11267 <lyxtabular version="3" rows="3" columns="7">
11268 <features tabularvalignment="middle">
11269 <column alignment="center" valignment="middle" width="6.8cm">
11270 <column alignment="center" valignment="top" width="0">
11271 <column alignment="center" valignment="top" width="0">
11272 <column alignment="center" valignment="top" width="0">
11273 <column alignment="center" valignment="top" width="0">
11274 <column alignment="center" valignment="top" width="0">
11275 <column alignment="center" valignment="top" width="0">
11277 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11280 \begin_layout Plain Layout
11286 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11289 \begin_layout Plain Layout
11297 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11300 \begin_layout Plain Layout
11308 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11311 \begin_layout Plain Layout
11319 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11322 \begin_layout Plain Layout
11330 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11333 \begin_layout Plain Layout
11341 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11344 \begin_layout Plain Layout
11354 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11357 \begin_layout Plain Layout
11362 keystrokes after inserting the protected space
11367 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11370 \begin_layout Plain Layout
11376 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11379 \begin_layout Plain Layout
11385 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11388 \begin_layout Plain Layout
11394 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11397 \begin_layout Plain Layout
11403 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11406 \begin_layout Plain Layout
11412 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11415 \begin_layout Plain Layout
11423 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11426 \begin_layout Plain Layout
11432 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11435 \begin_layout Plain Layout
11436 \begin_inset Formula $A\, B$
11444 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11447 \begin_layout Plain Layout
11448 \begin_inset Formula $A\: B$
11456 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11459 \begin_layout Plain Layout
11460 \begin_inset Formula $A\; B$
11468 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11471 \begin_layout Plain Layout
11472 \begin_inset Formula $A\quad B$
11480 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11483 \begin_layout Plain Layout
11484 \begin_inset Formula $A\qquad B$
11492 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11495 \begin_layout Plain Layout
11496 \begin_inset Formula $A\! B$
11512 \begin_layout Standard
11513 The last size seem to produce no space.
11514 It is displayed red in LyX contrary to the other sizes, because it is a
11516 There are two more negative spaces:
11519 \begin_layout Standard
11521 \begin_inset Tabular
11522 <lyxtabular version="3" rows="3" columns="3">
11523 <features tabularvalignment="middle">
11524 <column alignment="center" valignment="middle" width="6.8cm">
11525 <column alignment="center" valignment="top" width="0pt">
11526 <column alignment="center" valignment="top" width="0pt">
11528 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11531 \begin_layout Plain Layout
11537 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11540 \begin_layout Plain Layout
11548 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11551 \begin_layout Plain Layout
11561 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11564 \begin_layout Plain Layout
11569 keystrokes after inserting the protected space
11574 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11577 \begin_layout Plain Layout
11583 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11586 \begin_layout Plain Layout
11594 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11597 \begin_layout Plain Layout
11603 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11606 \begin_layout Plain Layout
11607 \begin_inset Formula $A\negmedspace B$
11615 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11618 \begin_layout Plain Layout
11619 \begin_inset Formula $A\negthickspace B$
11635 \begin_layout Standard
11636 Negative spaces can lead to characters overlapping each other.
11637 Thus they can be used to enforce ligatures, what is e.
11638 \begin_inset space \thinspace{}
11642 \begin_inset space \space{}
11645 useful for summation operators:
11648 \begin_layout Standard
11650 \begin_inset Tabular
11651 <lyxtabular version="3" rows="3" columns="2">
11652 <features tabularvalignment="middle">
11653 <column alignment="center" valignment="top" width="0">
11654 <column alignment="center" valignment="top" width="0">
11656 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11659 \begin_layout Plain Layout
11665 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11668 \begin_layout Plain Layout
11670 \begin_inset Note Note
11673 \begin_layout Plain Layout
11680 is only used as spacer.
11692 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11695 \begin_layout Plain Layout
11704 \begin_layout Plain Layout
11718 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11721 \begin_layout Plain Layout
11722 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
11732 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11735 \begin_layout Plain Layout
11746 \begin_layout Plain Layout
11760 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11763 \begin_layout Plain Layout
11764 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
11780 \begin_layout Standard
11781 Relations like for example equal signs, are always surrounded by space.
11782 To suppress this, the equal sign is placed into a TeX-brace.
11783 The following example demonstrates this:
11786 \begin_layout Standard
11788 \begin_inset Tabular
11789 <lyxtabular version="3" rows="2" columns="2">
11790 <features tabularvalignment="middle">
11791 <column alignment="center" valignment="top" width="0pt">
11792 <column alignment="center" valignment="top" width="0pt">
11794 <cell alignment="center" valignment="top" usebox="none">
11797 \begin_layout Plain Layout
11803 <cell alignment="center" valignment="top" usebox="none">
11806 \begin_layout Plain Layout
11807 \begin_inset Formula $A=B$
11817 <cell alignment="center" valignment="top" usebox="none">
11820 \begin_layout Plain Layout
11821 \begin_inset Note Note
11824 \begin_layout Plain Layout
11831 is only used as spacer.
11837 \begin_inset Formula $\raisebox{5mm}{}$
11840 equation without space
11845 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11848 \begin_layout Plain Layout
11849 \begin_inset Formula $A{=}B$
11865 \begin_layout Standard
11867 The command for the last formula is:
11872 \begin_inset Formula $\to$
11878 \begin_layout Standard
11879 \begin_inset VSpace bigskip
11882 Spaces are needed for physical units, because the space between the value
11883 and the unit is the smallest one and not a normal space.
11884 For units in text, the smallest space is inserted via the menu
11886 Insert\SpecialChar \menuseparator
11887 Formatting\SpecialChar \menuseparator
11889 \begin_inset space ~
11897 arg "space-insert thin"
11903 \begin_layout Standard
11904 An example to visualize the difference:
11907 \begin_layout Standard
11908 \begin_inset Tabular
11909 <lyxtabular version="3" rows="2" columns="2">
11910 <features tabularvalignment="middle">
11911 <column alignment="left" valignment="top" width="0">
11912 <column alignment="left" valignment="top" width="0">
11914 <cell alignment="center" valignment="top" usebox="none">
11917 \begin_layout Plain Layout
11919 \begin_inset Formula $\cdot$
11927 <cell alignment="center" valignment="top" usebox="none">
11930 \begin_layout Plain Layout
11931 space between value and unit
11938 <cell alignment="center" valignment="top" usebox="none">
11941 \begin_layout Plain Layout
11943 \begin_inset space \thinspace{}
11947 \begin_inset Formula $\cdot$
11955 <cell alignment="center" valignment="top" usebox="none">
11958 \begin_layout Plain Layout
11959 smallest space between value and unit
11972 \begin_layout Subsection
11977 \begin_layout Plain Layout
11990 \begin_layout Plain Layout
11991 for vertical space in formulas see
11992 \begin_inset CommandInset ref
11994 reference "sub:Line-Separation"
12007 \begin_layout Plain Layout
12015 \begin_inset Note Note
12018 \begin_layout Plain Layout
12021 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
12024 \begin_layout Plain Layout
12027 texorpdfstring is in section
12028 \begin_inset CommandInset ref
12030 reference "sub:Formulas-in-Section"
12040 \begin_inset CommandInset label
12042 name "sub:Variable-Space"
12047 \begin_inset Index idx
12050 \begin_layout Plain Layout
12051 Space ! horizontal ! variable
12059 \begin_layout Standard
12060 Space with a defined length can be inserted with the command
12067 \begin_inset Index idx
12070 \begin_layout Plain Layout
12080 \begin_inset Quotes eld
12089 \begin_layout Plain Layout
12101 \begin_inset Quotes erd
12105 The length can be specified by left-clicking on the
12106 \begin_inset Quotes eld
12115 \begin_layout Plain Layout
12127 \begin_inset Quotes erd
12131 The length may also be negative.
12132 To insert so many space that the formula uses all available space, the
12140 \begin_inset Index idx
12143 \begin_layout Plain Layout
12154 \begin_layout Standard
12155 \begin_inset VSpace -1mm
12161 \begin_layout Standard
12163 \begin_inset Tabular
12164 <lyxtabular version="3" rows="4" columns="2">
12165 <features tabularvalignment="middle">
12166 <column alignment="center" valignment="top" width="0">
12167 <column alignment="center" valignment="top" width="0">
12169 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12172 \begin_layout Plain Layout
12180 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12183 \begin_layout Plain Layout
12191 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12194 \begin_layout Plain Layout
12201 \begin_layout Plain Layout
12211 \begin_inset Formula $\to$
12217 \begin_inset space \thinspace{}
12225 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12228 \begin_layout Plain Layout
12229 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
12239 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12242 \begin_layout Plain Layout
12249 \begin_layout Plain Layout
12259 \begin_inset Formula $\to$
12265 \begin_inset space \thinspace{}
12273 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12276 \begin_layout Plain Layout
12277 \begin_inset Formula $A\hspace{-1mm}A\not=A$
12287 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12290 \begin_layout Plain Layout
12297 \begin_layout Plain Layout
12311 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12314 \begin_layout Plain Layout
12315 \begin_inset Formula $A=A\hfill B=B$
12331 \begin_layout Standard
12332 In the last example the available space is given by the longest column entry
12334 In an inline formula the space depends on the length of the line in which
12342 Thus, when the line uses the full width, no space will be created.
12349 only has an effect on displayed formulas when the formula style
12354 (Formula styles are explained in
12355 \begin_inset CommandInset ref
12357 reference "sec:Formula-Styles"
12364 \begin_layout Standard
12371 , there are the commands
12383 that fill the space with a pattern, see
12384 \begin_inset CommandInset ref
12386 reference "sub:Ellipses"
12393 \begin_layout Standard
12394 For text, variable space can be inserted via the menu
12396 Insert\SpecialChar \menuseparator
12397 Formatting\SpecialChar \menuseparator
12399 \begin_inset space ~
12407 \begin_layout Standard
12408 This is a line with
12409 \begin_inset space \hspace{}
12414 \begin_inset space \thinspace{}
12420 \begin_layout Standard
12421 This is a line with
12422 \begin_inset space \hfill{}
12428 \begin_layout Subsection
12429 Space besides inline Formulas
12430 \begin_inset Index idx
12433 \begin_layout Plain Layout
12434 Space ! besides inline formulas
12442 \begin_layout Standard
12443 The space that surrounds inline formulas can be adjusted with the length
12451 \begin_inset Index idx
12454 \begin_layout Plain Layout
12463 The value of a length is set with the command
12470 \begin_inset Index idx
12473 \begin_layout Plain Layout
12481 that has the following scheme:
12484 \begin_layout Standard
12489 setlength{length name}{value}
12492 \begin_layout Standard
12500 \begin_inset space \thinspace{}
12506 \begin_layout Standard
12516 \begin_layout Standard
12517 is inserted in TeX-mode.
12519 \begin_inset space \thinspace{}
12522 mm space will now be set around all inline formulas:
12526 \begin_layout Plain Layout
12540 \begin_layout Standard
12541 This is a line with an inline formula
12542 \begin_inset Formula $A=B$
12546 \begin_inset space \thinspace{}
12549 mm surrounding space.
12553 \begin_layout Plain Layout
12567 \begin_layout Standard
12568 To return to the predefined value,
12574 is set to the value 0
12575 \begin_inset space \thinspace{}
12581 \begin_layout Section
12583 \begin_inset Index idx
12586 \begin_layout Plain Layout
12593 \begin_inset Index idx
12596 \begin_layout Plain Layout
12601 \begin_layout Plain Layout
12612 \begin_layout Plain Layout
12627 \begin_layout Standard
12628 Boxes for text are described in chapter
12635 \begin_inset space ~
12643 \begin_layout Subsection
12645 \begin_inset CommandInset label
12647 name "sub:Boxes-with-Frame"
12652 \begin_inset Index idx
12655 \begin_layout Plain Layout
12664 \begin_layout Standard
12665 It is possible to frame formulas or parts of it with the commands
12672 \begin_inset Index idx
12675 \begin_layout Plain Layout
12690 \begin_inset Index idx
12693 \begin_layout Plain Layout
12704 \begin_layout Standard
12705 When one of these commands is inserted to a formula, a blue box appears
12706 within a frame to enter formula parts.
12713 an additional formula has to be created by
12717 within this box, because the box content will otherwise be treated as mathemati
12725 is used, a new formula is automatically created inside the frame.
12728 \begin_layout Standard
12735 is not suitable to frame displayed formulas because the formula will always
12736 be set in the size of the text.
12743 is in contrary not suitable to frame inline formulas, because the formula
12744 will always be set in the size of a displayed formula.
12747 \begin_layout Standard
12754 there is the command
12761 \begin_inset Index idx
12764 \begin_layout Plain Layout
12772 where additionally the frame width and the alignment can be specified.
12779 is used in the following scheme:
12782 \begin_layout Standard
12787 framebox[frame width][position]{box content}
12790 \begin_layout Standard
12791 The position can either be
12808 right aligns the formula in the box.
12809 When no position is given, the formula will be centered.
12810 \begin_inset Newline newline
12813 Is no width given, also no position can be given.
12814 In this case the frame width is adjusted to the box content like for
12823 \begin_layout Standard
12830 is inserted, a box appears containing three blue boxes.
12831 The first two boxes are surrounded by brackets and denote the two optional
12833 The third box is for formula parts like for
12842 \begin_layout Standard
12844 \begin_inset Tabular
12845 <lyxtabular version="3" rows="5" columns="2">
12846 <features tabularvalignment="middle">
12847 <column alignment="center" valignment="top" width="0">
12848 <column alignment="center" valignment="top" width="0">
12850 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12853 \begin_layout Plain Layout
12859 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12862 \begin_layout Plain Layout
12864 \begin_inset Note Note
12867 \begin_layout Plain Layout
12874 is only used as spacer.
12886 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12889 \begin_layout Plain Layout
12896 \begin_layout Plain Layout
12915 \begin_layout Plain Layout
12929 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12932 \begin_layout Plain Layout
12933 \begin_inset Formula $\raisebox{6mm}{}\fbox{\ensuremath{\int A=B}}\raisebox{-4mm}{}$
12943 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12946 \begin_layout Plain Layout
12953 \begin_layout Plain Layout
12968 \begin_layout Plain Layout
12982 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12985 \begin_layout Plain Layout
12986 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
12996 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12999 \begin_layout Plain Layout
13006 \begin_layout Plain Layout
13020 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13023 \begin_layout Plain Layout
13024 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
13034 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13037 \begin_layout Plain Layout
13044 \begin_layout Plain Layout
13054 \begin_inset Formula $\to$
13058 \begin_inset Formula $\to$
13071 \begin_layout Plain Layout
13081 \begin_inset Formula $\downarrow$
13089 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13092 \begin_layout Plain Layout
13093 \begin_inset Formula $\raisebox{6mm}{}$
13097 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
13101 \begin_inset Formula $\raisebox{-4mm}{}$
13117 \begin_layout Standard
13118 The frame thickness can also be adjusted.
13119 To do this the following commands have to be inserted in TeX-mode before
13123 \begin_layout Standard
13133 \begin_inset Quotes eld
13137 \begin_inset Quotes erd
13151 \begin_inset Quotes eld
13155 \begin_inset Quotes erd
13161 \begin_layout Standard
13162 \begin_inset Quotes eld
13166 \begin_inset Quotes erd
13169 specifies the minimal distance between the frame and the first character
13171 An example for this is the following framed formula:
13175 \begin_layout Plain Layout
13187 \begin_inset Formula
13194 Before this formula the commands
13197 \begin_layout Standard
13219 \begin_layout Standard
13220 were inserted in TeX-mode.
13221 The given values are used for all following boxes.
13224 \begin_layout Standard
13225 To return to the standard frame size, the command
13228 \begin_layout Standard
13253 \begin_layout Plain Layout
13267 \begin_layout Standard
13268 is inserted in TeX-mode before the next formula.
13271 \begin_layout Subsection
13272 Boxes without Frame
13273 \begin_inset CommandInset label
13275 name "sub:Boxes-without-Frame"
13280 \begin_inset Index idx
13283 \begin_layout Plain Layout
13284 Boxes ! without frame
13292 \begin_layout Standard
13293 For boxes without a frame there are the following box commands:
13300 \begin_inset Index idx
13303 \begin_layout Plain Layout
13318 \begin_inset Index idx
13321 \begin_layout Plain Layout
13336 \begin_inset Index idx
13339 \begin_layout Plain Layout
13350 \begin_layout Standard
13357 a box can be super- or subscripted.
13358 But in contrary to normal super- and subscripting, the characters in the
13359 box keep their font size.
13366 is used in the following scheme:
13369 \begin_layout Standard
13374 raisebox{height}{box content}
13377 \begin_layout Standard
13378 When the box should contain a formula, an extra formula is needed like for
13389 \begin_inset Note Greyedout
13392 \begin_layout Plain Layout
13403 this extra formula is created by pressing
13407 twice instead of once because LyX doesn't yet support
13421 \begin_layout Standard
13423 \begin_inset Tabular
13424 <lyxtabular version="3" rows="4" columns="2">
13425 <features tabularvalignment="middle">
13426 <column alignment="center" valignment="top" width="0">
13427 <column alignment="center" valignment="top" width="0">
13429 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13432 \begin_layout Plain Layout
13438 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13441 \begin_layout Plain Layout
13449 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13452 \begin_layout Plain Layout
13456 \begin_inset Formula $\to$
13462 \begin_inset Formula $\to$
13470 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13473 \begin_layout Plain Layout
13474 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13484 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13487 \begin_layout Plain Layout
13491 \begin_inset Formula $\to$
13497 \begin_inset Formula $\to$
13505 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13508 \begin_layout Plain Layout
13509 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13519 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13522 \begin_layout Plain Layout
13526 \begin_inset Formula $\to$
13545 \begin_layout Plain Layout
13559 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13562 \begin_layout Plain Layout
13563 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
13579 \begin_layout Standard
13604 , with the difference that there is no frame.
13607 \begin_layout Subsection
13609 \begin_inset CommandInset label
13611 name "sub:Colored-Boxes"
13616 \begin_inset Index idx
13619 \begin_layout Plain Layout
13628 \begin_layout Standard
13629 To be able to use all commands explained in this section, the LaTeX-package
13638 \begin_layout Plain Layout
13643 is part of every LaTeX standard installation.
13649 \begin_inset Index idx
13652 \begin_layout Plain Layout
13658 has to be loaded in the LaTeX-preamble with the line
13662 \begin_layout Plain Layout
13663 When text is colored somewhere in the document with a predefined color,
13664 LyX loads the LaTeX-package
13669 Thus it is possible that the package is loaded twice, but this doesn't
13676 \begin_inset Note Note
13679 \begin_layout Plain Layout
13680 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
13689 \begin_layout Standard
13697 \begin_layout Standard
13698 \begin_inset VSpace medskip
13701 To color boxes, the command
13708 \begin_inset Index idx
13711 \begin_layout Plain Layout
13719 is used in the following scheme:
13722 \begin_layout Standard
13727 colorbox{color}{box content}
13730 \begin_layout Standard
13731 The box content can also be a box and a
13737 can also be part of another box (see the 2nd and 3rd example).
13738 When the box should contain a formula, an extra formula has to be created,
13739 the same way as for
13749 \begin_layout Plain Layout
13750 This also applies for the command
13764 \begin_layout Standard
13765 One of the following predefined colors can be chosen:
13768 \begin_layout Standard
13802 \begin_layout Standard
13804 \begin_inset Tabular
13805 <lyxtabular version="3" rows="4" columns="2">
13806 <features tabularvalignment="middle">
13807 <column alignment="center" valignment="top" width="0">
13808 <column alignment="center" valignment="top" width="0">
13810 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13813 \begin_layout Plain Layout
13819 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13822 \begin_layout Plain Layout
13824 \begin_inset Note Note
13827 \begin_layout Plain Layout
13834 is only used as spacer.
13846 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13849 \begin_layout Plain Layout
13853 \begin_inset Formula $\to$
13863 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13866 \begin_layout Plain Layout
13867 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
13877 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13880 \begin_layout Plain Layout
13884 \begin_inset Formula $\to$
13895 \begin_layout Plain Layout
13909 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13912 \begin_layout Plain Layout
13913 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
13923 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13926 \begin_layout Plain Layout
13933 \begin_layout Plain Layout
13945 \begin_inset Formula $\to$
13964 \begin_layout Plain Layout
13978 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13981 \begin_layout Plain Layout
13982 \begin_inset Formula $\raisebox{7mm}{}\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}\raisebox{-5mm}{}$
13998 \begin_layout Standard
14005 only colors the box but not the characters in the box.
14006 To color all characters, the whole formula is highlighted and the wanted
14007 color is chosen in the
14010 \begin_inset space ~
14016 The dialog can be called with the toolbar button
14017 \begin_inset Graphics
14018 filename ../images/dialog-show_character.png
14025 Edit\SpecialChar \menuseparator
14027 \begin_inset space ~
14030 Style\SpecialChar \menuseparator
14034 The formula number has then the same color as the formula.
14035 When the formula number should get another color than the formula characters,
14036 the color must be changed within the formula.
14039 \begin_layout Standard
14043 \begin_layout Standard
14046 \begin_inset Formula
14048 \int A=B\label{eq:red}
14056 \begin_inset Formula
14058 \textcolor{red}{\int A=B}\label{eq:redgreen}
14066 \begin_layout Standard
14068 \begin_inset CommandInset ref
14074 is completely colored red.
14075 \begin_inset Newline newline
14079 \begin_inset CommandInset ref
14081 reference "eq:redgreen"
14085 was first completely colored green to set the color for the formula number.
14086 Subsequently the formula characters were colored red.
14089 \begin_layout Standard
14090 \begin_inset VSpace bigskip
14093 To color the frame different than the rest of the box, the command
14100 \begin_inset Index idx
14103 \begin_layout Plain Layout
14111 is used in the following scheme:
14114 \begin_layout Standard
14119 fcolorbox{frame color}{color}{box content}
14122 \begin_layout Standard
14129 is an extension of the command
14136 The frame width is set, like for
14159 \begin_layout Plain Layout
14171 \begin_inset Formula
14173 \fcolorbox{cyan}{magenta}{A=B}
14182 \begin_layout Plain Layout
14196 \begin_layout Standard
14197 This formula was created with the command
14198 \begin_inset Newline newline
14206 \begin_inset Formula $\to$
14212 \begin_inset Formula $\to$
14222 \begin_layout Standard
14223 \begin_inset VSpace bigskip
14226 To use other colors than the predefined ones, they have to be defined first.
14229 \begin_layout Standard
14230 One can for example define the color
14231 \begin_inset Quotes eld
14239 \begin_inset Quotes erd
14242 with the LaTeX-preamble line:
14245 \begin_layout Standard
14250 definecolor{darkgreen}{cmyk}{0.5,
14265 \begin_inset Index idx
14268 \begin_layout Plain Layout
14279 \begin_layout Standard
14284 is the color space that denotes the colors
14301 The four comma separated numbers are the portion factor for the corresponding
14302 colors of the color space.
14303 The factors can be in the range of 0
14304 \begin_inset space \thinspace{}
14308 \begin_inset space \thinspace{}
14316 also the color space
14320 can be used for definitions.
14337 , so that there are in this case three portion factors for the corresponding
14339 Furthermore there is the color space
14343 with one portion factor for the gray value.
14346 \begin_layout Standard
14347 As example a framed box with the new defined color
14351 where the characters have been colored
14356 \begin_inset Formula
14358 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}
14366 \begin_layout Standard
14367 Self-defined colors can also be used for text with the help of the command
14375 \begin_inset Index idx
14378 \begin_layout Plain Layout
14387 \begin_layout Standard
14391 \begin_layout Plain Layout
14395 textcolor{darkgreen}{
14401 \begin_inset Quotes eld
14405 \begin_inset Quotes erd
14412 \begin_layout Plain Layout
14422 \begin_layout Standard
14430 \begin_inset Index idx
14433 \begin_layout Plain Layout
14441 is used in the scheme
14445 textcolor{color}{characters to color}
14450 \begin_layout Subsection
14452 \begin_inset CommandInset label
14454 name "sub:Paragraph-Boxes"
14459 \begin_inset Index idx
14462 \begin_layout Plain Layout
14463 Boxes ! as paragraph
14471 \begin_layout Standard
14472 A box that can contain several lines and paragraphs, a so called paragraph
14473 box (parbox), can be created with the menu
14475 Insert\SpecialChar \menuseparator
14478 or the toolbar button
14479 \begin_inset Graphics
14480 filename ../images/box-insert.png
14488 \begin_layout Standard
14489 The following example shows a framed parbox in a line:
14492 \begin_layout Standard
14493 \begin_inset VSpace medskip
14497 \begin_inset Box Boxed
14507 height_special "totalheight"
14510 \begin_layout Plain Layout
14511 This is a paragraph box.
14513 \begin_inset space \thinspace{}
14516 cm long and can also contain formulas:
14517 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14528 \begin_layout Standard
14529 \begin_inset VSpace medskip
14535 \begin_layout Standard
14536 Such a box is created by right-clicking on the gray box inset.
14537 A dialog pops up showing the box properties.
14551 \begin_inset space \thinspace{}
14556 Vertical Box Alignment
14561 \begin_layout Standard
14562 \begin_inset VSpace medskip
14565 In LaTeX a parbox is created with the command
14572 \begin_inset Index idx
14575 \begin_layout Plain Layout
14583 that has the following scheme:
14586 \begin_layout Standard
14591 parbox[position]{width}{box content}
14594 \begin_layout Standard
14608 for bottom means that the box is aligned within the surrounding text with
14614 for top this is done with the first line.
14615 When no position is given, the box will be vertically centered, see section
14623 \begin_inset space ~
14628 manual for examples.
14631 \begin_layout Standard
14632 \begin_inset VSpace bigskip
14635 To frame formulas completely, including the formula number, the formula
14636 must be set into a parbox.
14637 To do this, the command
14651 is inserted in TeX-mode before the formula.
14659 \begin_inset Index idx
14662 \begin_layout Plain Layout
14670 is hereby the line width set for the document.
14671 Because the frame is outside the parbox, 2
14672 \begin_inset space \thinspace{}
14675 times the frame separation and the frame thickness must be subtracted from
14677 As this is not automatically done by LyX due to a bug
14681 \begin_layout Plain Layout
14682 \begin_inset CommandInset href
14684 name "LyX-bug #4483"
14685 target "http://www.lyx.org/trac/ticket/4483"
14694 , TeX-mode has to be used.
14695 To be able to multiply and subtract in arguments, the LaTeX-package
14703 \begin_layout Plain Layout
14708 is part of every LaTeX standard installation.
14714 \begin_inset Index idx
14717 \begin_layout Plain Layout
14723 must be loaded in the LaTeX-preamble with the line
14726 \begin_layout Standard
14734 \begin_layout Standard
14735 Behind the formula both boxes are closed by entering
14740 Here is an example:
14744 \begin_layout Plain Layout
14758 \begin_layout Standard
14762 \begin_layout Plain Layout
14780 \begin_inset Formula
14782 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}
14791 \begin_layout Plain Layout
14802 \begin_layout Plain Layout
14816 \begin_layout Standard
14817 \begin_inset VSpace medskip
14820 As a parbox is used as argument of
14826 , there is in this case no difference between
14841 \begin_layout Standard
14842 \begin_inset VSpace bigskip
14845 Paragraph boxes are very useful to comment formulas directly.
14852 is used in combination with the command
14866 \begin_inset CommandInset ref
14868 reference "sub:User-defined-Numbering"
14875 \begin_layout Standard
14876 An example of a formula commented with
14885 \begin_layout Standard
14889 \begin_layout Plain Layout
14902 This is a description.
14903 It is distinctly separated from the formula and multiline.
14907 \begin_layout Plain Layout
14919 \begin_layout Standard
14920 Such a formula must be inserted completely in TeX-mode because LyX does
14921 not yet support the command
14928 The formula is created with the following command sequence:
14931 \begin_layout Standard
14944 is inserted in TeX-mode.
14948 \begin_layout Plain Layout
14949 When the formula style
14961 can also be replaced by
14968 (formula styles see
14969 \begin_inset CommandInset ref
14971 reference "sec:Formula-Styles"
14980 Then the description follows as normal text and finally
14986 is inserted in TeX-mode.
14999 hereby create a displayed formula.
15002 \begin_layout Standard
15009 can be seen in this example that was
15010 \begin_inset Quotes eld
15014 \begin_inset Quotes erd
15017 using the mathematical textmode:
15018 \begin_inset Formula
15020 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}
15028 \begin_layout Section
15030 \begin_inset Index idx
15033 \begin_layout Plain Layout
15042 \begin_layout Subsection
15044 \begin_inset CommandInset label
15046 name "sub:Big-Operators"
15051 \begin_inset Index idx
15054 \begin_layout Plain Layout
15061 \begin_inset Index idx
15064 \begin_layout Plain Layout
15071 \begin_inset Index idx
15074 \begin_layout Plain Layout
15083 \begin_layout Standard
15084 To be able to use all integral operators listed here, the option
15086 Use esint package automatically
15088 must be set in the document settings under
15091 \begin_inset space ~
15099 \begin_layout Standard
15100 \begin_inset space \hfill{}
15104 \begin_inset Tabular
15105 <lyxtabular version="3" rows="11" columns="2">
15106 <features tabularvalignment="middle">
15107 <column alignment="center" valignment="top" width="0pt">
15108 <column alignment="center" valignment="top" width="0pt">
15110 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15113 \begin_layout Plain Layout
15119 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15122 \begin_layout Plain Layout
15130 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15133 \begin_layout Plain Layout
15137 \begin_inset Index idx
15140 \begin_layout Plain Layout
15153 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15156 \begin_layout Plain Layout
15157 \begin_inset Formula $\int$
15167 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15170 \begin_layout Plain Layout
15178 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15181 \begin_layout Plain Layout
15182 \begin_inset Formula $\oint$
15192 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15195 \begin_layout Plain Layout
15203 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15206 \begin_layout Plain Layout
15207 \begin_inset Formula $\ointctrclockwise$
15217 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15220 \begin_layout Plain Layout
15228 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15231 \begin_layout Plain Layout
15232 \begin_inset Formula $\ointclockwise$
15242 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15245 \begin_layout Plain Layout
15253 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15256 \begin_layout Plain Layout
15257 \begin_inset Formula $\sqint$
15267 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15270 \begin_layout Plain Layout
15278 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15281 \begin_layout Plain Layout
15283 \begin_inset Formula $\fint$
15293 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15296 \begin_layout Plain Layout
15304 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15307 \begin_layout Plain Layout
15309 \begin_inset Formula $\landupint$
15319 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15322 \begin_layout Plain Layout
15330 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15333 \begin_layout Plain Layout
15335 \begin_inset Formula $\landdownint$
15345 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15348 \begin_layout Plain Layout
15356 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15359 \begin_layout Plain Layout
15360 \begin_inset Formula $\bigcap$
15370 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15373 \begin_layout Plain Layout
15381 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15384 \begin_layout Plain Layout
15385 \begin_inset Formula $\bigcup$
15399 \begin_inset space \hfill{}
15403 \begin_inset Tabular
15404 <lyxtabular version="3" rows="11" columns="2">
15405 <features tabularvalignment="middle">
15406 <column alignment="center" valignment="top" width="0pt">
15407 <column alignment="center" valignment="top" width="0pt">
15409 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15412 \begin_layout Plain Layout
15418 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15421 \begin_layout Plain Layout
15429 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15432 \begin_layout Plain Layout
15436 \begin_inset Index idx
15439 \begin_layout Plain Layout
15452 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15455 \begin_layout Plain Layout
15456 \begin_inset Formula $\sum$
15466 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15469 \begin_layout Plain Layout
15473 \begin_inset Index idx
15476 \begin_layout Plain Layout
15489 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15492 \begin_layout Plain Layout
15493 \begin_inset Formula $\prod$
15503 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15506 \begin_layout Plain Layout
15514 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15517 \begin_layout Plain Layout
15518 \begin_inset Formula $\coprod$
15528 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15531 \begin_layout Plain Layout
15539 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15542 \begin_layout Plain Layout
15543 \begin_inset Formula $\bigodot$
15553 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15556 \begin_layout Plain Layout
15564 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15567 \begin_layout Plain Layout
15568 \begin_inset Formula $\bigotimes$
15578 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15581 \begin_layout Plain Layout
15589 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15592 \begin_layout Plain Layout
15593 \begin_inset Formula $\bigoplus$
15603 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15606 \begin_layout Plain Layout
15614 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15617 \begin_layout Plain Layout
15618 \begin_inset Formula $\bigwedge$
15628 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15631 \begin_layout Plain Layout
15639 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15642 \begin_layout Plain Layout
15643 \begin_inset Formula $\bigvee$
15653 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15656 \begin_layout Plain Layout
15664 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15667 \begin_layout Plain Layout
15668 \begin_inset Formula $\bigsqcup$
15678 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15681 \begin_layout Plain Layout
15689 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15692 \begin_layout Plain Layout
15693 \begin_inset Formula $\biguplus$
15707 \begin_inset space \hfill{}
15713 \begin_layout Standard
15714 All big operators can also be inserted via the math toolbar button
15715 \begin_inset Graphics
15716 filename ../images/math/intop.png
15724 \begin_layout Standard
15725 The operators are called big because they are bigger than the sometimes
15726 equal looking binary operators.
15727 All big operators can have limits as described in the next subsection.
15730 \begin_layout Standard
15731 For all integral operators there is a second version available, ending on
15749 These operators are different from
15756 \begin_inset space \space{}
15759 in the style the operator limits are displayed, see
15760 \begin_inset CommandInset ref
15762 reference "sub:Operator-Limits"
15770 \begin_layout Subsubsection*
15771 Advice for Integrals
15774 \begin_layout Standard
15779 in an integral is an operator, that therefore has to be set upright.
15780 This is done by highlighting the
15784 and using the keyboard shortcut
15794 \begin_layout Plain Layout
15800 \begin_inset CommandInset ref
15802 reference "sub:Font-Styles"
15812 Finally the smallest space is inserted before the
15816 , as this is usual for operators.
15820 \begin_layout Standard
15822 \begin_inset Formula $\int A(x)dx$
15826 \begin_inset Newline newline
15830 \begin_inset Phantom HPhantom
15833 \begin_layout Plain Layout
15840 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15846 \begin_layout Standard
15847 For multiple integrals there are the following commands:
15848 \begin_inset VSpace medskip
15854 \begin_layout Standard
15855 \begin_inset space \hfill{}
15859 \begin_inset Tabular
15860 <lyxtabular version="3" rows="4" columns="2">
15861 <features tabularvalignment="middle">
15862 <column alignment="center" valignment="top" width="0">
15863 <column alignment="center" valignment="top" width="0">
15865 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15868 \begin_layout Plain Layout
15874 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15877 \begin_layout Plain Layout
15879 \begin_inset Note Note
15882 \begin_layout Plain Layout
15889 is only used as spacer.
15901 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15904 \begin_layout Plain Layout
15912 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15915 \begin_layout Plain Layout
15916 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
15926 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15929 \begin_layout Plain Layout
15937 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15940 \begin_layout Plain Layout
15941 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
15951 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15954 \begin_layout Plain Layout
15962 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15965 \begin_layout Plain Layout
15966 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
15980 \begin_inset space \hfill{}
15984 \begin_inset Tabular
15985 <lyxtabular version="3" rows="4" columns="2">
15986 <features tabularvalignment="middle">
15987 <column alignment="center" valignment="top" width="0">
15988 <column alignment="center" valignment="top" width="0">
15990 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15993 \begin_layout Plain Layout
15999 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16002 \begin_layout Plain Layout
16010 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16013 \begin_layout Plain Layout
16021 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16024 \begin_layout Plain Layout
16025 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
16035 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16038 \begin_layout Plain Layout
16046 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16049 \begin_layout Plain Layout
16050 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
16060 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16063 \begin_layout Plain Layout
16071 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16074 \begin_layout Plain Layout
16075 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
16089 \begin_inset space \hfill{}
16095 \begin_layout Subsection
16097 \begin_inset CommandInset label
16099 name "sub:Operator-Limits"
16104 \begin_inset Index idx
16107 \begin_layout Plain Layout
16116 \begin_layout Standard
16117 Limits are created by super- and subscripts:
16120 \begin_layout Standard
16122 \begin_inset Tabular
16123 <lyxtabular version="3" rows="2" columns="2">
16124 <features tabularvalignment="middle">
16125 <column alignment="center" valignment="top" width="0pt">
16126 <column alignment="center" valignment="top" width="0pt">
16128 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16131 \begin_layout Plain Layout
16137 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16140 \begin_layout Plain Layout
16142 \begin_inset Note Note
16145 \begin_layout Plain Layout
16152 is only used as spacer.
16164 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16167 \begin_layout Plain Layout
16176 \begin_layout Plain Layout
16186 \begin_inset Formula $\to$
16190 \begin_inset Formula $\to$
16198 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16201 \begin_layout Plain Layout
16202 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
16218 \begin_layout Standard
16219 Limits of inline formulas are set right beside the operator.
16220 Limits in displayed formulas are set above or below the operator, except
16221 for integral limits.
16224 \begin_layout Standard
16225 To force that the limits are set beside the operator, the cursor is set
16226 directly behind the operator and the limits type is changed with the menu
16229 Edit\SpecialChar \menuseparator
16230 Math\SpecialChar \menuseparator
16249 \begin_layout Standard
16250 The default limits type is this:
16251 \begin_inset Formula
16253 \sum_{x=0}^{\infty}\frac{1}{x^{2}}
16258 This is how it looks when the limits type was changed to
16265 \begin_inset Formula
16267 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}
16272 For integrals, except those ending with
16288 etc., the limits are by default set beside the operator.
16289 But for multiple integrals the limits are often set below the operator.
16290 In the following example the limits type was therefore set to
16294 and so set below the integrals:
16295 \begin_inset Formula
16297 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}
16305 \begin_layout Standard
16306 \begin_inset VSpace medskip
16309 To specify conditions for limits, the commands
16316 \begin_inset Index idx
16319 \begin_layout Plain Layout
16334 \begin_inset Index idx
16337 \begin_layout Plain Layout
16346 To create for example this expression
16347 \begin_inset Formula
16349 \sum_{\begin{subarray}{c}
16353 \end{subarray}}^{n}k^{-2}\label{eq:substack}
16361 \begin_layout Standard
16362 the following has to be done:
16363 \begin_inset Newline newline
16378 \begin_layout Plain Layout
16390 One is now in a blue box under the summation operator and insert there
16399 \begin_layout Plain Layout
16411 The blue box is now within a purple box and now several lines can be written
16413 A new line is created by inserting a line break (
16416 arg "newline-insert newline"
16421 \begin_inset Newline newline
16426 0<k<1000 Ctrl+Return
16427 \begin_inset Newline newline
16432 is typed in, a new box appears below for the new line.
16435 \begin_layout Standard
16436 The alignment of the lines can be changed to left aligned with the
16446 Edit\SpecialChar \menuseparator
16450 To get right alignment,
16458 \begin_layout Plain Layout
16469 is inserted at the beginning of the line.
16472 \begin_layout Standard
16485 with the difference that the lines are always centered.
16488 \begin_layout Standard
16489 \begin_inset VSpace bigskip
16493 \begin_inset CommandInset ref
16495 reference "eq:substack"
16499 there can be too much space beside an operator, because the characters
16500 following the operator are set beside the limits.
16503 \begin_layout Standard
16504 To avoid this, the following macro can be used in the LaTeX-preamble:
16507 \begin_layout Standard
16521 \begin_inset Newline newline
16533 \begin_inset Newline newline
16540 mathclapinternal #1#2{
16544 mathsurround =0pt #1{#2}$}}
16547 \begin_layout Standard
16548 This defines the command
16555 \begin_inset Index idx
16558 \begin_layout Plain Layout
16566 that sets the width of the limit to 0
16567 \begin_inset space \thinspace{}
16571 The command scheme is
16574 \begin_layout Standard
16582 \begin_layout Standard
16583 where the limit can consist of several conditions.
16586 \begin_layout Standard
16588 \begin_inset CommandInset ref
16590 reference "eq:substack"
16594 , one uses the command
16597 \begin_layout Standard
16610 \begin_layout Plain Layout
16619 0<k<1000 Ctrl+Return
16622 \begin_layout Standard
16623 to create the lower limit.
16624 The summand is now directly behind the summation operator:
16625 \begin_inset Formula
16627 \sum_{\mathclap{\substack{0<k<1000\\
16639 \begin_layout Standard
16640 \begin_inset VSpace bigskip
16643 How to use one limit for several operators is described in
16644 \begin_inset CommandInset ref
16646 reference "sub:Self-defined-Operators"
16653 \begin_layout Subsection
16655 \begin_inset CommandInset label
16657 name "sub:Binary-Operators"
16662 \begin_inset Index idx
16665 \begin_layout Plain Layout
16674 \begin_layout Standard
16675 Binary operators are surrounded by space when there is a character before
16677 \begin_inset VSpace medskip
16683 \begin_layout Standard
16684 \begin_inset space \hfill{}
16688 \begin_inset Tabular
16689 <lyxtabular version="3" rows="13" columns="2">
16690 <features tabularvalignment="middle">
16691 <column alignment="center" valignment="top" width="0pt">
16692 <column alignment="center" valignment="top" width="0pt">
16694 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16697 \begin_layout Plain Layout
16699 \begin_inset Note Note
16702 \begin_layout Plain Layout
16709 is only used as spacer.
16719 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16722 \begin_layout Plain Layout
16730 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16733 \begin_layout Plain Layout
16739 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16742 \begin_layout Plain Layout
16743 \begin_inset Formula $+$
16753 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16756 \begin_layout Plain Layout
16762 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16765 \begin_layout Plain Layout
16766 \begin_inset Formula $-$
16776 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16779 \begin_layout Plain Layout
16787 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16790 \begin_layout Plain Layout
16791 \begin_inset Formula $\pm$
16801 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16804 \begin_layout Plain Layout
16812 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16815 \begin_layout Plain Layout
16816 \begin_inset Formula $\mp$
16826 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16829 \begin_layout Plain Layout
16837 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16840 \begin_layout Plain Layout
16841 \begin_inset Formula $\cdot$
16851 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16854 \begin_layout Plain Layout
16862 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16865 \begin_layout Plain Layout
16866 \begin_inset Formula $\times$
16876 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16879 \begin_layout Plain Layout
16887 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16890 \begin_layout Plain Layout
16891 \begin_inset Formula $\div$
16901 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16904 \begin_layout Plain Layout
16908 \begin_layout Plain Layout
16921 \begin_layout Plain Layout
16933 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16936 \begin_layout Plain Layout
16937 \begin_inset Formula $*$
16947 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16950 \begin_layout Plain Layout
16958 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16961 \begin_layout Plain Layout
16962 \begin_inset Formula $\star$
16972 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16975 \begin_layout Plain Layout
16983 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16986 \begin_layout Plain Layout
16987 \begin_inset Formula $\circ$
16997 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17000 \begin_layout Plain Layout
17008 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17011 \begin_layout Plain Layout
17012 \begin_inset Formula $\diamond$
17022 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17025 \begin_layout Plain Layout
17033 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17036 \begin_layout Plain Layout
17037 \begin_inset Formula $\bullet$
17051 \begin_inset space \hfill{}
17055 \begin_inset Tabular
17056 <lyxtabular version="3" rows="13" columns="2">
17057 <features tabularvalignment="middle">
17058 <column alignment="center" valignment="top" width="0pt">
17059 <column alignment="center" valignment="top" width="0pt">
17061 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17064 \begin_layout Plain Layout
17070 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17073 \begin_layout Plain Layout
17081 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17084 \begin_layout Plain Layout
17092 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17095 \begin_layout Plain Layout
17096 \begin_inset Formula $\nabla$
17106 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17109 \begin_layout Plain Layout
17117 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17120 \begin_layout Plain Layout
17121 \begin_inset Formula $\bigtriangledown$
17131 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17134 \begin_layout Plain Layout
17142 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17145 \begin_layout Plain Layout
17146 \begin_inset Formula $\bigtriangleup$
17156 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17159 \begin_layout Plain Layout
17167 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17170 \begin_layout Plain Layout
17171 \begin_inset Formula $\Box$
17181 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17184 \begin_layout Plain Layout
17192 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17195 \begin_layout Plain Layout
17196 \begin_inset Formula $\cap$
17206 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17209 \begin_layout Plain Layout
17217 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17220 \begin_layout Plain Layout
17221 \begin_inset Formula $\cup$
17231 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17234 \begin_layout Plain Layout
17242 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17245 \begin_layout Plain Layout
17246 \begin_inset Formula $\dagger$
17256 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17259 \begin_layout Plain Layout
17267 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17270 \begin_layout Plain Layout
17271 \begin_inset Formula $\ddagger$
17281 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17284 \begin_layout Plain Layout
17292 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17295 \begin_layout Plain Layout
17296 \begin_inset Formula $\wr$
17306 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17309 \begin_layout Plain Layout
17317 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17320 \begin_layout Plain Layout
17321 \begin_inset Formula $\bigcirc$
17331 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17334 \begin_layout Plain Layout
17342 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17345 \begin_layout Plain Layout
17346 \begin_inset Formula $\wedge$
17356 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17359 \begin_layout Plain Layout
17367 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17370 \begin_layout Plain Layout
17371 \begin_inset Formula $\vee$
17385 \begin_inset space \hfill{}
17389 \begin_inset Tabular
17390 <lyxtabular version="3" rows="13" columns="2">
17391 <features tabularvalignment="middle">
17392 <column alignment="center" valignment="top" width="0pt">
17393 <column alignment="center" valignment="top" width="0pt">
17395 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17398 \begin_layout Plain Layout
17404 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17407 \begin_layout Plain Layout
17415 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17418 \begin_layout Plain Layout
17426 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17429 \begin_layout Plain Layout
17430 \begin_inset Formula $\oplus$
17440 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17443 \begin_layout Plain Layout
17451 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17454 \begin_layout Plain Layout
17455 \begin_inset Formula $\ominus$
17465 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17468 \begin_layout Plain Layout
17476 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17479 \begin_layout Plain Layout
17480 \begin_inset Formula $\otimes$
17490 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17493 \begin_layout Plain Layout
17501 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17504 \begin_layout Plain Layout
17505 \begin_inset Formula $\oslash$
17515 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17518 \begin_layout Plain Layout
17526 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17529 \begin_layout Plain Layout
17530 \begin_inset Formula $\odot$
17540 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17543 \begin_layout Plain Layout
17551 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17554 \begin_layout Plain Layout
17555 \begin_inset Formula $\amalg$
17565 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17568 \begin_layout Plain Layout
17576 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17579 \begin_layout Plain Layout
17580 \begin_inset Formula $\uplus$
17590 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17593 \begin_layout Plain Layout
17601 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17604 \begin_layout Plain Layout
17605 \begin_inset Formula $\setminus$
17615 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17618 \begin_layout Plain Layout
17626 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17629 \begin_layout Plain Layout
17630 \begin_inset Formula $\sqcap$
17640 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17643 \begin_layout Plain Layout
17651 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17654 \begin_layout Plain Layout
17655 \begin_inset Formula $\sqcup$
17665 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17668 \begin_layout Plain Layout
17676 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17679 \begin_layout Plain Layout
17680 \begin_inset Formula $\triangleleft$
17690 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17693 \begin_layout Plain Layout
17701 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17704 \begin_layout Plain Layout
17705 \begin_inset Formula $\triangleright$
17719 \begin_inset space \hfill{}
17725 \begin_layout Standard
17726 All binary operators can also be inserted via the math toolbar button
17727 \begin_inset Graphics
17728 filename ../images/math/pm.png
17736 \begin_layout Standard
17737 To typeset the Laplace operator also
17754 \begin_inset Formula $\nabla^{2}$
17757 ) can be used instead of
17766 \begin_layout Standard
17773 Insert\SpecialChar \menuseparator
17785 \begin_layout Subsection
17786 Self-defined Operators
17787 \begin_inset CommandInset label
17789 name "sub:Self-defined-Operators"
17794 \begin_inset Index idx
17797 \begin_layout Plain Layout
17798 Operators ! self-defined
17806 \begin_layout Standard
17807 With the help of the command
17811 DeclareMathOperator
17814 \begin_inset Index idx
17817 \begin_layout Plain Layout
17822 DeclareMathOperator
17827 custom operators can be defined in the LaTeX-preamble.
17828 Its command scheme is:
17831 \begin_layout Standard
17836 DeclareMathOperator{new command}{display}
17839 \begin_layout Standard
17840 Display can be characters or symbols that define how the operator looks
17842 To define a big operator a * is set behind the command.
17843 All self-defined big operators can have limits as described in
17844 \begin_inset CommandInset ref
17846 reference "sub:Operator-Limits"
17853 \begin_layout Standard
17854 For example the LaTeX-preamble line
17857 \begin_layout Standard
17862 DeclareMathOperator*{
17869 \begin_layout Standard
17870 defines the command
17876 , that inserts a big operator consisting of the lozenge symbol from
17877 \begin_inset CommandInset ref
17879 reference "sub:Miscellaneous-Symbols"
17884 \begin_inset Formula
17886 \Lozenge_{n=1}^{\infty}
17891 The command for this formula is:
17902 \begin_inset Formula $\to$
17908 \begin_layout Standard
17909 \begin_inset VSpace bigskip
17912 When self-defined operators are not used several times in the document,
17913 they can also be defined with the commands
17920 \begin_inset Index idx
17923 \begin_layout Plain Layout
17938 \begin_inset Index idx
17941 \begin_layout Plain Layout
17949 , which have the following scheme:
17952 \begin_layout Standard
17966 \begin_layout Standard
17973 defines big operators,
17982 \begin_layout Standard
17990 \begin_inset space \thinspace{}
17994 \begin_inset space \space{}
17997 be used to use one limit for several operators:
18000 \begin_layout Standard
18001 \begin_inset Formula
18003 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
18011 \begin_layout Standard
18012 The command for the formula above is:
18013 \begin_inset Newline newline
18032 \begin_layout Plain Layout
18044 \begin_inset Formula $\to$
18053 \begin_layout Plain Layout
18067 \begin_layout Section
18069 \begin_inset Index idx
18072 \begin_layout Plain Layout
18081 \begin_layout Subsection
18083 \begin_inset CommandInset label
18085 name "sub:Font-Styles"
18090 \begin_inset Index idx
18093 \begin_layout Plain Layout
18102 \begin_layout Standard
18103 Latin letters in formulas can be set in one of the following font styles:
18104 \begin_inset VSpace -2mm
18110 \begin_layout Standard
18112 \begin_inset Tabular
18113 <lyxtabular version="3" rows="7" columns="3">
18114 <features tabularvalignment="middle">
18115 <column alignment="center" valignment="top" width="0">
18116 <column alignment="center" valignment="top" width="0">
18117 <column alignment="center" valignment="top" width="0">
18119 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18122 \begin_layout Plain Layout
18128 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18131 \begin_layout Plain Layout
18137 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18140 \begin_layout Plain Layout
18148 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18151 \begin_layout Plain Layout
18160 \begin_layout Plain Layout
18176 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18179 \begin_layout Plain Layout
18180 \begin_inset Formula $\mathbb{ABC}$
18188 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18191 \begin_layout Plain Layout
18204 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18207 \begin_layout Plain Layout
18216 \begin_layout Plain Layout
18232 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18235 \begin_layout Plain Layout
18236 \begin_inset Formula $\mathbf{AbC}$
18244 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18247 \begin_layout Plain Layout
18260 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18263 \begin_layout Plain Layout
18272 \begin_layout Plain Layout
18288 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18291 \begin_layout Plain Layout
18292 \begin_inset Formula $\boldsymbol{AbC}$
18300 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18303 \begin_layout Plain Layout
18306 arg "font-boldsymbol"
18316 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18319 \begin_layout Plain Layout
18328 \begin_layout Plain Layout
18344 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18347 \begin_layout Plain Layout
18348 \begin_inset Formula $\mathcal{ABC}$
18356 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18359 \begin_layout Plain Layout
18372 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18375 \begin_layout Plain Layout
18384 \begin_layout Plain Layout
18400 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18403 \begin_layout Plain Layout
18404 \begin_inset Formula $\mathfrak{AbC}$
18412 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18415 \begin_layout Plain Layout
18423 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18426 \begin_layout Plain Layout
18435 \begin_layout Plain Layout
18451 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18454 \begin_layout Plain Layout
18455 \begin_inset Formula $\mathscr{AbC}$
18463 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18466 \begin_layout Plain Layout
18480 \begin_layout Standard
18482 \begin_inset Tabular
18483 <lyxtabular version="3" rows="5" columns="3">
18484 <features tabularvalignment="middle">
18485 <column alignment="center" valignment="top" width="0">
18486 <column alignment="center" valignment="top" width="0">
18487 <column alignment="center" valignment="top" width="0">
18489 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18492 \begin_layout Plain Layout
18498 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18501 \begin_layout Plain Layout
18507 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18510 \begin_layout Plain Layout
18518 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18521 \begin_layout Plain Layout
18530 \begin_layout Plain Layout
18546 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18549 \begin_layout Plain Layout
18550 \begin_inset Formula $\mathit{AbC}$
18558 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18561 \begin_layout Plain Layout
18569 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18572 \begin_layout Plain Layout
18581 \begin_layout Plain Layout
18597 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18600 \begin_layout Plain Layout
18601 \begin_inset Formula $\mathrm{AbC}$
18609 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18612 \begin_layout Plain Layout
18625 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18628 \begin_layout Plain Layout
18637 \begin_layout Plain Layout
18653 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18656 \begin_layout Plain Layout
18657 \begin_inset Formula $\mathsf{AbC}$
18665 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18668 \begin_layout Plain Layout
18681 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18684 \begin_layout Plain Layout
18693 \begin_layout Plain Layout
18709 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18712 \begin_layout Plain Layout
18713 \begin_inset Formula $\mathtt{AbC}$
18721 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18724 \begin_layout Plain Layout
18727 arg "font-typewriter"
18743 \begin_layout Standard
18744 \begin_inset Note Greyedout
18747 \begin_layout Plain Layout
18764 can only be used for big letters.
18772 \begin_layout Standard
18773 Predefined is the style
18782 \begin_layout Standard
18783 The style commands work also for letters in mathematical constructs:
18784 \begin_inset Formula
18786 \mathfrak{A=\frac{b}{C}}
18794 \begin_layout Standard
18795 Characters in mathematical text don't appear in a math font style but in
18796 the text font style
18803 That their style can't be set correctly via the text style dialog is a
18808 \begin_layout Plain Layout
18809 \begin_inset CommandInset href
18811 name "LyX-bug #4629"
18812 target "http://www.lyx.org/trac/ticket/4629"
18824 \begin_layout Standard
18825 Instead of the style commands the dialog
18827 Edit\SpecialChar \menuseparator
18828 Math\SpecialChar \menuseparator
18831 or the toolbar button
18832 \begin_inset Graphics
18833 filename ../images/math/font.png
18841 \begin_layout Subsection
18843 \begin_inset CommandInset label
18845 name "sub:Bold-Formulas"
18850 \begin_inset Index idx
18853 \begin_layout Plain Layout
18862 \begin_layout Standard
18863 To make a complete formula bold, the command
18869 from the previous subsection cannot be used, because it doesn't work for
18870 small Greek letters.
18871 Furthermore it prints Latin letters always upright, like in the following
18875 \begin_layout Standard
18876 \begin_inset Formula
18878 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
18886 \begin_layout Standard
18887 To display the formula correctly, the command
18894 \begin_inset Formula
18896 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
18901 It is also possible to set the formula in a
18903 boldmath environment
18906 This environment is created by inserting the command
18913 \begin_inset Index idx
18916 \begin_layout Plain Layout
18925 To end the environment, the command
18932 \begin_inset Index idx
18935 \begin_layout Plain Layout
18943 is inserted in TeX-mode.
18947 \begin_layout Plain Layout
18957 \begin_inset Formula
18959 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
18968 \begin_layout Plain Layout
18980 \begin_layout Subsection
18982 \begin_inset Index idx
18985 \begin_layout Plain Layout
18994 \begin_layout Standard
18995 Formulas can be colored like normal text: Highlight a formula or a formula
19001 Here is a formula in magenta:
19002 \begin_inset Formula
19004 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
19012 \begin_layout Standard
19013 You can also define your own colors as described in
19014 \begin_inset CommandInset ref
19016 reference "sub:Colored-Boxes"
19021 They can be used with the TeX code command
19028 \begin_inset Index idx
19031 \begin_layout Plain Layout
19042 \begin_layout Standard
19047 textcolor{color}{characters or formula}
19050 \begin_layout Standard
19051 The following example was colored completely dark green and partly red:
19054 \begin_layout Standard
19058 \begin_layout Plain Layout
19062 textcolor{darkgreen}{
19068 \begin_inset Formula
19070 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
19079 \begin_layout Plain Layout
19089 \begin_layout Standard
19090 Due to a bug in LyX only complete formulas can be colored with self-defined
19095 \begin_layout Plain Layout
19096 \begin_inset CommandInset href
19098 name "LyX-bug #5269"
19099 target "http://www.lyx.org/trac/ticket/5269"
19111 \begin_layout Subsection
19113 \begin_inset CommandInset label
19115 name "sub:Font-Sizes"
19120 \begin_inset Index idx
19123 \begin_layout Plain Layout
19132 \begin_layout Standard
19133 For characters in formulas there are, analog to characters in text, the
19134 following size commands:
19137 \begin_layout Standard
19181 \begin_inset Newline newline
19203 \begin_layout Standard
19204 The size produced by the commands depends on the document font size, that
19205 corresponds with the command
19212 The other commands produce smaller or larger sizes than
19219 The font size can however not exceed a certain value.
19220 Is for example the document font size 12
19221 \begin_inset space \thinspace{}
19230 switches to the same size as
19240 \begin_layout Standard
19241 A size command is inserted in TeX-mode before the formula and sets the size
19242 for all following formula and text characters.
19243 To switch back to the initial size, the command
19249 is inserted behind the formula in TeX-mode.
19252 \begin_layout Standard
19253 \begin_inset Newpage newpage
19259 \begin_layout Standard
19260 Within a formula the size can be changed using the following size commands:
19263 \begin_layout Standard
19266 \begin_inset Tabular
19267 <lyxtabular version="3" rows="5" columns="2">
19268 <features tabularvalignment="middle">
19269 <column alignment="center" valignment="top" width="0">
19270 <column alignment="center" valignment="top" width="0">
19272 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19275 \begin_layout Plain Layout
19281 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19284 \begin_layout Plain Layout
19286 \begin_inset Note Note
19289 \begin_layout Plain Layout
19296 is only used as spacer.
19308 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19311 \begin_layout Plain Layout
19315 \begin_inset Index idx
19318 \begin_layout Plain Layout
19331 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19334 \begin_layout Plain Layout
19335 \begin_inset Formula $\raisebox{6.5mm}{}{\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-5.5mm}{}$
19345 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19348 \begin_layout Plain Layout
19356 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19359 \begin_layout Plain Layout
19360 \begin_inset Formula $\raisebox{4.5mm}{}{\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-4mm}{}$
19370 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19373 \begin_layout Plain Layout
19381 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19384 \begin_layout Plain Layout
19385 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
19395 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19398 \begin_layout Plain Layout
19406 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19409 \begin_layout Plain Layout
19410 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
19426 \begin_layout Standard
19427 After entering these commands, a blue box appears in which the formula parts
19431 \begin_layout Standard
19432 There is a further method to change the font size, that though only works
19433 for symbols or letters in mathematical text.
19434 To use it, one of the above text size commands is inserted in mathematical
19436 All following characters until the end of the mathematical text or until
19437 another size command will have the selected size.
19439 \begin_inset VSpace -2mm
19445 \begin_layout Standard
19449 \begin_layout Plain Layout
19459 \begin_inset Formula
19461 A=\frac{B}{c}\cdot\maltese
19467 \begin_inset Formula
19469 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
19478 \begin_layout Plain Layout
19490 \begin_layout Standard
19491 \begin_inset VSpace medskip
19494 Before both formulas the command
19501 The command for the second formula is:
19502 \begin_inset Newline newline
19513 \begin_layout Plain Layout
19528 \begin_layout Plain Layout
19543 \begin_layout Plain Layout
19558 \begin_layout Plain Layout
19568 \begin_inset Formula $\to$
19572 \begin_inset Formula $\to$
19576 \begin_inset Newline newline
19580 \begin_inset space \hspace*{}
19594 \begin_layout Plain Layout
19609 \begin_layout Plain Layout
19624 \begin_layout Plain Layout
19636 \begin_layout Standard
19637 If a symbol cannot be displayed in different sizes, it will always be displayed
19638 in the default size.
19641 \begin_layout Standard
19642 \begin_inset Newpage newpage
19648 \begin_layout Section
19650 \begin_inset Index idx
19653 \begin_layout Plain Layout
19662 \begin_layout Standard
19663 Greek letters can also be inserted via the toolbar button
19664 \begin_inset Graphics
19665 filename ../images/math/alpha.png
19671 All international typesetting norms purport that Greek letters in math
19672 have to be typeset italic/slanted.
19673 In some languages, like French or Russian, they are nevertheless sometimes
19677 \begin_layout Subsection
19679 \begin_inset Index idx
19682 \begin_layout Plain Layout
19683 Greek letters ! small
19691 \begin_layout Standard
19692 \begin_inset space \hfill{}
19696 \begin_inset Tabular
19697 <lyxtabular version="3" rows="11" columns="2">
19698 <features tabularvalignment="middle">
19699 <column alignment="center" valignment="top" width="0pt">
19700 <column alignment="center" valignment="top" width="0pt">
19702 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19705 \begin_layout Plain Layout
19711 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19714 \begin_layout Plain Layout
19722 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19725 \begin_layout Plain Layout
19733 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19736 \begin_layout Plain Layout
19737 \begin_inset Formula $\alpha$
19747 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19750 \begin_layout Plain Layout
19758 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19761 \begin_layout Plain Layout
19762 \begin_inset Formula $\beta$
19772 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19775 \begin_layout Plain Layout
19783 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19786 \begin_layout Plain Layout
19787 \begin_inset Formula $\gamma$
19797 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19800 \begin_layout Plain Layout
19808 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19811 \begin_layout Plain Layout
19812 \begin_inset Formula $\delta$
19822 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19825 \begin_layout Plain Layout
19833 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19836 \begin_layout Plain Layout
19837 \begin_inset Formula $\epsilon$
19847 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19850 \begin_layout Plain Layout
19858 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19861 \begin_layout Plain Layout
19862 \begin_inset Formula $\varepsilon$
19872 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19875 \begin_layout Plain Layout
19883 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19886 \begin_layout Plain Layout
19887 \begin_inset Formula $\zeta$
19897 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19900 \begin_layout Plain Layout
19908 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19911 \begin_layout Plain Layout
19912 \begin_inset Formula $\eta$
19922 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19925 \begin_layout Plain Layout
19933 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19936 \begin_layout Plain Layout
19937 \begin_inset Formula $\theta$
19947 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19950 \begin_layout Plain Layout
19958 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19961 \begin_layout Plain Layout
19962 \begin_inset Formula $\vartheta$
19976 \begin_inset space \hfill{}
19980 \begin_inset Tabular
19981 <lyxtabular version="3" rows="12" columns="2">
19982 <features tabularvalignment="middle">
19983 <column alignment="center" valignment="top" width="0pt">
19984 <column alignment="center" valignment="top" width="0pt">
19986 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19989 \begin_layout Plain Layout
19995 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19998 \begin_layout Plain Layout
20006 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20009 \begin_layout Plain Layout
20017 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20020 \begin_layout Plain Layout
20021 \begin_inset Formula $\iota$
20031 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20034 \begin_layout Plain Layout
20042 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20045 \begin_layout Plain Layout
20046 \begin_inset Formula $\kappa$
20056 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20059 \begin_layout Plain Layout
20067 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20070 \begin_layout Plain Layout
20071 \begin_inset Formula $\varkappa$
20081 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20084 \begin_layout Plain Layout
20092 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20095 \begin_layout Plain Layout
20096 \begin_inset Formula $\lambda$
20106 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20109 \begin_layout Plain Layout
20117 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20120 \begin_layout Plain Layout
20121 \begin_inset Formula $\mu$
20131 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20134 \begin_layout Plain Layout
20142 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20145 \begin_layout Plain Layout
20146 \begin_inset Formula $\nu$
20156 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20159 \begin_layout Plain Layout
20167 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20170 \begin_layout Plain Layout
20171 \begin_inset Formula $\xi$
20181 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20184 \begin_layout Plain Layout
20190 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20193 \begin_layout Plain Layout
20194 \begin_inset Formula $o$
20204 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20207 \begin_layout Plain Layout
20215 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20218 \begin_layout Plain Layout
20219 \begin_inset Formula $\pi$
20229 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20232 \begin_layout Plain Layout
20240 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20243 \begin_layout Plain Layout
20244 \begin_inset Formula $\varpi$
20254 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20257 \begin_layout Plain Layout
20265 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20268 \begin_layout Plain Layout
20269 \begin_inset Formula $\rho$
20283 \begin_inset space \hfill{}
20287 \begin_inset Tabular
20288 <lyxtabular version="3" rows="11" columns="2">
20289 <features tabularvalignment="middle">
20290 <column alignment="center" valignment="top" width="0pt">
20291 <column alignment="center" valignment="top" width="0pt">
20293 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20296 \begin_layout Plain Layout
20302 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20305 \begin_layout Plain Layout
20313 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20316 \begin_layout Plain Layout
20324 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20327 \begin_layout Plain Layout
20328 \begin_inset Formula $\varrho$
20338 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20341 \begin_layout Plain Layout
20349 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20352 \begin_layout Plain Layout
20353 \begin_inset Formula $\sigma$
20363 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20366 \begin_layout Plain Layout
20374 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20377 \begin_layout Plain Layout
20378 \begin_inset Formula $\varsigma$
20388 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20391 \begin_layout Plain Layout
20399 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20402 \begin_layout Plain Layout
20403 \begin_inset Formula $\tau$
20413 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20416 \begin_layout Plain Layout
20424 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20427 \begin_layout Plain Layout
20428 \begin_inset Formula $\upsilon$
20438 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20441 \begin_layout Plain Layout
20449 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20452 \begin_layout Plain Layout
20453 \begin_inset Formula $\phi$
20463 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20466 \begin_layout Plain Layout
20474 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20477 \begin_layout Plain Layout
20478 \begin_inset Formula $\varphi$
20488 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20491 \begin_layout Plain Layout
20499 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20502 \begin_layout Plain Layout
20503 \begin_inset Formula $\chi$
20513 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20516 \begin_layout Plain Layout
20524 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20527 \begin_layout Plain Layout
20528 \begin_inset Formula $\psi$
20538 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20541 \begin_layout Plain Layout
20549 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20552 \begin_layout Plain Layout
20553 \begin_inset Formula $\omega$
20567 \begin_inset space \hfill{}
20573 \begin_layout Standard
20574 \begin_inset VSpace medskip
20580 \begin_layout Standard
20581 How to create special upright Greek letters is explained in
20582 \begin_inset CommandInset ref
20584 reference "sub:Upright-small-Greek"
20591 \begin_layout Subsection
20593 \begin_inset Index idx
20596 \begin_layout Plain Layout
20597 Greek letters ! big
20605 \begin_layout Standard
20606 \begin_inset space \hfill{}
20610 \begin_inset Tabular
20611 <lyxtabular version="3" rows="7" columns="2">
20612 <features tabularvalignment="middle">
20613 <column alignment="center" valignment="top" width="0pt">
20614 <column alignment="center" valignment="top" width="0pt">
20616 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20619 \begin_layout Plain Layout
20625 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20628 \begin_layout Plain Layout
20636 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20639 \begin_layout Plain Layout
20647 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20650 \begin_layout Plain Layout
20651 \begin_inset Formula $\Gamma$
20661 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20664 \begin_layout Plain Layout
20672 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20675 \begin_layout Plain Layout
20676 \begin_inset Formula $\Delta$
20686 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20689 \begin_layout Plain Layout
20697 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20700 \begin_layout Plain Layout
20701 \begin_inset Formula $\Theta$
20711 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20714 \begin_layout Plain Layout
20722 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20725 \begin_layout Plain Layout
20726 \begin_inset Formula $\Lambda$
20736 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20739 \begin_layout Plain Layout
20747 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20750 \begin_layout Plain Layout
20751 \begin_inset Formula $\Xi$
20761 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20764 \begin_layout Plain Layout
20772 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20775 \begin_layout Plain Layout
20776 \begin_inset Formula $\Pi$
20790 \begin_inset space \hfill{}
20794 \begin_inset Tabular
20795 <lyxtabular version="3" rows="6" columns="2">
20796 <features tabularvalignment="middle">
20797 <column alignment="center" valignment="top" width="0pt">
20798 <column alignment="center" valignment="top" width="0pt">
20800 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20803 \begin_layout Plain Layout
20809 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20812 \begin_layout Plain Layout
20820 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20823 \begin_layout Plain Layout
20831 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20834 \begin_layout Plain Layout
20835 \begin_inset Formula $\Sigma$
20845 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20848 \begin_layout Plain Layout
20856 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20859 \begin_layout Plain Layout
20860 \begin_inset Formula $\Upsilon$
20870 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20873 \begin_layout Plain Layout
20881 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20884 \begin_layout Plain Layout
20885 \begin_inset Formula $\Phi$
20895 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20898 \begin_layout Plain Layout
20906 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20909 \begin_layout Plain Layout
20910 \begin_inset Formula $\Psi$
20920 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20923 \begin_layout Plain Layout
20931 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20934 \begin_layout Plain Layout
20935 \begin_inset Formula $\Omega$
20949 \begin_inset space \hfill{}
20955 \begin_layout Standard
20956 \begin_inset VSpace medskip
20959 That the big Greek letters appear upright is caused by a design bug when
20961 To get correct italic big letters, begin every command with
20966 For example the command
20973 \begin_inset Formula $\varGamma$
20977 Another way is to load the package
20985 \begin_layout Plain Layout
20990 is part of the LaTeX-package
20995 \begin_inset Index idx
20998 \begin_layout Plain Layout
21003 \begin_layout Plain Layout
21023 \begin_inset Index idx
21026 \begin_layout Plain Layout
21032 with the LaTeX-preamble line
21035 \begin_layout Standard
21040 usepackage{fixmath}
21043 \begin_layout Standard
21044 Then all big Greek letters in a document will automatically be typeset italic.
21047 \begin_layout Subsection
21049 \begin_inset Index idx
21052 \begin_layout Plain Layout
21053 Greek letters ! bold
21061 \begin_layout Standard
21062 Greek letters cannot be set with different font styles like Latin letters.
21063 They can only be made bold with the command
21070 \begin_inset Index idx
21073 \begin_layout Plain Layout
21084 \begin_layout Standard
21086 \begin_inset Tabular
21087 <lyxtabular version="3" rows="3" columns="2">
21088 <features tabularvalignment="middle">
21089 <column alignment="center" valignment="top" width="0">
21090 <column alignment="center" valignment="top" width="0">
21092 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21095 \begin_layout Plain Layout
21101 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21104 \begin_layout Plain Layout
21112 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21115 \begin_layout Plain Layout
21127 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21130 \begin_layout Plain Layout
21131 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
21141 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21144 \begin_layout Plain Layout
21156 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21159 \begin_layout Plain Layout
21160 \begin_inset Formula $\theta\boldsymbol{\theta}$
21176 \begin_layout Section
21181 \begin_layout Plain Layout
21194 \begin_layout Plain Layout
21195 A list with all symbols of most of the LaTeX-packages can be found in
21196 \begin_inset CommandInset citation
21211 \begin_layout Plain Layout
21219 \begin_inset Note Note
21222 \begin_layout Plain Layout
21225 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
21228 \begin_layout Plain Layout
21231 texorpdfstring is in section
21232 \begin_inset CommandInset ref
21234 reference "sub:Formulas-in-Section"
21244 \begin_inset Index idx
21247 \begin_layout Plain Layout
21256 \begin_layout Standard
21257 Many of the symbols listed in this section can also be inserted via the
21259 \begin_inset Graphics
21260 filename ../images/math/nabla.png
21266 \begin_inset Graphics
21267 filename ../images/math/digamma.png
21275 \begin_layout Subsection
21276 Mathematical Symbols
21277 \begin_inset CommandInset label
21279 name "sub:Mathematical-Symbols"
21284 \begin_inset Index idx
21287 \begin_layout Plain Layout
21288 Symbols ! mathematical
21296 \begin_layout Standard
21297 \begin_inset space \hfill{}
21301 \begin_inset Tabular
21302 <lyxtabular version="3" rows="10" columns="2">
21303 <features tabularvalignment="middle">
21304 <column alignment="center" valignment="top" width="0pt">
21305 <column alignment="center" valignment="top" width="0pt">
21307 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21310 \begin_layout Plain Layout
21316 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21319 \begin_layout Plain Layout
21327 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21330 \begin_layout Plain Layout
21338 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21341 \begin_layout Plain Layout
21342 \begin_inset Formula $\neg$
21352 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21355 \begin_layout Plain Layout
21363 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21366 \begin_layout Plain Layout
21367 \begin_inset Formula $\Im$
21377 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21380 \begin_layout Plain Layout
21388 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21391 \begin_layout Plain Layout
21392 \begin_inset Formula $\Re$
21402 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21405 \begin_layout Plain Layout
21413 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21416 \begin_layout Plain Layout
21417 \begin_inset Formula $\aleph$
21427 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21430 \begin_layout Plain Layout
21438 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21441 \begin_layout Plain Layout
21442 \begin_inset Formula $\partial$
21452 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21455 \begin_layout Plain Layout
21463 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21466 \begin_layout Plain Layout
21467 \begin_inset Formula $\infty$
21477 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21480 \begin_layout Plain Layout
21488 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21491 \begin_layout Plain Layout
21492 \begin_inset Formula $\wp$
21502 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21505 \begin_layout Plain Layout
21513 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21516 \begin_layout Plain Layout
21517 \begin_inset Formula $\imath$
21527 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21530 \begin_layout Plain Layout
21538 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21541 \begin_layout Plain Layout
21542 \begin_inset Formula $\jmath$
21556 \begin_inset space \hfill{}
21560 \begin_inset Tabular
21561 <lyxtabular version="3" rows="10" columns="2">
21562 <features tabularvalignment="middle">
21563 <column alignment="center" valignment="top" width="0pt">
21564 <column alignment="center" valignment="top" width="0pt">
21566 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21569 \begin_layout Plain Layout
21575 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21578 \begin_layout Plain Layout
21580 \begin_inset Note Note
21583 \begin_layout Plain Layout
21590 is only used as spacer.
21602 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21605 \begin_layout Plain Layout
21613 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21616 \begin_layout Plain Layout
21617 \begin_inset Formula $\forall$
21627 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21630 \begin_layout Plain Layout
21638 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21641 \begin_layout Plain Layout
21642 \begin_inset Formula $\exists$
21652 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21655 \begin_layout Plain Layout
21663 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21666 \begin_layout Plain Layout
21667 \begin_inset Formula $\nexists$
21677 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21680 \begin_layout Plain Layout
21688 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21691 \begin_layout Plain Layout
21692 \begin_inset Formula $\emptyset$
21702 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21705 \begin_layout Plain Layout
21713 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21716 \begin_layout Plain Layout
21717 \begin_inset Formula $\varnothing$
21727 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21730 \begin_layout Plain Layout
21738 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21741 \begin_layout Plain Layout
21742 \begin_inset Formula $\dag$
21752 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21755 \begin_layout Plain Layout
21763 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21766 \begin_layout Plain Layout
21767 \begin_inset Formula $\ddag$
21777 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21780 \begin_layout Plain Layout
21788 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21791 \begin_layout Plain Layout
21795 \begin_layout Plain Layout
21805 \begin_inset Formula $\complement$
21812 \begin_layout Plain Layout
21826 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21829 \begin_layout Plain Layout
21837 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21840 \begin_layout Plain Layout
21841 \begin_inset Formula $\Bbbk$
21855 \begin_inset space \hfill{}
21859 \begin_inset Tabular
21860 <lyxtabular version="3" rows="10" columns="2">
21861 <features tabularvalignment="middle">
21862 <column alignment="center" valignment="top" width="0pt">
21863 <column alignment="center" valignment="top" width="0pt">
21865 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21868 \begin_layout Plain Layout
21874 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21877 \begin_layout Plain Layout
21885 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21888 \begin_layout Plain Layout
21896 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21899 \begin_layout Plain Layout
21900 \begin_inset Formula $\prime$
21910 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21913 \begin_layout Plain Layout
21921 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21924 \begin_layout Plain Layout
21925 \begin_inset Formula $\backprime$
21935 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21938 \begin_layout Plain Layout
21946 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21949 \begin_layout Plain Layout
21950 \begin_inset Formula $\mho$
21960 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21963 \begin_layout Plain Layout
21971 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21974 \begin_layout Plain Layout
21975 \begin_inset Formula $\triangle$
21985 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21988 \begin_layout Plain Layout
21996 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21999 \begin_layout Plain Layout
22000 \begin_inset Formula $\angle$
22010 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22013 \begin_layout Plain Layout
22021 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22024 \begin_layout Plain Layout
22025 \begin_inset Formula $\measuredangle$
22035 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22038 \begin_layout Plain Layout
22046 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22049 \begin_layout Plain Layout
22050 \begin_inset Formula $\sphericalangle$
22060 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22063 \begin_layout Plain Layout
22071 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22074 \begin_layout Plain Layout
22075 \begin_inset Formula $\top$
22085 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22088 \begin_layout Plain Layout
22096 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22099 \begin_layout Plain Layout
22100 \begin_inset Formula $\bot$
22114 \begin_inset space \hfill{}
22120 \begin_layout Subsection
22121 Miscellaneous Symbols
22122 \begin_inset CommandInset label
22124 name "sub:Miscellaneous-Symbols"
22129 \begin_inset Index idx
22132 \begin_layout Plain Layout
22133 Symbols ! miscellaneous
22141 \begin_layout Standard
22144 \begin_inset Tabular
22145 <lyxtabular version="3" rows="10" columns="2">
22146 <features tabularvalignment="middle">
22147 <column alignment="center" valignment="top" width="0pt">
22148 <column alignment="center" valignment="top" width="0pt">
22150 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22153 \begin_layout Plain Layout
22159 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22162 \begin_layout Plain Layout
22170 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22173 \begin_layout Plain Layout
22181 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22184 \begin_layout Plain Layout
22185 \begin_inset Formula $\flat$
22195 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22198 \begin_layout Plain Layout
22206 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22209 \begin_layout Plain Layout
22210 \begin_inset Formula $\natural$
22220 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22223 \begin_layout Plain Layout
22231 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22234 \begin_layout Plain Layout
22235 \begin_inset Formula $\sharp$
22245 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22248 \begin_layout Plain Layout
22256 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22259 \begin_layout Plain Layout
22260 \begin_inset Formula $\surd$
22270 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22273 \begin_layout Plain Layout
22281 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22284 \begin_layout Plain Layout
22285 \begin_inset Formula $\checkmark$
22295 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22298 \begin_layout Plain Layout
22306 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22309 \begin_layout Plain Layout
22310 \begin_inset Formula $\yen$
22320 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22323 \begin_layout Plain Layout
22331 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22334 \begin_layout Plain Layout
22335 \begin_inset Formula $\pounds$
22345 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22348 \begin_layout Plain Layout
22354 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22357 \begin_layout Plain Layout
22358 \begin_inset Formula $\$$
22368 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22371 \begin_layout Plain Layout
22377 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22380 \begin_layout Plain Layout
22381 \begin_inset Formula $§$
22395 \begin_inset Tabular
22396 <lyxtabular version="3" rows="10" columns="2">
22397 <features tabularvalignment="middle">
22398 <column alignment="center" valignment="top" width="0">
22399 <column alignment="center" valignment="top" width="0">
22401 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22404 \begin_layout Plain Layout
22410 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22413 \begin_layout Plain Layout
22421 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22424 \begin_layout Plain Layout
22432 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22435 \begin_layout Plain Layout
22436 \begin_inset Formula $\hbar$
22446 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22449 \begin_layout Plain Layout
22457 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22460 \begin_layout Plain Layout
22461 \begin_inset Formula $\hslash$
22471 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22474 \begin_layout Plain Layout
22482 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22485 \begin_layout Plain Layout
22486 \begin_inset Formula $\clubsuit$
22496 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22499 \begin_layout Plain Layout
22507 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22510 \begin_layout Plain Layout
22511 \begin_inset Formula $\spadesuit$
22521 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22524 \begin_layout Plain Layout
22532 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22535 \begin_layout Plain Layout
22536 \begin_inset Formula $\bigstar$
22546 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22549 \begin_layout Plain Layout
22557 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22560 \begin_layout Plain Layout
22561 \begin_inset Formula $\blacklozenge$
22571 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22574 \begin_layout Plain Layout
22582 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22585 \begin_layout Plain Layout
22586 \begin_inset Formula $\blacktriangle$
22596 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22599 \begin_layout Plain Layout
22607 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22610 \begin_layout Plain Layout
22611 \begin_inset Formula $\blacktriangledown$
22621 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22624 \begin_layout Plain Layout
22632 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22635 \begin_layout Plain Layout
22636 \begin_inset Formula $\bullet$
22650 \begin_inset Tabular
22651 <lyxtabular version="3" rows="10" columns="2">
22652 <features tabularvalignment="middle">
22653 <column alignment="center" valignment="top" width="0pt">
22654 <column alignment="center" valignment="top" width="0pt">
22656 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22659 \begin_layout Plain Layout
22665 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22668 \begin_layout Plain Layout
22676 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22679 \begin_layout Plain Layout
22687 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22690 \begin_layout Plain Layout
22691 \begin_inset Formula $\diamondsuit$
22701 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22704 \begin_layout Plain Layout
22712 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22715 \begin_layout Plain Layout
22716 \begin_inset Formula $\Diamond$
22726 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22729 \begin_layout Plain Layout
22737 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22740 \begin_layout Plain Layout
22741 \begin_inset Formula $\heartsuit$
22751 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22754 \begin_layout Plain Layout
22762 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22765 \begin_layout Plain Layout
22766 \begin_inset Formula $\P$
22776 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22779 \begin_layout Plain Layout
22787 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22790 \begin_layout Plain Layout
22791 \begin_inset Formula $\copyright$
22801 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22804 \begin_layout Plain Layout
22812 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22815 \begin_layout Plain Layout
22816 \begin_inset Formula $\circledR$
22826 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22829 \begin_layout Plain Layout
22837 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22840 \begin_layout Plain Layout
22841 \begin_inset Formula $\maltese$
22851 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22854 \begin_layout Plain Layout
22862 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22865 \begin_layout Plain Layout
22866 \begin_inset Formula $\diagup$
22876 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22879 \begin_layout Plain Layout
22887 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22890 \begin_layout Plain Layout
22891 \begin_inset Formula $\diagdown$
22907 \begin_layout Standard
22908 \begin_inset VSpace medskip
22911 More symbols are listed in
22912 \begin_inset CommandInset ref
22914 reference "sub:Miscellaneous-special-Characters"
22921 \begin_layout Standard
22922 Some symbols can be displayed in different sizes, see
22923 \begin_inset CommandInset ref
22925 reference "sub:Font-Sizes"
22932 \begin_layout Subsection
22934 \begin_inset Index idx
22937 \begin_layout Plain Layout
22938 Symbols ! Euro-symbol
22944 \begin_inset Index idx
22947 \begin_layout Plain Layout
22954 \begin_layout Plain Layout
22971 \begin_layout Standard
22972 To use the Euro symbol in formulas, the LaTeX-package
22977 \begin_inset Index idx
22980 \begin_layout Plain Layout
22986 must be installed and loaded with the LaTeX-preamble line
22989 \begin_layout Standard
22994 usepackage[gennarrow]{eurosym}
22997 \begin_layout Standard
22998 The Euro symbol can now be inserted with the command
23005 \begin_inset Index idx
23008 \begin_layout Plain Layout
23019 \begin_layout Standard
23020 The Euro symbol can directly be inserted with the € key in mathematical
23021 text, without having
23036 can also be inserted in TeX-mode.
23037 The official currency symbol can then be inserted with the command
23044 \begin_inset Index idx
23047 \begin_layout Plain Layout
23055 , that is only available in TeX-mode.
23058 \begin_layout Standard
23062 \begin_layout Plain Layout
23072 \begin_inset Note Note
23075 \begin_layout Plain Layout
23076 The following table will only be displayed when the LaTeX-package
23088 \begin_layout Standard
23089 An overview about the different Euro symbols:
23092 \begin_layout Standard
23094 \begin_inset Tabular
23095 <lyxtabular version="3" rows="4" columns="3">
23096 <features tabularvalignment="middle">
23097 <column alignment="center" valignment="top" width="0pt">
23098 <column alignment="center" valignment="top" width="0pt">
23099 <column alignment="center" valignment="top" width="0pt">
23101 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
23104 \begin_layout Plain Layout
23110 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23113 \begin_layout Plain Layout
23119 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23122 \begin_layout Plain Layout
23130 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23133 \begin_layout Plain Layout
23139 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23142 \begin_layout Plain Layout
23150 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23153 \begin_layout Plain Layout
23154 \begin_inset Formula $\euro$
23164 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23167 \begin_layout Plain Layout
23173 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23176 \begin_layout Plain Layout
23182 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23185 \begin_layout Plain Layout
23186 \begin_inset Formula $\mbox{€}$
23196 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23199 \begin_layout Plain Layout
23205 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23208 \begin_layout Plain Layout
23216 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23219 \begin_layout Plain Layout
23223 \begin_layout Plain Layout
23245 \begin_layout Standard
23249 \begin_layout Plain Layout
23259 \begin_inset Note Note
23262 \begin_layout Plain Layout
23263 The following will be displayed when the LaTeX-package
23275 \begin_layout Standard
23276 You need to install the LaTeX-package
23280 to see the rest of this subsection in the output.
23283 \begin_layout Standard
23287 \begin_layout Plain Layout
23299 \begin_layout Section
23301 \begin_inset CommandInset label
23303 name "sec:Relations"
23308 \begin_inset Index idx
23311 \begin_layout Plain Layout
23318 \begin_inset Index idx
23321 \begin_layout Plain Layout
23326 \begin_layout Plain Layout
23337 \begin_layout Plain Layout
23352 \begin_layout Standard
23353 All relations can also be inserted via the toolbar button
23354 \begin_inset Graphics
23355 filename ../images/math/leq.png
23363 \begin_layout Standard
23364 \begin_inset space \hfill{}
23368 \begin_inset Tabular
23369 <lyxtabular version="3" rows="17" columns="2">
23370 <features tabularvalignment="middle">
23371 <column alignment="center" valignment="top" width="0pt">
23372 <column alignment="center" valignment="top" width="0pt">
23374 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23377 \begin_layout Plain Layout
23383 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23386 \begin_layout Plain Layout
23394 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23397 \begin_layout Plain Layout
23403 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23406 \begin_layout Plain Layout
23407 \begin_inset Formula $<$
23417 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23420 \begin_layout Plain Layout
23428 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23431 \begin_layout Plain Layout
23432 \begin_inset Formula $\le$
23442 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23445 \begin_layout Plain Layout
23453 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23456 \begin_layout Plain Layout
23457 \begin_inset Formula $\ll$
23467 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23470 \begin_layout Plain Layout
23478 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23481 \begin_layout Plain Layout
23482 \begin_inset Formula $\prec$
23492 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23495 \begin_layout Plain Layout
23503 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23506 \begin_layout Plain Layout
23507 \begin_inset Formula $\preceq$
23517 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23520 \begin_layout Plain Layout
23528 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23531 \begin_layout Plain Layout
23532 \begin_inset Formula $\subset$
23542 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23545 \begin_layout Plain Layout
23553 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23556 \begin_layout Plain Layout
23557 \begin_inset Formula $\subseteq$
23567 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23570 \begin_layout Plain Layout
23578 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23581 \begin_layout Plain Layout
23582 \begin_inset Formula $\sqsubseteq$
23592 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23595 \begin_layout Plain Layout
23603 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23606 \begin_layout Plain Layout
23607 \begin_inset Formula $\in$
23617 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23620 \begin_layout Plain Layout
23628 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23631 \begin_layout Plain Layout
23632 \begin_inset Formula $\vdash$
23642 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23645 \begin_layout Plain Layout
23653 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23656 \begin_layout Plain Layout
23657 \begin_inset Formula $\smile$
23667 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23670 \begin_layout Plain Layout
23678 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23681 \begin_layout Plain Layout
23682 \begin_inset Formula $\lhd$
23692 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23695 \begin_layout Plain Layout
23703 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23706 \begin_layout Plain Layout
23707 \begin_inset Formula $\unlhd$
23717 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23720 \begin_layout Plain Layout
23728 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23731 \begin_layout Plain Layout
23732 \begin_inset Formula $\gtrless$
23742 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23745 \begin_layout Plain Layout
23753 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23756 \begin_layout Plain Layout
23757 \begin_inset Formula $\mid$
23767 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23770 \begin_layout Plain Layout
23778 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23781 \begin_layout Plain Layout
23782 \begin_inset Formula $\nmid$
23796 \begin_inset space \hfill{}
23800 \begin_inset Tabular
23801 <lyxtabular version="3" rows="17" columns="2">
23802 <features tabularvalignment="middle">
23803 <column alignment="center" valignment="top" width="0pt">
23804 <column alignment="center" valignment="top" width="0pt">
23806 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23809 \begin_layout Plain Layout
23815 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23818 \begin_layout Plain Layout
23826 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23829 \begin_layout Plain Layout
23835 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23838 \begin_layout Plain Layout
23839 \begin_inset Formula $=$
23849 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23852 \begin_layout Plain Layout
23860 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23863 \begin_layout Plain Layout
23864 \begin_inset Formula $\not=$
23874 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23877 \begin_layout Plain Layout
23885 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23888 \begin_layout Plain Layout
23889 \begin_inset Formula $\equiv$
23899 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23902 \begin_layout Plain Layout
23910 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23913 \begin_layout Plain Layout
23914 \begin_inset Formula $\sim$
23924 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23927 \begin_layout Plain Layout
23935 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23938 \begin_layout Plain Layout
23939 \begin_inset Formula $\simeq$
23949 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23952 \begin_layout Plain Layout
23960 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23963 \begin_layout Plain Layout
23964 \begin_inset Formula $\approx$
23974 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23977 \begin_layout Plain Layout
23985 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23988 \begin_layout Plain Layout
23989 \begin_inset Formula $\cong$
23999 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24002 \begin_layout Plain Layout
24010 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24013 \begin_layout Plain Layout
24014 \begin_inset Formula $\bowtie$
24024 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24027 \begin_layout Plain Layout
24035 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24038 \begin_layout Plain Layout
24039 \begin_inset Formula $\notin$
24049 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24052 \begin_layout Plain Layout
24060 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24063 \begin_layout Plain Layout
24064 \begin_inset Formula $\perp$
24074 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24077 \begin_layout Plain Layout
24085 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24088 \begin_layout Plain Layout
24089 \begin_inset Formula $\propto$
24099 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24102 \begin_layout Plain Layout
24110 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24113 \begin_layout Plain Layout
24114 \begin_inset Formula $\asymp$
24124 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24127 \begin_layout Plain Layout
24135 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24138 \begin_layout Plain Layout
24139 \begin_inset Formula $\doteq$
24149 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24152 \begin_layout Plain Layout
24160 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24163 \begin_layout Plain Layout
24164 \begin_inset Formula $\circeq$
24174 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24177 \begin_layout Plain Layout
24185 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24188 \begin_layout Plain Layout
24189 \begin_inset Formula $\models$
24199 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24202 \begin_layout Plain Layout
24210 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24213 \begin_layout Plain Layout
24214 \begin_inset Formula $\widehat{=}$
24228 \begin_inset space \hfill{}
24232 \begin_inset Tabular
24233 <lyxtabular version="3" rows="17" columns="2">
24234 <features tabularvalignment="middle">
24235 <column alignment="center" valignment="top" width="0pt">
24236 <column alignment="center" valignment="top" width="0pt">
24238 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24241 \begin_layout Plain Layout
24247 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24250 \begin_layout Plain Layout
24258 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24261 \begin_layout Plain Layout
24267 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24270 \begin_layout Plain Layout
24271 \begin_inset Formula $>$
24281 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24284 \begin_layout Plain Layout
24292 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24295 \begin_layout Plain Layout
24296 \begin_inset Formula $\ge$
24306 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24309 \begin_layout Plain Layout
24317 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24320 \begin_layout Plain Layout
24321 \begin_inset Formula $\gg$
24331 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24334 \begin_layout Plain Layout
24342 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24345 \begin_layout Plain Layout
24346 \begin_inset Formula $\succ$
24356 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24359 \begin_layout Plain Layout
24367 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24370 \begin_layout Plain Layout
24371 \begin_inset Formula $\succeq$
24381 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24384 \begin_layout Plain Layout
24392 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24395 \begin_layout Plain Layout
24396 \begin_inset Formula $\supset$
24406 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24409 \begin_layout Plain Layout
24417 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24420 \begin_layout Plain Layout
24421 \begin_inset Formula $\supseteq$
24431 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24434 \begin_layout Plain Layout
24442 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24445 \begin_layout Plain Layout
24446 \begin_inset Formula $\sqsupseteq$
24456 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24459 \begin_layout Plain Layout
24467 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24470 \begin_layout Plain Layout
24471 \begin_inset Formula $\ni$
24481 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24484 \begin_layout Plain Layout
24492 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24495 \begin_layout Plain Layout
24496 \begin_inset Formula $\dashv$
24506 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24509 \begin_layout Plain Layout
24517 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24520 \begin_layout Plain Layout
24521 \begin_inset Formula $\frown$
24531 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24534 \begin_layout Plain Layout
24542 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24545 \begin_layout Plain Layout
24546 \begin_inset Formula $\rhd$
24556 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24559 \begin_layout Plain Layout
24567 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24570 \begin_layout Plain Layout
24571 \begin_inset Formula $\unrhd$
24581 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24584 \begin_layout Plain Layout
24592 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24595 \begin_layout Plain Layout
24596 \begin_inset Formula $\lessgtr$
24606 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24609 \begin_layout Plain Layout
24617 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24620 \begin_layout Plain Layout
24621 \begin_inset Formula $\parallel$
24631 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24634 \begin_layout Plain Layout
24642 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24645 \begin_layout Plain Layout
24646 \begin_inset Formula $\nparallel$
24660 \begin_inset space \hfill{}
24666 \begin_layout Standard
24667 \begin_inset VSpace medskip
24682 are bigger than the equal looking operators
24697 \begin_layout Standard
24698 Relations are, in contrary to symbols, always surrounded by space.
24701 \begin_layout Standard
24702 Relations with labels can be created with the command
24709 \begin_inset Index idx
24712 \begin_layout Plain Layout
24723 \begin_layout Standard
24725 \begin_inset Tabular
24726 <lyxtabular version="3" rows="2" columns="2">
24727 <features tabularvalignment="middle">
24728 <column alignment="center" valignment="top" width="0">
24729 <column alignment="center" valignment="top" width="0">
24731 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24734 \begin_layout Plain Layout
24740 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24743 \begin_layout Plain Layout
24745 \begin_inset Note Note
24748 \begin_layout Plain Layout
24755 is only used as spacer.
24767 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24770 \begin_layout Plain Layout
24777 \begin_layout Plain Layout
24794 \begin_layout Plain Layout
24804 \begin_inset Formula $\downarrow$
24813 \begin_layout Plain Layout
24826 \begin_layout Plain Layout
24840 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24843 \begin_layout Plain Layout
24844 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
24860 \begin_layout Section
24864 \begin_layout Subsection
24865 Predefined Functions
24866 \begin_inset CommandInset label
24868 name "sub:Predefined-Functions"
24873 \begin_inset Index idx
24876 \begin_layout Plain Layout
24877 Functions ! predefined
24885 \begin_layout Standard
24886 In general, variables are set
24890 in mathematical expressions, but not function names, because
24891 \begin_inset Formula $sin$
24894 could be misunderstood as
24895 \begin_inset Formula $s\cdot i\cdot n$
24899 Therefore there are predefined functions, that are additionally a bit separated
24901 They are inserted as commands starting with a backslash before their name.
24904 \begin_layout Standard
24906 \begin_inset Tabular
24907 <lyxtabular version="3" rows="2" columns="4">
24908 <features tabularvalignment="middle">
24909 <column alignment="center" valignment="top" width="0pt">
24910 <column alignment="center" valignment="top" width="0pt">
24911 <column alignment="center" valignment="top" width="0pt">
24912 <column alignment="center" valignment="top" width="0pt">
24914 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24917 \begin_layout Plain Layout
24923 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24926 \begin_layout Plain Layout
24932 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24935 \begin_layout Plain Layout
24941 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24944 \begin_layout Plain Layout
24952 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24955 \begin_layout Plain Layout
24961 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24964 \begin_layout Plain Layout
24965 \begin_inset Formula $Asin(x)+B$
24973 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24976 \begin_layout Plain Layout
24984 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24987 \begin_layout Plain Layout
24988 \begin_inset Formula $A\sin(x)+B$
25004 \begin_layout Standard
25005 The following functions are predefined:
25008 \begin_layout Standard
25009 \begin_inset VSpace -2mm
25015 \begin_layout Standard
25017 \begin_inset Tabular
25018 <lyxtabular version="3" rows="9" columns="4">
25019 <features tabularvalignment="middle">
25020 <column alignment="center" valignment="top" width="0pt">
25021 <column alignment="center" valignment="top" width="0pt">
25022 <column alignment="center" valignment="top" width="0pt">
25023 <column alignment="center" valignment="top" width="0pt">
25025 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25028 \begin_layout Plain Layout
25034 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25037 \begin_layout Plain Layout
25043 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25046 \begin_layout Plain Layout
25052 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25055 \begin_layout Plain Layout
25063 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25066 \begin_layout Plain Layout
25074 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25077 \begin_layout Plain Layout
25085 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25088 \begin_layout Plain Layout
25096 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25099 \begin_layout Plain Layout
25109 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25112 \begin_layout Plain Layout
25120 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25123 \begin_layout Plain Layout
25131 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25134 \begin_layout Plain Layout
25142 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25145 \begin_layout Plain Layout
25155 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25158 \begin_layout Plain Layout
25166 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25169 \begin_layout Plain Layout
25177 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25180 \begin_layout Plain Layout
25188 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25191 \begin_layout Plain Layout
25201 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25204 \begin_layout Plain Layout
25212 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25215 \begin_layout Plain Layout
25223 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25226 \begin_layout Plain Layout
25234 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25237 \begin_layout Plain Layout
25247 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25250 \begin_layout Plain Layout
25258 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25261 \begin_layout Plain Layout
25269 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25272 \begin_layout Plain Layout
25280 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25283 \begin_layout Plain Layout
25293 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25296 \begin_layout Plain Layout
25304 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25307 \begin_layout Plain Layout
25315 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25318 \begin_layout Plain Layout
25326 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25329 \begin_layout Plain Layout
25339 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25342 \begin_layout Plain Layout
25350 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25353 \begin_layout Plain Layout
25361 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25364 \begin_layout Plain Layout
25372 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25375 \begin_layout Plain Layout
25385 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25388 \begin_layout Plain Layout
25396 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25399 \begin_layout Plain Layout
25407 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25410 \begin_layout Plain Layout
25418 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25421 \begin_layout Plain Layout
25437 \begin_layout Standard
25438 They can also be inserted with the math toolbar button
25439 \begin_inset Graphics
25440 filename ../images/math/functions.png
25448 \begin_layout Subsection
25449 Self-defined Functions
25450 \begin_inset Index idx
25453 \begin_layout Plain Layout
25454 Functions ! self-defined
25462 \begin_layout Standard
25463 To use a function that is not predefined, like for example the sign function
25464 sgn(x), there are two possibilities:
25467 \begin_layout Itemize
25468 Define the function by inserting the following line to the LaTeX-preamble
25472 \begin_layout Plain Layout
25477 DeclareMathOperator
25480 \begin_inset CommandInset ref
25482 reference "sub:Self-defined-Operators"
25492 \begin_inset Newline newline
25496 \begin_inset VSpace -3mm
25500 \begin_inset Newline newline
25507 DeclareMathOperator{
25512 \begin_inset Index idx
25515 \begin_layout Plain Layout
25520 DeclareMathOperator
25526 \begin_inset Newline newline
25530 \begin_inset VSpace -2mm
25534 \begin_inset Newline newline
25537 Now the new defined function can be called with the command
25546 \begin_layout Itemize
25547 Write the formula as usual, mark the formula name, in our example the letters
25552 , and change it to mathematical text.
25553 At last a space is inserted between prefactor and function.
25556 \begin_layout Standard
25557 The result is the same with both methods as with a predefined function
25561 \begin_layout Plain Layout
25562 In LyX self-defined functions are displayed red, predefined ones black.
25570 \begin_layout Standard
25572 \begin_inset Tabular
25573 <lyxtabular version="3" rows="3" columns="2">
25574 <features tabularvalignment="middle">
25575 <column alignment="center" valignment="top" width="0pt">
25576 <column alignment="center" valignment="top" width="0pt">
25578 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25581 \begin_layout Plain Layout
25587 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25590 \begin_layout Plain Layout
25598 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25601 \begin_layout Plain Layout
25609 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25612 \begin_layout Plain Layout
25613 \begin_inset Formula $A\sgn(x)+B$
25623 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25626 \begin_layout Plain Layout
25630 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
25638 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25641 \begin_layout Plain Layout
25642 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
25658 \begin_layout Standard
25659 The first method is more suitable when the self-defined function should
25660 be used several times.
25663 \begin_layout Subsection
25665 \begin_inset Index idx
25668 \begin_layout Plain Layout
25677 \begin_layout Standard
25678 For limits there are defined besides
25685 \begin_inset Index idx
25688 \begin_layout Plain Layout
25708 furthermore the following functions:
25711 \begin_layout Standard
25713 \begin_inset Tabular
25714 <lyxtabular version="3" rows="5" columns="2">
25715 <features tabularvalignment="middle">
25716 <column alignment="center" valignment="top" width="0">
25717 <column alignment="center" valignment="top" width="0">
25719 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25722 \begin_layout Plain Layout
25728 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25731 \begin_layout Plain Layout
25733 \begin_inset Note Note
25736 \begin_layout Plain Layout
25743 is only used as spacer.
25755 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25758 \begin_layout Plain Layout
25766 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25769 \begin_layout Plain Layout
25770 \begin_inset Formula $\varliminf$
25780 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25783 \begin_layout Plain Layout
25791 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25794 \begin_layout Plain Layout
25795 \begin_inset Formula $\varlimsup$
25805 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25808 \begin_layout Plain Layout
25816 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25819 \begin_layout Plain Layout
25820 \begin_inset Formula $\varprojlim$
25830 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25833 \begin_layout Plain Layout
25841 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25844 \begin_layout Plain Layout
25845 \begin_inset Formula $\varinjlim$
25849 \begin_inset Formula $\raisebox{-2.5mm}{}$
25865 \begin_layout Standard
25866 \begin_inset VSpace medskip
25869 The limit is created by inserting a subscript.
25870 It is set right beside the function in an inline formula:
25873 \begin_layout Standard
25875 \begin_inset Tabular
25876 <lyxtabular version="3" rows="2" columns="2">
25877 <features tabularvalignment="middle">
25878 <column alignment="center" valignment="top" width="0pt">
25879 <column alignment="center" valignment="top" width="0pt">
25881 <cell alignment="center" valignment="top" usebox="none">
25884 \begin_layout Plain Layout
25890 <cell alignment="center" valignment="top" usebox="none">
25893 \begin_layout Plain Layout
25894 \begin_inset space \hspace{}
25899 \begin_inset Note Note
25902 \begin_layout Plain Layout
25909 are used here as spacer.
25921 <cell alignment="center" valignment="top" usebox="none">
25924 \begin_layout Plain Layout
25933 \begin_layout Plain Layout
25946 \begin_layout Plain Layout
25960 <cell alignment="center" valignment="top" usebox="none">
25963 \begin_layout Plain Layout
25964 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
25980 \begin_layout Standard
25981 In a displayed formula the limit is set below the formula, as usual:
25982 \begin_inset Formula
25992 \begin_layout Subsection
25994 \begin_inset Index idx
25997 \begin_layout Plain Layout
25998 Functions ! modulo-
26006 \begin_layout Standard
26007 The modulo-function is special, because it exists in four variants.
26010 \begin_layout Standard
26011 The variants in a displayed formula:
26012 \begin_inset Formula
26014 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
26015 \mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
26016 \mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
26017 \mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
26018 \mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b
26026 \begin_layout Standard
26027 In an inline formula less space is set before the function names for all
26031 \begin_layout Section
26033 \begin_inset Index idx
26036 \begin_layout Plain Layout
26045 \begin_layout Subsection
26046 Special Characters in Mathematical Text
26049 \begin_layout Standard
26050 The following commands can only be used in mathematical text or in TeX-mode:
26053 \begin_layout Standard
26054 \begin_inset space \hfill{}
26058 \begin_inset Tabular
26059 <lyxtabular version="3" rows="8" columns="2">
26060 <features tabularvalignment="middle">
26061 <column alignment="block" valignment="top" width="0">
26062 <column alignment="block" valignment="top" width="0">
26064 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26067 \begin_layout Plain Layout
26073 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26076 \begin_layout Plain Layout
26084 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26087 \begin_layout Plain Layout
26095 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26098 \begin_layout Plain Layout
26099 \begin_inset Formula $\textrm{œ}$
26109 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26112 \begin_layout Plain Layout
26120 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26123 \begin_layout Plain Layout
26124 \begin_inset Formula $\textrm{Œ}$
26134 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26137 \begin_layout Plain Layout
26145 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26148 \begin_layout Plain Layout
26149 \begin_inset Formula $\textrm{æ}$
26159 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26162 \begin_layout Plain Layout
26170 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26173 \begin_layout Plain Layout
26174 \begin_inset Formula $\textrm{Æ}$
26184 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26187 \begin_layout Plain Layout
26195 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26198 \begin_layout Plain Layout
26199 \begin_inset Formula $\textrm{\aa}$
26209 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26212 \begin_layout Plain Layout
26216 \begin_inset Index idx
26219 \begin_layout Plain Layout
26226 \begin_layout Plain Layout
26247 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26250 \begin_layout Plain Layout
26251 \begin_inset Formula $\textrm{Å}$
26261 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26264 \begin_layout Plain Layout
26272 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26275 \begin_layout Plain Layout
26276 \begin_inset Formula $\textrm{ı}$
26290 \begin_inset space \hfill{}
26294 \begin_inset Tabular
26295 <lyxtabular version="3" rows="8" columns="2">
26296 <features tabularvalignment="middle">
26297 <column alignment="block" valignment="top" width="0">
26298 <column alignment="center" valignment="top" width="0">
26300 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26303 \begin_layout Plain Layout
26305 \begin_inset Note Note
26308 \begin_layout Plain Layout
26310 \begin_inset space \thinspace{}
26313 mm is used for separation, because otherwise the output will be ¡ and ¿
26324 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26327 \begin_layout Plain Layout
26335 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26338 \begin_layout Plain Layout
26346 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26349 \begin_layout Plain Layout
26350 \begin_inset Formula $\textrm{ø}$
26360 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26363 \begin_layout Plain Layout
26371 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26374 \begin_layout Plain Layout
26375 \begin_inset Formula $\textrm{Ø}$
26385 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26388 \begin_layout Plain Layout
26396 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26399 \begin_layout Plain Layout
26400 \begin_inset Formula $\textrm{ł}$
26410 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26413 \begin_layout Plain Layout
26421 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26424 \begin_layout Plain Layout
26425 \begin_inset Formula $\textrm{Ł}$
26435 <cell alignment="center" valignment="top" topline="true" 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" topline="true" 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
26481 \begin_inset space \hspace{}
26489 \begin_layout Plain Layout
26503 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26506 \begin_layout Plain Layout
26507 \begin_inset Formula $\textrm{?`}$
26517 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26520 \begin_layout Plain Layout
26528 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26531 \begin_layout Plain Layout
26532 \begin_inset Formula $\textrm{ȷ}$
26546 \begin_inset space \hfill{}
26552 \begin_layout Standard
26554 \begin_inset Formula $\textrm{\textrm{Å}}$
26558 \begin_inset Formula $\textrm{\textrm{Ø}}$
26561 can also be inserted via the math toolbar button
26562 \begin_inset Graphics
26563 filename ../images/math/digamma.png
26571 \begin_layout Standard
26572 An exception are the commands
26575 \begin_inset space \hspace{}
26584 \begin_inset space \hspace{}
26590 , because they can be inserted in LyX directly to text.
26593 \begin_layout Subsection
26595 \begin_inset CommandInset label
26597 name "sub:Accents-in-Text"
26602 \begin_inset Index idx
26605 \begin_layout Plain Layout
26614 \begin_layout Standard
26615 With the following commands all letters can be accented.
26616 The commands must be inserted in TeX-mode.
26619 \begin_layout Standard
26620 \begin_inset space \hfill{}
26624 \begin_inset Tabular
26625 <lyxtabular version="3" rows="8" columns="2">
26626 <features tabularvalignment="middle">
26627 <column alignment="block" valignment="top" width="0">
26628 <column alignment="block" valignment="top" width="0">
26630 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26633 \begin_layout Plain Layout
26639 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26642 \begin_layout Plain Layout
26650 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26653 \begin_layout Plain Layout
26657 \begin_inset Quotes grd
26665 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26668 \begin_layout Plain Layout
26672 \begin_layout Plain Layout
26688 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26691 \begin_layout Plain Layout
26699 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26702 \begin_layout Plain Layout
26706 \begin_layout Plain Layout
26722 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26725 \begin_layout Plain Layout
26732 \begin_layout Plain Layout
26746 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26749 \begin_layout Plain Layout
26753 \begin_layout Plain Layout
26769 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26772 \begin_layout Plain Layout
26780 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26783 \begin_layout Plain Layout
26787 \begin_layout Plain Layout
26803 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26806 \begin_layout Plain Layout
26813 \begin_layout Plain Layout
26827 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26830 \begin_layout Plain Layout
26834 \begin_layout Plain Layout
26850 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26853 \begin_layout Plain Layout
26860 \begin_layout Plain Layout
26874 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26877 \begin_layout Plain Layout
26881 \begin_layout Plain Layout
26897 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26900 \begin_layout Plain Layout
26907 \begin_layout Plain Layout
26921 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26924 \begin_layout Plain Layout
26928 \begin_layout Plain Layout
26948 \begin_inset space \hfill{}
26952 \begin_inset Tabular
26953 <lyxtabular version="3" rows="8" columns="2">
26954 <features tabularvalignment="middle">
26955 <column alignment="block" valignment="top" width="0">
26956 <column alignment="center" valignment="top" width="0">
26958 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26961 \begin_layout Plain Layout
26967 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26970 \begin_layout Plain Layout
26978 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26981 \begin_layout Plain Layout
26988 \begin_layout Plain Layout
27002 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27005 \begin_layout Plain Layout
27009 \begin_layout Plain Layout
27025 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27028 \begin_layout Plain Layout
27036 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27039 \begin_layout Plain Layout
27043 \begin_layout Plain Layout
27059 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27062 \begin_layout Plain Layout
27066 \begin_inset Index idx
27069 \begin_layout Plain Layout
27080 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27083 \begin_layout Plain Layout
27087 \begin_layout Plain Layout
27103 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27106 \begin_layout Plain Layout
27114 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27117 \begin_layout Plain Layout
27121 \begin_layout Plain Layout
27137 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27140 \begin_layout Plain Layout
27147 \begin_layout Plain Layout
27161 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27164 \begin_layout Plain Layout
27168 \begin_layout Plain Layout
27184 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27187 \begin_layout Plain Layout
27194 \begin_layout Plain Layout
27208 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27211 \begin_layout Plain Layout
27215 \begin_layout Plain Layout
27231 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27234 \begin_layout Plain Layout
27241 \begin_layout Plain Layout
27255 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27258 \begin_layout Plain Layout
27262 \begin_layout Plain Layout
27282 \begin_inset space \hfill{}
27288 \begin_layout Standard
27289 \begin_inset VSpace medskip
27298 also two different characters can be accented.
27307 \begin_layout Plain Layout
27322 \begin_layout Plain Layout
27334 \begin_layout Standard
27347 can in combination with vowels directly be inserted with the keyboard without
27349 The same applies for the tilde
27353 \begin_layout Plain Layout
27354 This only applies for keyboards where the tilde is defined as accent.
27363 in combination with
27378 \begin_layout Standard
27421 and accents that are inserted directly with the keyboard are also available
27422 in mathematical text.
27423 For the other accents there are special math commands to be used in formulas,
27425 \begin_inset CommandInset ref
27427 reference "sub:Accents-for-one"
27434 \begin_layout Standard
27435 \begin_inset VSpace bigskip
27438 Furthermore, with the command
27445 \begin_inset Index idx
27448 \begin_layout Plain Layout
27456 all numbers and letters can be set into a circle, quasi accented with a
27457 circle, similar to the copyright symbol.
27460 \begin_layout Standard
27462 \begin_inset Tabular
27463 <lyxtabular version="3" rows="3" columns="2">
27464 <features tabularvalignment="middle">
27465 <column alignment="center" valignment="top" width="0">
27466 <column alignment="center" valignment="top" width="0">
27468 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27471 \begin_layout Plain Layout
27477 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27480 \begin_layout Plain Layout
27482 \begin_inset Note Note
27485 \begin_layout Plain Layout
27492 is only used as spacer.
27504 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27507 \begin_layout Plain Layout
27515 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27518 \begin_layout Plain Layout
27522 \begin_layout Plain Layout
27538 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27541 \begin_layout Plain Layout
27552 raisebox{-1.5pt}{W}}
27557 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27560 \begin_layout Plain Layout
27561 \begin_inset Formula $\raisebox{4.5mm}{}$
27568 \begin_layout Plain Layout
27586 \begin_inset Formula $\raisebox{-2mm}{}$
27602 \begin_layout Standard
27603 One has to take care that the character fits in the circle.
27614 \begin_layout Plain Layout
27616 \begin_inset CommandInset ref
27618 reference "sub:Font-Sizes"
27627 specifies thereby the size of the circle.
27638 \begin_layout Plain Layout
27640 \begin_inset CommandInset ref
27642 reference "sub:Boxes-without-Frame"
27651 the character can be centered.
27654 \begin_layout Subsection
27656 \begin_inset Index idx
27659 \begin_layout Plain Layout
27668 \begin_layout Standard
27669 Minuscule numbers are created with the command
27676 \begin_inset Index idx
27679 \begin_layout Plain Layout
27688 The command can be used in formulas and in TeX-mode.
27689 The command scheme is:
27692 \begin_layout Standard
27697 oldstylenums{number}
27700 \begin_layout Standard
27705 oldstylenums{0123456789
27708 \begin_inset Formula $\oldstylenums{0123456789}$
27714 \begin_layout Subsection
27715 Miscellaneous special Characters
27716 \begin_inset CommandInset label
27718 name "sub:Miscellaneous-special-Characters"
27723 \begin_inset Index idx
27726 \begin_layout Plain Layout
27727 Special characters ! miscellaneous
27735 \begin_layout Standard
27736 The following characters can only be inserted to formulas by using commands:
27739 \begin_layout Standard
27741 \begin_inset Tabular
27742 <lyxtabular version="3" rows="4" columns="2">
27743 <features tabularvalignment="middle">
27744 <column alignment="center" valignment="top" width="0">
27745 <column alignment="center" valignment="top" width="0">
27747 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27750 \begin_layout Plain Layout
27756 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27759 \begin_layout Plain Layout
27767 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27770 \begin_layout Plain Layout
27777 \begin_layout Plain Layout
27791 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27794 \begin_layout Plain Layout
27795 \begin_inset Formula $\mathcircumflex$
27805 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27808 \begin_layout Plain Layout
27816 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27819 \begin_layout Plain Layout
27820 \begin_inset Formula $\_$
27830 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27833 \begin_layout Plain Layout
27838 \begin_layout Plain Layout
27850 \begin_inset Index idx
27853 \begin_layout Plain Layout
27866 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27869 \begin_layout Plain Layout
27870 \begin_inset Formula $^{\circ}$
27886 \begin_layout Standard
27887 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
27888 contains the following line
27892 \begin_layout Plain Layout
27893 More about this is described in
27894 \begin_inset CommandInset ref
27896 reference "sub:Text-Characters-in"
27908 \begin_layout Standard
27913 DeclareInputtext{176}{
27926 \begin_layout Section
27928 \begin_inset CommandInset label
27930 name "sec:Formula-Styles"
27935 \begin_inset Index idx
27938 \begin_layout Plain Layout
27947 \begin_layout Itemize
27948 There are two different alignment styles:
27952 \begin_layout Description
27953 Centered is the predefined standard
27956 \begin_layout Description
27957 Indented for this the option
27961 must be inserted in the menu
27963 Document\SpecialChar \menuseparator
27969 \begin_inset space ~
27975 \begin_layout Standard
27980 is used, the indentation can be adjusted with the length
27987 \begin_inset Index idx
27990 \begin_layout Plain Layout
27999 Should the distance be 15
28000 \begin_inset space \thinspace{}
28003 mm, the following command line is inserted in the LaTeX-preamble
28006 \begin_layout Standard
28016 \begin_layout Standard
28017 When no length is specified, the predefined value of 30
28018 \begin_inset space \thinspace{}
28025 \begin_layout Itemize
28026 And two different numbering styles:
28030 \begin_layout Description
28031 Right is the predefined standard
28034 \begin_layout Description
28035 Left for this the option
28039 must be inserted in the menu
28041 Document\SpecialChar \menuseparator
28047 \begin_inset space ~
28054 \begin_layout Standard
28063 can also be used together.
28064 In this case both options are inserted, separated by a comma.
28067 \begin_layout Standard
28068 The chosen styles are used for all displayed formulas of the document.
28069 When both, centered and indented formulas should be created in a document,
28075 The indented formulas are then set in a flalign environment, see
28076 \begin_inset CommandInset ref
28078 reference "sub:Flalign-Environment"
28085 \begin_layout Section
28087 \begin_inset CommandInset label
28089 name "sec:Multiline-Formulas"
28094 \begin_inset Index idx
28097 \begin_layout Plain Layout
28098 Formula ! multiline
28106 \begin_layout Subsection
28110 \begin_layout Standard
28111 In LyX multiline formulas are created by pressing
28116 arg "newline-insert newline"
28122 This creates either an
28124 eqnarray environment
28126 that is described in
28127 \begin_inset CommandInset ref
28129 reference "sub:Eqnarray-Environment"
28133 or, when the option
28135 Use AMS math package
28137 in the document settings is selected, an
28141 that is described in
28142 \begin_inset CommandInset ref
28144 reference "sub:Standard-align-Environment"
28151 \begin_layout Standard
28152 There are other multiline formula environments that can be created via the
28155 Insert\SpecialChar \menuseparator
28159 These environments are described in the following sections.
28162 \begin_layout Standard
28163 In all multiline formula environments a new line is created by pressing
28167 arg "newline-insert newline"
28171 To add or delete lines, the math toolbar buttons
28172 \begin_inset Graphics
28173 filename ../images/tabular-feature_append-row.png
28179 \begin_inset Graphics
28180 filename ../images/tabular-feature_delete-row.png
28185 , respectively, or the menu
28187 Edit\SpecialChar \menuseparator
28193 \begin_layout Subsubsection
28195 \begin_inset CommandInset label
28197 name "sub:Line-Separation"
28202 \begin_inset Index idx
28205 \begin_layout Plain Layout
28206 Formula ! multiline ! Line separation
28214 \begin_layout Standard
28215 There is sometimes not enough space in multiline formulas between the lines:
28216 \begin_inset Formula
28218 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}\\
28219 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
28227 \begin_layout Standard
28228 In LaTeX additional line space is specified as optional argument of the
28230 This is not yet possible in LyX
28234 \begin_layout Plain Layout
28236 \begin_inset CommandInset href
28238 name "LyX-bug #1505"
28239 target "http://www.lyx.org/trac/ticket/1505"
28248 , therefore the whole formula must be inserted in TeX-mode.
28249 To add in our example space, the command
28257 is inserted at the end of the first line.
28262 \begin_layout Plain Layout
28269 \begin_layout Plain Layout
28271 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
28274 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
28281 \begin_layout Plain Layout
28285 left(B^{2}+x_{0}^{2}
28293 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
28298 \begin_layout Plain Layout
28310 \begin_layout Standard
28311 \begin_inset VSpace bigskip
28314 To set the line separation for all lines in a formula, the length
28321 \begin_inset Index idx
28324 \begin_layout Plain Layout
28334 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
28345 \begin_inset space \thinspace{}
28350 \begin_inset space \thinspace{}
28353 mm additional line separation as in the previous example, the command
28356 \begin_layout Standard
28366 \begin_layout Standard
28367 is inserted in TeX-mode before the formula.
28368 This requires that the LaTeX-package
28376 \begin_layout Plain Layout
28381 is part of every LaTeX standard installation.
28387 \begin_inset Index idx
28390 \begin_layout Plain Layout
28396 was loaded in LaTeX-preamble with the line
28399 \begin_layout Standard
28407 \begin_layout Standard
28412 \begin_layout Plain Layout
28424 \begin_inset Formula
28426 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}\\
28427 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
28435 \begin_layout Standard
28439 \begin_layout Plain Layout
28450 To get back to the predefined distance,
28456 is set to the value 3
28457 \begin_inset space \thinspace{}
28463 \begin_layout Subsubsection
28465 \begin_inset CommandInset label
28467 name "sub:Column-Separation"
28472 \begin_inset Index idx
28475 \begin_layout Plain Layout
28476 Formula ! multiline ! Column separation
28484 \begin_layout Standard
28485 Multiline formulas form a matrix.
28486 A formula in the eqnarray environment is for example a matrix with three
28488 By changing the column separation in this environment, the space beside
28489 the relation sign can be changed.
28492 \begin_layout Standard
28493 The column separation is specified with the length
28500 \begin_inset Index idx
28503 \begin_layout Plain Layout
28512 \begin_inset Newline newline
28515 column separation = 2
28516 \begin_inset space \thinspace{}
28526 \begin_inset Newline newline
28532 \begin_layout Standard
28542 \begin_layout Standard
28543 inserted in TeX-mode, sets for all following formulas a column separation
28545 \begin_inset space \thinspace{}
28549 To get back to the predefined distance,
28556 \begin_inset space \thinspace{}
28562 \begin_layout Standard
28564 \begin_inset space \thinspace{}
28567 cm column separation:
28571 \begin_layout Plain Layout
28583 \begin_inset Formula
28591 A formula with the predefined column separation for matrices of 10
28592 \begin_inset space \thinspace{}
28599 \begin_layout Plain Layout
28611 \begin_inset Formula
28622 \begin_layout Subsubsection
28624 \begin_inset Index idx
28627 \begin_layout Plain Layout
28636 \begin_layout Standard
28637 Long formulas can be typeset using these methods:
28640 \begin_layout Itemize
28641 When one side of the equation is much shorther than the line width, this
28642 one is chosen for the left side and the right side is typeset over two
28644 \begin_inset Formula
28646 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 \\
28647 & & -\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}
28652 The minus sign at the beginning of the second line does normally not appear
28653 as operator because it is the first character of the line.
28654 Thus it would not be surrounded by space and could not be distinguished
28655 from the fraction bar.
28657 \begin_inset space \thinspace{}
28660 pt space was inserted behind the minus sign with the command
28670 \begin_layout Plain Layout
28678 \begin_inset CommandInset ref
28680 reference "sub:Variable-Space"
28690 \begin_inset Index idx
28693 \begin_layout Plain Layout
28704 \begin_layout Itemize
28705 When both sides of the equation are too long, the command
28712 \begin_inset Index idx
28715 \begin_layout Plain Layout
28724 It is inserted to the first column of the first line and effects that all
28725 further insertions overwrite the following columns:
28726 \begin_inset Formula
28728 \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 \\
28729 & & -\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 \\
28730 & & =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}
28735 After the insertion of
28741 , the cursor is in a purple box that is a bit shifted to the left from the
28743 In this the formula is inserted.
28744 \begin_inset Newline newline
28747 The content of the further lines is inserted to the second or another formula
28749 The greater the column number where it was inserted, the larger the indentation.
28750 \begin_inset VSpace medskip
28754 \begin_inset Newline newline
28758 \begin_inset Note Greyedout
28761 \begin_layout Plain Layout
28762 Note the following when using
28771 \begin_layout Itemize
28772 The formula doesn't use the full page width.
28774 \begin_inset space \thinspace{}
28778 \begin_inset space \space{}
28782 \begin_inset Formula $-B^{2}$
28785 is added to the first line in the above example, it would have been outside
28787 To better use the width, negative space can be inserted at the beginning
28791 \begin_layout Itemize
28792 Due to a bug in LyX the cursor cannot be set with the mouse into the first
28797 \begin_layout Plain Layout
28798 \begin_inset CommandInset href
28800 name "LyX-bug #1429"
28801 target "http://www.lyx.org/trac/ticket/1429"
28810 One can only set the cursor at the beginning of the line and move it with
28819 \begin_layout Itemize
28820 Other methods to set long formulas are offered by the environments described
28822 \begin_inset CommandInset ref
28824 reference "sub:Multline-Environment"
28829 \begin_inset CommandInset ref
28831 reference "sub:Multiline-Formula-Parts"
28838 \begin_layout Subsubsection
28840 \begin_inset CommandInset label
28842 name "sub:Multiline-Brackets"
28847 \begin_inset Index idx
28850 \begin_layout Plain Layout
28851 Brackets ! for multiline expressions
28859 \begin_layout Standard
28860 For brackets spanning multiple lines the following problem occurs:
28861 \begin_inset Formula
28863 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28864 & & \left.\cdots+B-D\right]
28872 \begin_layout Standard
28873 The closing bracket is smaller than the opening bracket because brackets
28874 with variable size may not span multiple lines.
28877 \begin_layout Standard
28878 To set the bracket size for the second line correctly, the first line is
28886 \begin_inset Index idx
28889 \begin_layout Plain Layout
28897 and the second line with
28905 \begin_layout Plain Layout
28919 \begin_inset CommandInset ref
28921 reference "sub:Automatic-Bracket-Size"
28933 \begin_inset Index idx
28936 \begin_layout Plain Layout
28962 \begin_layout Plain Layout
28981 \begin_layout Plain Layout
29000 \begin_layout Plain Layout
29012 \begin_inset Formula $\downarrow$
29018 \begin_inset Index idx
29021 \begin_layout Plain Layout
29029 is inserted, because the multiplication operator with its limits is the
29030 largest symbol in the first line and this should be the size for the bracket
29031 in the second line.
29034 \begin_layout Standard
29035 The result is this:
29036 \begin_inset Formula
29038 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
29039 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
29047 \begin_layout Subsection
29051 \begin_layout Standard
29052 Align environments can be used for every kind of multiline formulas.
29053 They are specially useful to set several formulas side by side.
29056 \begin_layout Standard
29057 Align environments consist of columns.
29058 The odd columns are right aligned, the even ones left aligned.
29059 Every line in an Align environment can be numbered.
29062 \begin_layout Standard
29063 Align environments are created via the menu
29065 Insert\SpecialChar \menuseparator
29071 Edit\SpecialChar \menuseparator
29072 Math\SpecialChar \menuseparator
29073 Change Formula Type
29075 already existing formulas can be converted to Align environments.
29078 \begin_layout Standard
29079 To add or delete columns, the math toolbar buttons
29080 \begin_inset Graphics
29081 filename ../images/tabular-feature_append-column.png
29087 \begin_inset Graphics
29088 filename ../images/tabular-feature_delete-column.png
29093 , respectively, or the menu
29095 Edit\SpecialChar \menuseparator
29101 \begin_layout Subsubsection
29102 Standard align Environment
29103 \begin_inset CommandInset label
29105 name "sub:Standard-align-Environment"
29110 \begin_inset Index idx
29113 \begin_layout Plain Layout
29114 Formula ! multiline ! align environment
29122 \begin_layout Standard
29123 This Align environment is created by presssing
29126 arg "newline-insert newline"
29129 in a formula or by the menu
29131 Insert\SpecialChar \menuseparator
29132 Math\SpecialChar \menuseparator
29133 AMS align Environment
29138 \begin_layout Standard
29139 An example for two formulas set side by side, that are created with a four
29140 column align environment:
29141 \begin_inset Formula
29143 A & =\sin(B) & C & =D\\
29144 C & \ne A & B & \ne D
29149 As it can be seen, the formulas in this environment are placed so as if
29158 \begin_layout Plain Layout
29166 \begin_inset CommandInset ref
29168 reference "sub:Variable-Space"
29179 before the first and after every even column.
29180 When the formula style
29186 \begin_layout Plain Layout
29188 \begin_inset CommandInset ref
29190 reference "sec:Formula-Styles"
29201 is used, the formula is set without the
29207 before the first column.
29210 \begin_layout Subsubsection
29211 Alignat Environment
29212 \begin_inset Index idx
29215 \begin_layout Plain Layout
29216 Formula ! multiline ! alignat environment
29224 \begin_layout Standard
29225 The alignat environment has no predefined column separation.
29226 It can be inserted manually with the spaces that are described
29227 \begin_inset CommandInset ref
29229 reference "sub:Space"
29236 \begin_layout Standard
29237 The above example in the alignat environment where 1
29238 \begin_inset space \thinspace{}
29241 cm space was inserted at the beginning of the second formula:
29242 \begin_inset Formula
29243 \begin{alignat*}{2}
29244 A & =\sin(B) & \hspace{1cm}C & =D\\
29245 C & \ne A & B & \ne D
29250 Because the column separation can be set separately for every column, this
29251 environment is especially suitable to set three and more formulas side
29255 \begin_layout Subsubsection
29256 Flalign Environment
29257 \begin_inset CommandInset label
29259 name "sub:Flalign-Environment"
29264 \begin_inset Index idx
29267 \begin_layout Plain Layout
29268 Formula ! multiline ! flalign environment
29276 \begin_layout Standard
29277 In this environment the first two columns are always set as much as possible
29278 to the left and the last two ones to the right.
29280 \begin_inset Formula
29282 A & =1 & B & =2 & C & =3\\
29283 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
29291 \begin_layout Standard
29292 By creating a flalign environment with an odd number of columns where an
29293 empty TeX-brace is inserted to the last column, several formulas in a document
29294 can be set to the left, although the formula style
29299 As example the indented formula
29300 \begin_inset CommandInset ref
29302 reference "eq:VolInt"
29307 \begin_inset Formula
29309 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}
29314 The first two columns contain the formula.
29315 To indent it as with the formula style
29320 \begin_inset space \thinspace{}
29323 pt space was inserted at the beginning of the first column.
29326 \begin_layout Subsection
29327 Eqnarray Environment
29328 \begin_inset CommandInset label
29330 name "sub:Eqnarray-Environment"
29335 \begin_inset Index idx
29338 \begin_layout Plain Layout
29339 Formula ! multiline ! eqnarray environment
29347 \begin_layout Standard
29348 When this environment has been created, three blue boxes appear.
29349 The content of the first box is right aligned, the content of the last
29351 The content of the middle box appears centered and a bit smaller, because
29352 it is designed to insert there only relation characters.
29353 \begin_inset Formula
29355 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
29365 \begin_layout Subsection
29367 \begin_inset Index idx
29370 \begin_layout Plain Layout
29371 Formula ! multiline ! gather environment
29379 \begin_layout Standard
29380 This environment consists of only one centered column.
29381 Every line can be numbered.
29382 \begin_inset Formula
29393 \begin_layout Subsection
29394 Multline Environment
29395 \begin_inset CommandInset label
29397 name "sub:Multline-Environment"
29402 \begin_inset Index idx
29405 \begin_layout Plain Layout
29406 Formula ! multiline ! multline environment
29414 \begin_layout Standard
29415 The multline environment consists, like the gather environment, of only
29417 But the first line is left aligned, the last one right aligned.
29418 All other lines are centered.
29419 Therefore this environment is suitable for long formulas.
29421 \begin_inset CommandInset ref
29423 reference "eq:lefteqn"
29427 in the multline environment:
29428 \begin_inset Formula
29430 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}\\
29431 -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}\\
29432 =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}}
29440 \begin_layout Standard
29441 In the output only the last (first) line of a multline environment appears
29442 numbered when the document numbering is right (left).
29446 \begin_layout Plain Layout
29447 numbering styles see
29448 \begin_inset CommandInset ref
29450 reference "sec:Formula-Styles"
29462 \begin_layout Standard
29470 \begin_inset Index idx
29473 \begin_layout Plain Layout
29488 \begin_inset Index idx
29491 \begin_layout Plain Layout
29499 a centered line can be right or left aligned, respectively.
29500 The commands are used as follows:
29503 \begin_layout Standard
29508 shoveright{line content}
29514 shoveleft{line content}
29517 \begin_layout Standard
29518 \begin_inset VSpace medskip
29528 \begin_inset Index idx
29531 \begin_layout Plain Layout
29539 specifies the distance of the first line from the left page margin.
29540 Predefined is the length 0
29541 \begin_inset space \thinspace{}
29547 \begin_layout Standard
29548 As example the above formula where the command
29551 \begin_layout Standard
29561 \begin_layout Standard
29562 was inserted in TeX-mode before:
29566 \begin_layout Plain Layout
29578 \begin_inset Formula
29580 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}\\
29581 \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}}\\
29582 =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}}
29591 \begin_layout Plain Layout
29602 The second line was left aligned using
29611 \begin_layout Subsection
29612 Multiline Formula Parts
29613 \begin_inset CommandInset label
29615 name "sub:Multiline-Formula-Parts"
29620 \begin_inset Index idx
29623 \begin_layout Plain Layout
29624 Formula ! multiline ! formula parts
29632 \begin_layout Standard
29633 To display only parts of a formula with multiple lines, one of the following
29634 environments are used:
29651 They can be inserted via the menu
29653 Insert\SpecialChar \menuseparator
29656 or by using the commands described in this section.
29659 \begin_layout Standard
29660 The first three have the same properties as the corresponding multiline
29661 formula environments, but it is possible to set further formula parts beside
29664 \begin_inset Formula
29666 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29667 \Delta E\Delta t & \ge\frac{\hbar}{2}
29669 \right\} \textrm{Uncertainty relations}
29677 \begin_layout Standard
29678 To get this formula, a displayed formula is created where the command
29685 \begin_inset Index idx
29688 \begin_layout Plain Layout
29697 A purple box appears around the blue formula box where now columns and
29698 lines can be added.
29699 Outside the multiline environment other formula parts can be set, like
29703 \begin_layout Standard
29704 The aligned environment is also suitable for long formulas whose lines are
29705 horizontally aligned.
29706 Using aligned in a displayed formula has the advantage that the formula
29707 number is vertically centered behind the lines.
29709 \begin_inset CommandInset ref
29711 reference "eq:shortlong"
29715 in the aligned environment:
29716 \begin_inset Formula
29718 \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}|}\\
29719 & -\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}|}
29728 \begin_layout Standard
29729 To use the environments
29748 \begin_inset Index idx
29751 \begin_layout Plain Layout
29766 \begin_inset Index idx
29769 \begin_layout Plain Layout
29784 \begin_inset Index idx
29787 \begin_layout Plain Layout
29795 are inserted, respectively.
29796 The split environment has the same properties as the aligned environment
29797 but it can only have two columns.
29800 \begin_layout Subsection
29801 Text in multiline Formulas
29802 \begin_inset CommandInset label
29804 name "sub:Text-in-multiline"
29809 \begin_inset Index idx
29812 \begin_layout Plain Layout
29819 \begin_inset Index idx
29822 \begin_layout Plain Layout
29823 Formula ! multiline ! text
29831 \begin_layout Standard
29832 In the Align environments, and the multline and gather environment, text
29833 can be inserted that will appear in a separate line and doesn't affect
29834 the column alignment.
29835 To do this, the command
29842 \begin_inset Index idx
29845 \begin_layout Plain Layout
29853 is used in the following scheme:
29856 \begin_layout Standard
29864 \begin_layout Standard
29865 The text should not be longer than a line because it cannot be hyphenated.
29866 As LyX doesn't yet support
29872 directly, the text is written as mathematical text.
29879 must hereby be at the beginning of a line and appears in the output above
29881 An example where the text was inserted at the beginning of the second line:
29882 \begin_inset Formula
29884 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29885 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29893 \begin_layout Section
29895 \begin_inset Index idx
29898 \begin_layout Plain Layout
29905 \begin_inset Index idx
29908 \begin_layout Plain Layout
29909 Formula ! numbering|see
29913 \begin_layout Plain Layout
29924 \begin_layout Plain Layout
29939 \begin_layout Subsection
29943 \begin_layout Standard
29944 Numbered formulas can be created with the menu
29946 Insert\SpecialChar \menuseparator
29947 Math\SpecialChar \menuseparator
29949 \begin_inset space ~
29957 \begin_inset space ~
29963 Existing formulas can be numbered with the menu
29965 Edit\SpecialChar \menuseparator
29966 Math\SpecialChar \menuseparator
29968 \begin_inset space ~
29976 arg "math-number-toggle"
29980 The formula number is displayed in LyX behind the formula as number sign
29982 The number sign is replaced in the output by the formula number.
29985 \begin_layout Standard
29986 When numbering is turned on in multiline formulas, all lines will be numbered.
29987 But the numbering can be controlled with the menu
29989 Edit\SpecialChar \menuseparator
29990 Math\SpecialChar \menuseparator
29992 \begin_inset space ~
29996 \begin_inset space ~
30000 \begin_inset space ~
30008 arg "math-number-line-toggle"
30014 \begin_layout Standard
30015 Except for inline formulas, all formulas can be numbered with two different
30017 \begin_inset CommandInset ref
30019 reference "sec:Formula-Styles"
30026 \begin_layout Subsection
30028 \begin_inset Index idx
30031 \begin_layout Plain Layout
30032 Cross-references ! to formulas
30040 \begin_layout Standard
30041 All labeled formulas can be cross-referenced.
30042 A label is added by the menu
30044 Insert\SpecialChar \menuseparator
30047 or the toolbar button
30048 \begin_inset Graphics
30049 filename ../images/label-insert.png
30055 The cursor must hereby be inside a displayed formula.
30056 A dialog pops up displaying the prefix
30061 The label is inserted there behind the prefix.
30062 The predefined prefix means
30063 \begin_inset Quotes eld
30067 \begin_inset Quotes erd
30070 and makes it easier to find labels in large documents because it marks
30071 it as formula label to divide it from e.
30072 \begin_inset space \thinspace{}
30076 \begin_inset space \space{}
30080 To change a label, the menu
30082 Insert\SpecialChar \menuseparator
30088 \begin_layout Standard
30089 The name of the label is displayed in LyX within two parentheses behind
30091 A formula with a label is always numbered.
30094 \begin_layout Standard
30095 Cross-references are inserted via the menu
30097 Insert\SpecialChar \menuseparator
30100 or with the toolbar button
30101 \begin_inset Graphics
30102 filename ../images/dialog-show-new-inset_ref.png
30108 A formula cross-reference appears in the output as formula number.
30109 When in the cross-reference dialog window the format
30113 is chosen, the cross-reference appears in the output as formula number
30115 \begin_inset Newline newline
30118 By right-clicking on a cross-reference in LyX, one jumps to the formula
30119 that is referenced.
30122 \begin_layout Standard
30123 Here are as examples cross-references to formulas of the following subsections:
30124 \begin_inset Note Note
30127 \begin_layout Plain Layout
30128 Note the different cross-reference types.
30136 \begin_layout Standard
30138 \begin_inset CommandInset ref
30145 \begin_inset CommandInset ref
30153 \begin_inset CommandInset ref
30159 ) big Latin letters are used for the numbering in contrary to (
30160 \begin_inset CommandInset ref
30169 \begin_layout Standard
30170 \begin_inset VSpace medskip
30173 When the argument of
30181 \begin_layout Plain Layout
30189 \begin_inset CommandInset ref
30191 reference "sub:User-defined-Numbering"
30202 contains a box like in
30203 \begin_inset CommandInset ref
30205 reference "sub:Paragraph-Boxes"
30209 , the formula cannot be referenced.
30212 \begin_layout Subsection
30214 \begin_inset Index idx
30217 \begin_layout Plain Layout
30218 Formula numbering ! subnumbering
30226 \begin_layout Standard
30227 With the help of the commands
30231 begin{subequations}
30239 formulas can be subnumbered.
30240 Both commands are inserted in TeX-mode.
30243 \begin_layout Standard
30245 \begin_inset Formula
30256 \begin_layout Plain Layout
30260 addtocounter{equation}{-1}
30269 \begin_layout Plain Layout
30273 begin{subequations}
30279 \begin_inset VSpace -5mm
30283 \begin_inset Formula
30291 \begin_inset Formula
30301 \begin_layout Standard
30305 \begin_layout Plain Layout
30317 \begin_layout Standard
30318 To create the example, the following is done:
30321 \begin_layout Enumerate
30322 first formula is inserted
30325 \begin_layout Enumerate
30330 addtocounter{equation}{-1}
30332 begin{subequations}
30333 \begin_inset Index idx
30336 \begin_layout Plain Layout
30345 \begin_inset Newline newline
30350 is inserted after the first formula
30353 \begin_layout Enumerate
30354 second formula is inserted
30357 \begin_layout Enumerate
30358 third formula is inserted
30361 \begin_layout Enumerate
30368 is inserted after the third formula
30371 \begin_layout Standard
30372 Every formula between the commands
30384 is subnumbered as a, b,
30385 \begin_inset Newline linebreak
30388 c, \SpecialChar \ldots{}
30389 For multiline formulas every line will be subnumbered.
30390 All subnumbered formulas are treated as
30395 But as every numbered formula increases the counter
30399 by one, the command
30405 is needed to decrease it.
30406 Otherwise the formulas
30407 \begin_inset CommandInset ref
30414 \begin_inset CommandInset ref
30421 \begin_inset CommandInset ref
30427 would be numbered as
30428 \begin_inset CommandInset ref
30435 \begin_inset CommandInset ref
30442 \begin_inset CommandInset ref
30451 \begin_layout Standard
30452 By inserting the commands in TeX-mode, a space is created between the first
30455 \begin_inset space \thinspace{}
30458 mm vertical space is inserted after the command
30462 begin{subequations}
30465 When the formula style
30471 \begin_layout Plain Layout
30473 \begin_inset CommandInset ref
30475 reference "sec:Formula-Styles"
30487 \begin_inset space \thinspace{}
30490 mm space is inserted instead.
30493 \begin_layout Standard
30494 Here is an example for a multiline formula where the numbering was turned
30495 off for the second line:
30499 \begin_layout Plain Layout
30503 begin{subequations}
30509 \begin_inset Formula
30511 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
30512 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
30513 & = & B^{2}-2BZ+Z^{2}\label{eq:f}
30522 \begin_layout Plain Layout
30534 \begin_layout Subsection
30535 User-defined Numbering
30536 \begin_inset CommandInset label
30538 name "sub:User-defined-Numbering"
30543 \begin_inset Index idx
30546 \begin_layout Plain Layout
30547 Formula numbering ! user-defined
30555 \begin_layout Standard
30556 \begin_inset Index idx
30559 \begin_layout Plain Layout
30560 Formula numbering ! self-defined delimiters
30565 With the standard numbering parentheses are set around the formula number.
30566 To replace the parentheses for example by vertical bars, the following
30567 line is added to the LaTeX-preamble:
30570 \begin_layout Standard
30582 \begin_inset Note Note
30585 \begin_layout Plain Layout
30586 This macro is already declared in the LaTeX-preamble for testing.
30587 To activate it, remove the percent sign at the beginning.
30595 \begin_layout Standard
30596 To use other characters, the vertical bars besides the
30600 are replaced by one ore more characters.
30601 To get only the formula number the vertical bars are omitted.
30604 \begin_layout Standard
30605 \begin_inset VSpace bigskip
30608 When there should be an expression of your choice instead of the consecutive
30609 formula number in parentheses behind the formula, the command
30616 \begin_inset Index idx
30619 \begin_layout Plain Layout
30628 \begin_inset Formula
30630 A+B=C\tag{something}\label{eq:tag}
30635 In this example the command
30643 \begin_layout Plain Layout
30654 was inserted to the formula.
30657 \begin_layout Standard
30666 \begin_layout Plain Layout
30677 is inserted instead, the star prevents the parentheses around the expression:
30678 \begin_inset Formula
30680 A+B=C\tag*{something}
30688 \begin_layout Standard
30689 \begin_inset VSpace bigskip
30692 To restart the formula numbering with new document parts or sections, the
30693 following command is used:
30696 \begin_layout Standard
30701 @addtoreset{equation}{part}
30704 \begin_inset Index idx
30707 \begin_layout Plain Layout
30712 \begin_layout Plain Layout
30723 \begin_layout Plain Layout
30736 \begin_layout Plain Layout
30747 \begin_layout Plain Layout
30760 \begin_inset Newline newline
30764 \begin_inset Newline newline
30771 @addtoreset{equation}{section}
30774 \begin_layout Standard
30775 To be able to use these commands in TeX-mode, the
30776 \begin_inset Quotes eld
30780 \begin_inset Quotes erd
30783 character has to be made
30784 \begin_inset Quotes eld
30788 \begin_inset Quotes erd
30791 for LaTeX using the command
30805 So the command sequence in TeX-mode is:
30808 \begin_layout Standard
30814 \begin_inset Newline newline
30819 @addtoreset{equation}{section}
30820 \begin_inset Newline newline
30828 \begin_layout Standard
30829 In the LaTeX-preamble
30841 can be omitted as they are automatically internally inserted by LyX.
30844 \begin_layout Standard
30859 \begin_layout Plain Layout
30864 is part of the LaTeX-package
30869 \begin_inset Index idx
30872 \begin_layout Plain Layout
30873 Packages ! carlisle
30878 that is part of every LaTeX standard installation.
30884 \begin_inset Index idx
30887 \begin_layout Plain Layout
30888 Packages ! remreset
30893 has to be loaded in the LaTeX-preamble with the line
30896 \begin_layout Standard
30901 usepackage{remreset}
30904 \begin_layout Standard
30912 \begin_inset Index idx
30915 \begin_layout Plain Layout
30920 \begin_layout Plain Layout
30931 \begin_layout Plain Layout
30944 \begin_layout Plain Layout
30955 \begin_layout Plain Layout
30967 can be used with the same scheme as
30976 \begin_layout Standard
30977 \begin_inset VSpace bigskip
30980 Sometimes formulas should be numbered in the following form:
30983 \begin_layout Standard
30986 (section number.formula number)
30989 \begin_layout Standard
30990 The formula number should start with every section with
30991 \begin_inset Quotes eld
30995 \begin_inset Quotes erd
31001 \begin_layout Standard
31002 For this case there is the command
31009 \begin_inset Index idx
31012 \begin_layout Plain Layout
31020 , which is used with the following scheme:
31023 \begin_layout Standard
31028 numberwithin{counter}{sectioning}
31031 \begin_layout Standard
31032 Counter denotes what kind of numbering is affected, sectioning denotes what
31033 number is before the dot.
31036 \begin_layout Standard
31037 Thus in our case the following LaTeX-preamble or TeX-Code line is used:
31040 \begin_layout Standard
31045 numberwithin{equation}{section}
31048 \begin_layout Standard
31049 This is the result:
31053 \begin_layout Plain Layout
31057 numberwithin{equation}{section}
31063 \begin_inset Formula
31073 \begin_layout Standard
31075 \begin_inset space \thinspace{}
31079 \begin_inset space \space{}
31082 tables so that the number of the part is the sectioning,
31083 \begin_inset Newline newline
31090 numberwithin{table}{part}
31095 \begin_layout Standard
31096 To go back to the standard numbering or to prevent this kind of numbering
31097 when it is defined by the document class, the following command is inserted
31098 as TeX-Code or to the LaTeX-preamble:
31101 \begin_layout Standard
31111 \begin_inset Index idx
31114 \begin_layout Plain Layout
31128 \begin_layout Plain Layout
31144 \begin_inset Newline newline
31152 \begin_inset Newline newline
31164 \begin_layout Standard
31171 uses internally the command
31177 , described above, that also needs to be reverted.
31181 \begin_layout Plain Layout
31188 \begin_layout Plain Layout
31192 @removefromreset{equation}{section}
31195 \begin_layout Plain Layout
31207 \begin_layout Subsection
31208 Numbering with Roman Numbers and Letters
31209 \begin_inset Index idx
31212 \begin_layout Plain Layout
31213 Formula numbering ! with letters
31219 \begin_inset Index idx
31222 \begin_layout Plain Layout
31223 Formula numbering ! with Roman numbers
31231 \begin_layout Standard
31232 Formulas can also be numbered with Roman numbers and Latin letters.
31233 To number for example with small Roman numbers, the command
31236 \begin_layout Standard
31248 \begin_layout Standard
31249 is inserted before the formula in TeX-mode.
31257 \begin_inset Index idx
31260 \begin_layout Plain Layout
31268 redefines the predefined command
31284 \begin_layout Plain Layout
31291 has the same scheme like the command
31297 that is described in
31298 \begin_inset CommandInset ref
31300 reference "sub:The-Command-newcommand"
31313 is the formula counter.
31320 is used as prefix for a counter, the value of the counter is output as
31322 When a formula is numbered, LaTeX sets internally the command
31328 behind the formula.
31334 \begin_inset Index idx
31337 \begin_layout Plain Layout
31347 outputs the counter as small Roman number.
31350 \begin_layout Standard
31351 All formulas behind the command
31361 are now numbered Roman.
31362 To switch to numbering with big Roman numbers, the command is inserted
31376 \begin_inset Index idx
31379 \begin_layout Plain Layout
31391 \begin_inset Quotes eld
31395 \begin_inset Quotes erd
31398 with small Latin letters there is the command
31405 \begin_inset Index idx
31408 \begin_layout Plain Layout
31416 , for big ones there is the command
31423 \begin_inset Index idx
31426 \begin_layout Plain Layout
31439 \begin_layout Standard
31440 \begin_inset Note Greyedout
31443 \begin_layout Plain Layout
31448 Only maximal 26 formulas can be numbered with Latin letters in one document.
31456 \begin_layout Standard
31460 \begin_layout Plain Layout
31476 \begin_layout Standard
31477 \begin_inset Formula
31479 A=\textrm{small roman}
31488 \begin_layout Plain Layout
31502 \begin_inset Formula
31504 B=\textrm{big Roman}\label{eq:Rom}
31513 \begin_layout Plain Layout
31527 \begin_inset Formula
31529 C=\textrm{small Latin}
31538 \begin_layout Plain Layout
31552 \begin_inset Formula
31554 D=\textrm{big Latin}\label{eq:Lat}
31562 \begin_layout Standard
31563 To switch back to the default numbering, insert the command:
31566 \begin_layout Standard
31576 \begin_inset Index idx
31579 \begin_layout Plain Layout
31590 \begin_layout Standard
31594 \begin_layout Plain Layout
31608 \begin_inset Formula
31618 \begin_layout Standard
31619 \begin_inset VSpace medskip
31622 As you see, formulas are numbered serially independent from the numbering
31624 When then numbering should start with
31625 \begin_inset Quotes eld
31629 \begin_inset Quotes erd
31632 when the style is changed, new equation counters have to be defined.
31633 A description about this can be found in the file
31634 \begin_inset CommandInset href
31636 name "Formula-numbering.lyx"
31637 target "run:Formula-numbering.lyx"
31644 \begin_layout Section
31645 Chemical Symbols and Equations
31646 \begin_inset CommandInset label
31648 name "sub:Chemical-Symbols-and"
31653 \begin_inset Index idx
31656 \begin_layout Plain Layout
31657 Chemical characters ! Symbols
31663 \begin_inset Index idx
31666 \begin_layout Plain Layout
31673 \begin_inset Index idx
31676 \begin_layout Plain Layout
31685 \begin_layout Standard
31686 An example text from chemistry:
31689 \begin_layout Quote
31691 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
31694 -ion reacts with two
31695 \begin_inset Formula $\mathrm{Na^{+}}$
31698 -ions to sodium sulfate
31699 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
31703 The chemical equation for this is:
31704 \begin_inset Formula
31706 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
31714 \begin_layout Standard
31715 This chemical equation can directly be created as formula.
31716 To avoid that the symbols appear italic, everything is highlighted and
31717 changed by the shortcut
31723 to the upright font style.
31727 \begin_layout Plain Layout
31733 \begin_inset CommandInset ref
31735 reference "sub:Font-Styles"
31747 \begin_layout Standard
31748 A more convenient way to typeset chemical formulas is to use the command
31756 \begin_inset Index idx
31759 \begin_layout Plain Layout
31767 that is available when the LaTeX-package
31772 \begin_inset Index idx
31775 \begin_layout Plain Layout
31788 to a formula a new blue box appears where chemical formulas can be inserted
31789 in an intuitive way.
31792 \begin_layout Standard
31794 \begin_inset Tabular
31795 <lyxtabular version="3" rows="9" columns="2">
31796 <features tabularvalignment="middle">
31797 <column alignment="center" valignment="top" width="0">
31798 <column alignment="center" valignment="top" width="0">
31800 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31803 \begin_layout Plain Layout
31809 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31812 \begin_layout Plain Layout
31814 \begin_inset Note Note
31817 \begin_layout Plain Layout
31824 is only used as spacer.
31836 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31839 \begin_layout Plain Layout
31846 \begin_layout Plain Layout
31860 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31863 \begin_layout Plain Layout
31864 \begin_inset Formula $\raisebox{4.5mm}{}\ce{H2CO3}\raisebox{-2mm}{}$
31874 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31877 \begin_layout Plain Layout
31884 \begin_layout Plain Layout
31898 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31901 \begin_layout Plain Layout
31902 \begin_inset Formula $\raisebox{5mm}{}\ce{SO4^{2-}}\raisebox{-2mm}{}$
31912 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31915 \begin_layout Plain Layout
31922 \begin_layout Plain Layout
31936 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31939 \begin_layout Plain Layout
31940 \begin_inset Formula $\raisebox{4.5mm}{}\ce{(NH4)2S}\raisebox{-2mm}{}$
31950 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31953 \begin_layout Plain Layout
31960 \begin_layout Plain Layout
31974 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31977 \begin_layout Plain Layout
31978 \begin_inset Formula $\raisebox{4.5mm}{}\ce{KCr(SO4)2.12H2O}\raisebox{-2mm}{}$
31988 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31991 \begin_layout Plain Layout
31998 \begin_layout Plain Layout
32013 \begin_layout Plain Layout
32028 \begin_layout Plain Layout
32042 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32045 \begin_layout Plain Layout
32046 \begin_inset Formula $\raisebox{4.5mm}{}\ce{A-B\dbond C\tbond D}\raisebox{-2mm}{}$
32056 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32059 \begin_layout Plain Layout
32066 \begin_layout Plain Layout
32076 \begin_inset Formula $\downarrow$
32080 \begin_inset Formula $\to$
32088 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32091 \begin_layout Plain Layout
32092 \begin_inset Formula $\raisebox{5mm}{}\ce{_{90}^{227}Th+}\raisebox{-2mm}{}$
32102 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32105 \begin_layout Plain Layout
32112 \begin_layout Plain Layout
32125 \begin_layout Plain Layout
32138 \begin_layout Plain Layout
32151 \begin_layout Plain Layout
32164 \begin_layout Plain Layout
32178 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32181 \begin_layout Plain Layout
32182 \begin_inset Formula $\raisebox{4.5mm}{}\ce{CO2 + C <=> 2CO}\raisebox{-2mm}{}$
32192 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32195 \begin_layout Plain Layout
32202 \begin_layout Plain Layout
32215 \begin_layout Plain Layout
32228 \begin_layout Plain Layout
32241 \begin_layout Plain Layout
32258 \begin_layout Plain Layout
32272 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32275 \begin_layout Plain Layout
32276 \begin_inset Formula $\raisebox{5mm}{}\ce{CO2 + C ->[\alpha][\beta] 2CO}\raisebox{-4mm}{}$
32292 \begin_layout Standard
32293 \begin_inset Note Greyedout
32296 \begin_layout Plain Layout
32301 Inserting a formula to a
32307 box will lead to LaTeX errors.
32308 In this case TeX code has to be used like for
32322 \begin_layout Plain Layout
32343 \begin_layout Standard
32350 the command for equation
32351 \begin_inset space ~
32355 \begin_inset CommandInset ref
32357 reference "eq:chem-reaction"
32362 \begin_inset Newline newline
32373 \begin_layout Plain Layout
32386 \begin_layout Plain Layout
32399 \begin_layout Plain Layout
32412 \begin_layout Plain Layout
32425 \begin_layout Plain Layout
32438 \begin_layout Plain Layout
32450 \begin_layout Standard
32451 To create multiline chemical equations first a multiline formula is created
32453 \begin_inset CommandInset ref
32455 reference "sec:Multiline-Formulas"
32460 Afterwards the command
32466 is used in every small blue box of the formula.
32468 \begin_inset CommandInset ref
32470 reference "eq:TEOS-reaction-1"
32475 \begin_inset CommandInset ref
32477 reference "eq:TEOS-reaction-2"
32481 are an example of a multi-stage chemical reaction where every equation
32482 has its own number.
32483 \begin_inset Formula
32485 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
32486 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
32494 \begin_layout Standard
32505 package provides the command
32512 \begin_inset Index idx
32515 \begin_layout Plain Layout
32523 that has to be used for special cases.
32524 For more information about
32530 and more examples have a look at the documentation of
32535 \begin_inset CommandInset citation
32544 \begin_layout Standard
32545 \begin_inset Newpage newpage
32551 \begin_layout Section
32555 \begin_layout Standard
32556 LyX supports two types of commutative diagrams:
32564 that are explained in the following.
32567 \begin_layout Subsection
32569 \begin_inset Index idx
32572 \begin_layout Plain Layout
32581 \begin_layout Standard
32582 Diagrams of this type visualize relations by vertical and horizontal lines
32584 \begin_inset Formula
32586 \begin{CD}A@>>>B@>>>C\\
32597 \begin_layout Standard
32598 To get them, the command
32603 \begin_inset Index idx
32606 \begin_layout Plain Layout
32616 is inserted to a formula.
32617 A blue box appears with two dashed lines where further commands can be
32622 arg "newline-insert newline"
32625 a new line is created.
32626 Horizontal relations are inserted in odd, vertical in even formula lines.
32629 \begin_layout Standard
32630 To create the relations there are the following commands:
32633 \begin_layout Itemize
32638 creates a left arrow,
32649 \begin_layout Itemize
32654 creates an up arrow,
32662 a vertical equal sign
32665 \begin_layout Itemize
32671 is a placeholder for non-existent relations
32674 \begin_layout Standard
32675 All arrows can be labeled as follows:
32678 \begin_layout Itemize
32679 Is text inserted between the first and second < or >, resp., it is placed
32681 When it is inserted between the second and third one, it appears under
32685 \begin_layout Itemize
32686 When text for vertical arrows is inserted between the first and second A
32687 or V, resp., it is placed left beside the arrow.
32688 When it is inserted between the second and third one, it appears right
32690 If the text contains an A or V, these letters must be set into a TeX-brace.
32693 \begin_layout Standard
32694 As example a diagram with all possible relations:
32697 \begin_layout Standard
32698 \begin_inset Formula
32700 \begin{CD}A@>j>>B@>>k>C@=F\\
32711 \begin_layout Standard
32712 The command for this is:
32713 \begin_inset Newline newline
32724 \begin_layout Plain Layout
32733 A@>j>>B@>>k>C@=F Ctrl+Return
32734 \begin_inset Newline newline
32738 \begin_inset Phantom HPhantom
32741 \begin_layout Plain Layout
32750 \begin_layout Plain Layout
32769 \begin_inset Formula $\to$
32775 \begin_inset Newline newline
32779 \begin_inset Phantom HPhantom
32782 \begin_layout Plain Layout
32791 \begin_layout Plain Layout
32808 \begin_layout Subsection
32810 \begin_inset Index idx
32813 \begin_layout Plain Layout
32814 Diagrams ! xymatrix
32822 \begin_layout Standard
32823 To be able to use xymatrices, the LaTeX-package
32828 A xymatrix is created by inserting the command
32835 Then you are able to add new matrix columns and rows like for normal matrices,
32837 \begin_inset CommandInset ref
32839 reference "sec:Matrices"
32846 \begin_layout Standard
32847 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
32849 All possibilities to create commutative diagrams and decorations are explained
32854 that you find in the menu
32856 Help\SpecialChar \menuseparator
32858 \begin_inset space ~
32866 \begin_layout Subsection
32872 \begin_inset Index idx
32875 \begin_layout Plain Layout
32884 \begin_layout Standard
32889 -diagrams, the LaTeX-package
32898 -diagram is created by inserting the command
32905 Then you are able to add new matrix columns and rows like for normal matrices,
32907 \begin_inset CommandInset ref
32909 reference "sec:Matrices"
32916 \begin_layout Standard
32917 Examples how to create
32921 diagrams in LyX is given in the
32923 Feynman-diagram manual
32925 that you find in the menu
32927 Help\SpecialChar \menuseparator
32929 \begin_inset space ~
32937 \begin_layout Section
32938 User-defined Commands
32939 \begin_inset Index idx
32942 \begin_layout Plain Layout
32943 User-defined commands
32951 \begin_layout Standard
32952 \begin_inset Note Greyedout
32955 \begin_layout Plain Layout
32960 The names of user-defined commands and macros may only consist of Latin
32969 \begin_layout Subsection
32973 \begin_inset CommandInset label
32975 name "sub:The-Command-newcommand"
32980 \begin_inset Index idx
32983 \begin_layout Plain Layout
32984 User-defined commands !
32992 \begin_inset Index idx
32995 \begin_layout Plain Layout
33006 \begin_layout Standard
33007 Many LaTeX-commands are too long to be used frequently.
33008 But it is possible to define with the command
33014 new shorter commands.
33017 \begin_layout Standard
33018 The command scheme of
33027 \begin_layout Standard
33032 newcommand{new command name}[number of arguments][optional
33037 \begin_inset Newline newline
33041 \begin_inset Phantom HPhantom
33044 \begin_layout Plain Layout
33054 {command definition}
33057 \begin_layout Standard
33058 \begin_inset Note Greyedout
33061 \begin_layout Plain Layout
33066 Assure that the name of the new command is not already used in your document
33067 or by LaTeX-packages that you use.
33068 When you for example define the command
33080 , you get an error message because
33086 is already defined as command for
33087 \begin_inset Quotes eld
33091 \begin_inset Formula $\le$
33095 \begin_inset Quotes erd
33106 \begin_layout Standard
33107 The number of arguments is an integer in the range 0
33108 \begin_inset space \thinspace{}
33112 \begin_inset space \thinspace{}
33115 9 and specifies how many arguments the new command should have.
33116 With the optional value a value for an optional argument can be predefined.
33117 When this is done, the
33125 rgument of the new command is automatically an optional one.
33128 \begin_layout Standard
33129 Here are some examples:
33132 \begin_layout Itemize
33133 To define the command
33145 , the LaTeX-preamble line is:
33146 \begin_inset VSpace medskip
33150 \begin_inset Newline newline
33164 \begin_layout Itemize
33165 To define the command
33177 , the argument (that should be underlined) must be taken into account.
33178 For this the preamble line is:
33179 \begin_inset VSpace medskip
33183 \begin_inset Newline newline
33197 \begin_inset VSpace medskip
33201 \begin_inset Newline newline
33208 acts as argument placeholder, the
33212 behind it denotes that it is the placeholder for the first argument.
33215 \begin_layout Itemize
33223 \begin_inset space \thinspace{}
33227 \begin_inset space \space{}
33237 \begin_inset VSpace medskip
33241 \begin_inset Newline newline
33252 framebox#1#2{$#3$}}
33255 \begin_inset VSpace medskip
33259 \begin_inset Newline newline
33262 The two Dollar signs creates the extra formula needed for
33269 \begin_inset CommandInset ref
33271 reference "sub:Boxes-with-Frame"
33278 \begin_layout Itemize
33279 To create a new command for
33285 where the color for the box needn't to be specified, the argument for the
33286 color is defined optional:
33287 \begin_inset VSpace medskip
33291 \begin_inset Newline newline
33302 fcolorbox{#2}{#1}{$#3$}}
33305 \begin_inset VSpace medskip
33309 \begin_inset Newline newline
33312 When the color is not specified when using
33318 , the predefined color
33325 \begin_layout Standard
33326 A test of the new defined commands:
33329 \begin_layout Standard
33331 \begin_inset Tabular
33332 <lyxtabular version="3" rows="6" columns="2">
33333 <features tabularvalignment="middle">
33334 <column alignment="center" valignment="top" width="0">
33335 <column alignment="center" valignment="top" width="0">
33337 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33340 \begin_layout Plain Layout
33346 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33349 \begin_layout Plain Layout
33351 \begin_inset Note Note
33354 \begin_layout Plain Layout
33361 is only used as spacer.
33373 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33376 \begin_layout Plain Layout
33383 \begin_layout Plain Layout
33397 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33400 \begin_layout Plain Layout
33401 \begin_inset Formula $A\gr B$
33411 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33414 \begin_layout Plain Layout
33422 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33425 \begin_layout Plain Layout
33426 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
33436 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33439 \begin_layout Plain Layout
33443 \begin_inset Formula $\to$
33449 \begin_inset Formula $\to$
33460 \begin_layout Plain Layout
33474 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33477 \begin_layout Plain Layout
33478 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
33488 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33491 \begin_layout Plain Layout
33495 \begin_inset Formula $\to$
33506 \begin_layout Plain Layout
33520 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33523 \begin_layout Plain Layout
33524 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
33534 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33537 \begin_layout Plain Layout
33543 \begin_inset Formula $\to$
33554 \begin_layout Plain Layout
33568 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33571 \begin_layout Plain Layout
33572 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
33588 \begin_layout Subsection
33590 \begin_inset Index idx
33593 \begin_layout Plain Layout
33594 User-defined commands! Math macros
33600 \begin_inset Index idx
33603 \begin_layout Plain Layout
33612 \begin_layout Standard
33613 User-defined commands are especially convenient for complex expressions.
33614 When you are for example dealing in a document with quadratic equations,
33615 the same solution type occurs several times.
33616 The general form of a quadratic equation is
33617 \begin_inset Formula
33619 0=\lambda^{2}+p\lambda+q
33624 The general form of the solution is
33625 \begin_inset Formula
33627 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
33635 \begin_layout Standard
33636 To define a command for the solution formula where only the three parameters
33638 \begin_inset Formula $\lambda$
33642 \begin_inset Formula $p$
33646 \begin_inset Formula $q$
33649 need to be specified and the index of
33650 \begin_inset Formula $\lambda$
33653 can be given optionally, the LaTeX-preamble line is
33654 \begin_inset Newline newline
33670 \begin_inset Newline newline
33674 \begin_inset Phantom HPhantom
33677 \begin_layout Plain Layout
33691 frac{#3^{2}}{4}-#4}}
33694 \begin_layout Standard
33695 To create with this the solution formula, the command
33696 \begin_inset Newline newline
33706 \begin_inset Formula $\to$
33712 \begin_inset Formula $\to$
33719 is inserted to a formula
33724 \begin_layout Standard
33725 The definition of the new command is unintuitive because one has to know
33726 the schemes of all used LaTeX commands, e.
33727 \begin_inset space \thinspace{}
33731 \begin_inset space \space{}
33734 that a fraction is inserted in LaTeX as
33738 frac{numerator}{denominator}
33741 Furthermore one can easily forget a brace in the definition and cannot
33742 see in LyX what the new command is doing.
33743 To avoid these problems LyX offers the possibility to use math macros instead
33753 \begin_layout Standard
33754 A math macro is created by using the menu
33756 Insert\SpecialChar \menuseparator
33757 Math\SpecialChar \menuseparator
33760 or the toolbar button
33761 \begin_inset Graphics
33762 filename ../images/math-macro_newmacroname_newcommand.png
33768 The math macro toolbar appears together with the following box where the
33770 \begin_inset Newline newline
33774 \begin_inset space \hspace*{\fill}
33778 \begin_inset Graphics
33779 filename clipart/macrobox.png
33784 \begin_inset space \hspace*{\fill}
33788 \begin_inset Newline newline
33792 \begin_inset FormulaMacro
33793 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
33798 newmacroname is the default name of the macro that should be changed to
33799 something sensible.
33800 The wanted formula is inserted in the first blue box.
33801 An argument placeholder is inserted with the command
33808 \begin_inset space \thinspace{}
33812 \begin_inset space \space{}
33821 or by using the macro toolbar button
33822 \begin_inset Graphics
33823 filename ../images/math-macro-add-param.png
33829 Argument placeholders are displayed red.
33830 Maximum 9 arguments are possible.
33831 Optional arguments are created with the toolbar button
33832 \begin_inset Graphics
33833 filename ../images/math-macro-add-optional-param.png
33839 The first non-optional argument can be transformed to an optional one with
33841 \begin_inset Graphics
33842 filename ../images/math-macro-make-optional.png
33848 In the second blue box the appearance of the macro in LyX can be defined.
33849 Normally you want to see it as it is defined, so the box is kept empty.
33850 But when you have created a macro that needs lot of space on the screen,
33851 you can insert in the box for example
33852 \begin_inset Newline newline
33882 \begin_inset Newline newline
33887 For the macro only the arguments with the macro name in front of them will
33888 then be displayed in LyX, leading to a better overview.
33889 The formula appears in the output as defined in the first box.
33890 \begin_inset Newline newline
33893 The appearance of macros in formulas can furthermore be changed for single
33894 macros by setting the cursor in the macro and using the menu
33896 View\SpecialChar \menuseparator
33898 \begin_inset space ~
33902 \begin_inset space ~
33910 \begin_layout Standard
33911 To use a macro, the macro name is inserted as command to a formula, in our
33919 Our macro looks in LyX like this:
33920 \begin_inset Newline newline
33924 \begin_inset space \hspace*{\fill}
33928 \begin_inset Graphics
33929 filename clipart/macrouse.png
33934 \begin_inset space \hspace*{\fill}
33938 \begin_inset Newline newline
33941 Here is our macro example with the arguments
33942 \begin_inset Formula $x$
33946 \begin_inset Formula $\ln(x)$
33950 \begin_inset Formula $B$
33956 \begin_layout Standard
33957 \begin_inset Formula
33967 \begin_layout Standard
33968 LyX offers in the menu
33970 Tools\SpecialChar \menuseparator
33971 Preferences\SpecialChar \menuseparator
33972 Editing\SpecialChar \menuseparator
33975 different styles to edit macros.
33976 To find the style that suits you the most, choose a style and set the cursor
33977 in a macro formula to see the difference.
33980 \begin_layout Standard
33981 A math macro is transformed internally to a
33987 command when exporting the document.
33994 command is not placed in the LaTeX-preamble, therefore macros can only
33995 be used in formulas that are in the document below the macro definition
33999 \begin_layout Standard
34000 Math macros can also be directly be created from a
34007 When writing for example the command
34010 \begin_inset Newline newline
34019 xleftarrow[#2]{#1}}
34020 \begin_inset Newline newline
34025 in LyX as normal text, highlighting it completely and using then the shortcut
34030 , the command will be transformed to a math macro.
34031 Using this method you need to be careful that the
34037 command is typed correctly, otherwise you get a faulty macro leading to
34041 \begin_layout Standard
34042 Math macros currently yet have the problem that further formulas in macro
34043 definitions are handled wrongly.
34044 Therefore the example
34051 \begin_inset CommandInset ref
34053 reference "sub:The-Command-newcommand"
34057 cannot be created as macro.
34060 \begin_layout Standard
34061 When the cursor is in a macro definition box, you will see the macro toolbar
34065 \begin_layout Standard
34066 \begin_inset VSpace defskip
34072 \begin_layout Standard
34073 \begin_inset Graphics
34074 filename clipart/MacroToolbar.png
34079 \begin_inset Index idx
34082 \begin_layout Plain Layout
34091 \begin_layout Standard
34092 \begin_inset VSpace defskip
34098 \begin_layout Standard
34099 The macro toolbar contains from left to right the following buttons:
34102 \begin_layout Standard
34103 \begin_inset VSpace defskip
34109 \begin_layout Standard
34110 \begin_inset Tabular
34111 <lyxtabular version="3" rows="9" columns="2">
34112 <features islongtable="true" longtabularalignment="center">
34113 <column alignment="left" valignment="top" width="0">
34114 <column alignment="left" valignment="top" width="85col%">
34115 <row interlinespace="2.5mm">
34116 <cell alignment="center" valignment="top" usebox="none">
34119 \begin_layout Plain Layout
34120 \begin_inset Graphics
34121 filename ../images/math-macro-remove-param.png
34122 rotateOrigin center
34131 <cell alignment="center" valignment="top" usebox="none">
34134 \begin_layout Plain Layout
34137 Edit\SpecialChar \menuseparator
34138 Math\SpecialChar \menuseparator
34140 \begin_inset space ~
34143 Definition\SpecialChar \menuseparator
34144 Remove Last Argument
34150 <row interlinespace="2.5mm">
34151 <cell alignment="center" valignment="top" usebox="none">
34154 \begin_layout Plain Layout
34155 \begin_inset Graphics
34156 filename ../images/math-macro-add-param.png
34157 rotateOrigin center
34166 <cell alignment="center" valignment="top" usebox="none">
34169 \begin_layout Plain Layout
34172 Edit\SpecialChar \menuseparator
34173 Math\SpecialChar \menuseparator
34175 \begin_inset space ~
34178 Definition\SpecialChar \menuseparator
34185 <row interlinespace="2.5mm">
34186 <cell alignment="center" valignment="top" usebox="none">
34189 \begin_layout Plain Layout
34190 \begin_inset Graphics
34191 filename ../images/math-macro-make-optional.png
34192 rotateOrigin center
34201 <cell alignment="center" valignment="top" usebox="none">
34204 \begin_layout Plain Layout
34207 Edit\SpecialChar \menuseparator
34208 Math\SpecialChar \menuseparator
34210 \begin_inset space ~
34213 Definition\SpecialChar \menuseparator
34214 Make First Non-Optional into
34215 \begin_inset Newline newline
34219 \begin_inset Phantom HPhantom
34222 \begin_layout Plain Layout
34225 Edit\SpecialChar \menuseparator
34226 Math\SpecialChar \menuseparator
34228 \begin_inset space ~
34231 Definition\SpecialChar \menuseparator
34243 <row interlinespace="2.5mm">
34244 <cell alignment="center" valignment="top" usebox="none">
34247 \begin_layout Plain Layout
34248 \begin_inset Graphics
34249 filename ../images/math-macro-make-nonoptional.png
34250 rotateOrigin center
34259 <cell alignment="center" valignment="top" usebox="none">
34262 \begin_layout Plain Layout
34265 Edit\SpecialChar \menuseparator
34266 Math\SpecialChar \menuseparator
34268 \begin_inset space ~
34271 Definition\SpecialChar \menuseparator
34272 Make Last Optional into
34273 \begin_inset Newline newline
34277 \begin_inset Phantom HPhantom
34280 \begin_layout Plain Layout
34283 Edit\SpecialChar \menuseparator
34284 Math\SpecialChar \menuseparator
34286 \begin_inset space ~
34289 Definition\SpecialChar \menuseparator
34295 Non-Optional Argument
34301 <row interlinespace="2.5mm">
34302 <cell alignment="center" valignment="top" usebox="none">
34305 \begin_layout Plain Layout
34306 \begin_inset Graphics
34307 filename ../images/math-macro-remove-optional-param.png
34308 rotateOrigin center
34317 <cell alignment="center" valignment="top" usebox="none">
34320 \begin_layout Plain Layout
34323 Edit\SpecialChar \menuseparator
34324 Math\SpecialChar \menuseparator
34326 \begin_inset space ~
34329 Definition\SpecialChar \menuseparator
34330 Remove Optional Argument
34336 <row interlinespace="2.5mm">
34337 <cell alignment="center" valignment="top" usebox="none">
34340 \begin_layout Plain Layout
34341 \begin_inset Graphics
34342 filename ../images/math-macro-add-optional-param.png
34343 rotateOrigin center
34352 <cell alignment="center" valignment="top" usebox="none">
34355 \begin_layout Plain Layout
34358 Edit\SpecialChar \menuseparator
34359 Math\SpecialChar \menuseparator
34361 \begin_inset space ~
34364 Definition\SpecialChar \menuseparator
34365 Insert Optional Argument
34371 <row interlinespace="2.5mm">
34372 <cell alignment="center" valignment="top" usebox="none">
34375 \begin_layout Plain Layout
34376 \begin_inset Graphics
34377 filename ../images/math-macro-remove-greedy-param.png
34378 rotateOrigin center
34387 <cell alignment="center" valignment="top" usebox="none">
34390 \begin_layout Plain Layout
34393 Edit\SpecialChar \menuseparator
34394 Math\SpecialChar \menuseparator
34396 \begin_inset space ~
34399 Definition\SpecialChar \menuseparator
34400 Remove Last Argument
34401 \begin_inset Newline newline
34405 \begin_inset Phantom HPhantom
34408 \begin_layout Plain Layout
34411 Edit\SpecialChar \menuseparator
34412 Math\SpecialChar \menuseparator
34414 \begin_inset space ~
34417 Definition\SpecialChar \menuseparator
34423 Spitting Out To The Right
34429 <row interlinespace="2.5mm">
34430 <cell alignment="center" valignment="top" usebox="none">
34433 \begin_layout Plain Layout
34434 \begin_inset Graphics
34435 filename ../images/math-macro-append-greedy-param.png
34436 rotateOrigin center
34445 <cell alignment="center" valignment="top" usebox="none">
34448 \begin_layout Plain Layout
34451 Edit\SpecialChar \menuseparator
34452 Math\SpecialChar \menuseparator
34454 \begin_inset space ~
34457 Definition\SpecialChar \menuseparator
34459 \begin_inset Newline newline
34463 \begin_inset Phantom HPhantom
34466 \begin_layout Plain Layout
34469 Edit\SpecialChar \menuseparator
34470 Math\SpecialChar \menuseparator
34472 \begin_inset space ~
34475 Definition\SpecialChar \menuseparator
34481 Eating From The Right
34487 <row interlinespace="2.5mm">
34488 <cell alignment="center" valignment="top" usebox="none">
34491 \begin_layout Plain Layout
34492 \begin_inset Graphics
34493 filename ../images/math-macro-add-greedy-optional-param.png
34494 rotateOrigin center
34503 <cell alignment="center" valignment="top" usebox="none">
34506 \begin_layout Plain Layout
34509 Edit\SpecialChar \menuseparator
34510 Math\SpecialChar \menuseparator
34512 \begin_inset space ~
34515 Definition\SpecialChar \menuseparator
34516 Append Optional Argument
34517 \begin_inset Newline newline
34521 \begin_inset Phantom HPhantom
34524 \begin_layout Plain Layout
34527 Edit\SpecialChar \menuseparator
34528 Math\SpecialChar \menuseparator
34530 \begin_inset space ~
34533 Definition\SpecialChar \menuseparator
34539 Eating From The Right
34552 \begin_layout Section
34553 Computer Algebra Systems
34556 \begin_layout Standard
34557 LyX offers the exchange between mathematical expressions written in LyX's
34558 math editor and external applications or user defined scripts.
34559 Currently supported applications are
34576 Note that the set of supported mathematical constructs is limited only
34577 to very simple cases.
34580 \begin_layout Subsection
34584 \begin_layout Standard
34585 Write some expression in a formula, go to the
34587 Edit\SpecialChar \menuseparator
34588 Math\SpecialChar \menuseparator
34589 Use Computer Algebra System
34591 menu and choose the application you have installed on the computer.
34592 After that the result of computation should show on the right side of the
34593 expression together with the
34594 \begin_inset Quotes eld
34598 \begin_inset Quotes erd
34604 \begin_layout Standard
34605 Here are few simple examples (with results from
34609 ) to show what kind of computations can be performed:
34612 \begin_layout Itemize
34613 \begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$
34619 \begin_layout Itemize
34620 \begin_inset Formula $\frac{37.0}{3}=12.33333333333333$
34626 \begin_layout Itemize
34627 \begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$
34633 \begin_layout Itemize
34634 \begin_inset Formula $\det\left[\begin{array}{ccc}
34638 \end{array}\right]=-56$
34644 \begin_layout Itemize
34645 \begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$
34651 \begin_layout Subsection
34655 \begin_layout Standard
34656 Currently there is no keyboard shortcut for calling the algebra applications.
34657 One can easily bind a shortcut to the
34661 LyX function (see the
34669 \begin_inset space \thinspace{}
34673 \begin_inset space ~
34680 key inside the math editor.
34685 one would use this shortcut definition command:
34688 \begin_layout Standard
34691 command-alternatives break-paragraph;math-extern maxima
34694 \begin_layout Standard
34695 \begin_inset Newpage newpage
34701 \begin_layout Section
34703 \begin_inset Index idx
34706 \begin_layout Plain Layout
34715 \begin_layout Subsection
34717 \begin_inset Index idx
34720 \begin_layout Plain Layout
34729 \begin_layout Standard
34730 Negative numbers often look ugly in formulas because the minus sign before
34731 the number is set with the same length as the minus operator sign.
34732 When writing the negative number in normal text, the minus sign appears
34736 \begin_layout Standard
34737 Thus, the problem disappears when converting the minus sign to mathematical
34741 \begin_layout Standard
34742 An example to visualize the problem:
34745 \begin_layout Standard
34747 \begin_inset Tabular
34748 <lyxtabular version="3" rows="3" columns="2">
34749 <features tabularvalignment="middle">
34750 <column alignment="right" valignment="top" width="0">
34751 <column alignment="left" valignment="top" width="0">
34753 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34756 \begin_layout Plain Layout
34762 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
34765 \begin_layout Plain Layout
34773 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34776 \begin_layout Plain Layout
34782 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34785 \begin_layout Plain Layout
34786 \begin_inset Formula $x=-2$
34796 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34799 \begin_layout Plain Layout
34805 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34808 \begin_layout Plain Layout
34809 \begin_inset Formula $x=\textrm{-}2$
34825 \begin_layout Subsection
34826 Comma as decimal Separator
34827 \begin_inset Index idx
34830 \begin_layout Plain Layout
34839 \begin_layout Standard
34840 In LaTeX a comma inside a formula is used, according to the English convention,
34841 as number group separator.
34842 So there will be space added behind all commas in formulas.
34845 \begin_layout Standard
34846 To avoid this, the comma is highlighted and changed to mathematical text
34856 \begin_layout Standard
34857 To use all formula commas in the document as decimal separator, the file
34866 \begin_layout Plain Layout
34871 is part of the LaTeX-package
34876 \begin_inset Index idx
34879 \begin_layout Plain Layout
34884 \begin_layout Plain Layout
34904 \begin_inset Index idx
34907 \begin_layout Plain Layout
34913 is loaded with the LaTeX-preamble line
34916 \begin_layout Standard
34924 \begin_layout Subsection
34926 \begin_inset CommandInset label
34928 name "sub:Physical-Vectors"
34933 \begin_inset Index idx
34936 \begin_layout Plain Layout
34945 \begin_layout Standard
34946 Predefined vectors are offered by the LaTeX-package
34951 \begin_inset Index idx
34954 \begin_layout Plain Layout
34960 that is loaded with the LaTeX-preamble line
34963 \begin_layout Standard
34971 \begin_layout Standard
34975 \begin_layout Plain Layout
34985 \begin_inset Note Note
34988 \begin_layout Plain Layout
34989 The following table will only be displayed when the LaTeX-package
35001 \begin_layout Standard
35002 The following commands are defined:
35005 \begin_layout Standard
35007 \begin_inset Tabular
35008 <lyxtabular version="3" rows="4" columns="2">
35009 <features tabularvalignment="middle">
35010 <column alignment="center" valignment="top" width="0">
35011 <column alignment="center" valignment="top" width="0">
35013 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35016 \begin_layout Plain Layout
35022 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35025 \begin_layout Plain Layout
35033 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35036 \begin_layout Plain Layout
35046 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35049 \begin_layout Plain Layout
35050 \begin_inset Formula $\Bra{\psi}$
35060 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35063 \begin_layout Plain Layout
35073 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35076 \begin_layout Plain Layout
35077 \begin_inset Formula $\Ket{\psi}$
35087 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35090 \begin_layout Plain Layout
35102 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35105 \begin_layout Plain Layout
35106 \begin_inset Formula $\Braket{\psi|\phi}$
35122 \begin_layout Standard
35129 assures that all vertical bars are set in the size of the surrounding brackets:
35130 \begin_inset Formula
35132 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}
35141 \begin_layout Plain Layout
35151 \begin_inset Note Note
35154 \begin_layout Plain Layout
35155 The following will be displayed when the LaTeX-package
35167 \begin_layout Standard
35168 You need to install the LaTeX-package
35172 to see the rest of this subsection in the output.
35175 \begin_layout Standard
35179 \begin_layout Plain Layout
35191 \begin_layout Standard
35198 can also be achieved using the command
35204 , that is described in
35205 \begin_inset CommandInset ref
35207 reference "sub:Automatic-Bracket-Size"
35214 \begin_layout Subsection
35215 Self-defined Fractions
35216 \begin_inset CommandInset label
35218 name "sub:Self-defined-Fractions"
35223 \begin_inset Index idx
35226 \begin_layout Plain Layout
35227 Fractions ! self-defined
35235 \begin_layout Standard
35236 To define custom commands for fractions, the command
35243 \begin_inset Index idx
35246 \begin_layout Plain Layout
35254 is used in the following scheme:
35257 \begin_layout Standard
35270 bracket}{fraction bar thickness}{style}
35271 \begin_inset Newline newline
35275 \begin_inset Phantom HPhantom
35278 \begin_layout Plain Layout
35288 {numerator}{denominator}
35291 \begin_layout Standard
35292 The style is a number in the range of 0
35293 \begin_inset space \thinspace{}
35297 \begin_inset space \thinspace{}
35303 \begin_layout Standard
35305 \begin_inset Tabular
35306 <lyxtabular version="3" rows="5" columns="2">
35307 <features tabularvalignment="middle">
35308 <column alignment="center" valignment="top" width="0">
35309 <column alignment="center" valignment="top" width="0">
35311 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35314 \begin_layout Plain Layout
35320 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35323 \begin_layout Plain Layout
35331 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35334 \begin_layout Plain Layout
35340 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35343 \begin_layout Plain Layout
35344 display style formula
35351 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35354 \begin_layout Plain Layout
35360 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35363 \begin_layout Plain Layout
35371 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35374 \begin_layout Plain Layout
35380 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35383 \begin_layout Plain Layout
35391 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35394 \begin_layout Plain Layout
35400 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35403 \begin_layout Plain Layout
35417 \begin_layout Standard
35418 When no style is given, the size is adjusted to the surrounding environment
35419 like for the command
35428 \begin_layout Standard
35429 When no fraction bar thickness is given, the predefined value of 0.4
35430 \begin_inset space \thinspace{}
35436 \begin_layout Standard
35437 \begin_inset VSpace medskip
35440 For example, the commands
35453 \begin_inset CommandInset ref
35455 reference "sub:Fractions"
35459 are defined with the commands
35462 \begin_layout Standard
35471 genfrac{}{}{}{0}{#1}{#2}}
35474 \begin_layout Standard
35478 \begin_layout Standard
35487 genfrac{(}{)}{0pt}{1}{#1}{#2}}
35490 \begin_layout Standard
35491 \begin_inset VSpace medskip
35494 To define a fraction where the fraction bar thickness can be given as optional
35495 argument, the following line is inserted to the LaTeX-preamble:
35498 \begin_layout Standard
35507 genfrac{}{}{#1}{}{#2}{#3}}
35510 \begin_layout Standard
35512 \begin_inset Formula
35514 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
35515 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
35520 As one can see, the distance of the numerator and the denominator to the
35521 fraction bar is round about three times the bar thickness.
35524 \begin_layout Subsection
35526 \begin_inset Index idx
35529 \begin_layout Plain Layout
35538 \begin_layout Standard
35539 To cancel formulas or formula parts, the LaTeX-package
35544 \begin_inset Index idx
35547 \begin_layout Plain Layout
35553 has to be loaded with the LaTeX-preamble line
35556 \begin_layout Standard
35561 usepackage[samesize]{cancel}
35564 \begin_layout Standard
35568 \begin_layout Plain Layout
35578 \begin_inset Note Note
35581 \begin_layout Plain Layout
35582 The following table will only be displayed when the LaTeX-package
35594 \begin_layout Standard
35595 There are four ways to cancel formulas:
35598 \begin_layout Standard
35600 \begin_inset Tabular
35601 <lyxtabular version="3" rows="5" columns="2">
35602 <features tabularvalignment="middle">
35603 <column alignment="center" valignment="top" width="0">
35604 <column alignment="center" valignment="top" width="0">
35606 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35609 \begin_layout Plain Layout
35615 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35618 \begin_layout Plain Layout
35620 \begin_inset Note Note
35623 \begin_layout Plain Layout
35630 are used here as spacer.
35642 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35645 \begin_layout Plain Layout
35654 \begin_layout Plain Layout
35668 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35671 \begin_layout Plain Layout
35672 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
35682 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35685 \begin_layout Plain Layout
35694 \begin_layout Plain Layout
35708 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35711 \begin_layout Plain Layout
35712 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
35722 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35725 \begin_layout Plain Layout
35734 \begin_layout Plain Layout
35748 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35751 \begin_layout Plain Layout
35752 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
35762 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35765 \begin_layout Plain Layout
35769 \begin_inset Formula $\to$
35780 \begin_layout Plain Layout
35794 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35797 \begin_layout Plain Layout
35798 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
35814 \begin_layout Standard
35821 is especially suitable to visualize the reduction of fractions within formulas:
35822 \begin_inset Formula
35824 \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}}}
35832 \begin_layout Standard
35836 \begin_layout Plain Layout
35846 \begin_inset Note Note
35849 \begin_layout Plain Layout
35850 The following will be displayed when the LaTeX-package
35862 \begin_layout Standard
35863 You need to install the LaTeX-package
35867 to see the rest of this subsection in the output.
35870 \begin_layout Standard
35874 \begin_layout Plain Layout
35886 \begin_layout Subsection
35887 Formulas in Section Headings
35888 \begin_inset CommandInset label
35890 name "sub:Formulas-in-Section"
35895 \begin_inset Index idx
35898 \begin_layout Plain Layout
35899 Formula ! in section headings
35907 \begin_layout Standard
35908 When formulas are used in section headings, the following has to be taken
35912 \begin_layout Standard
35913 \begin_inset Note Greyedout
35916 \begin_layout Plain Layout
35922 \begin_inset Index idx
35925 \begin_layout Plain Layout
35926 Packages ! hyperref
35931 support is enabled in the document settings dialog under
35934 \begin_inset space ~
35939 , PDF-bookmarks are created for every section heading in the table of contents.
35940 If a section heading contains formulas, they are incorrectly displayed
35941 in the bookmark text, because formulas in bookmarks infringe the PDF convention
35950 \begin_layout Standard
35951 Both problems can be solved by inserting at the end of the section heading
35952 a short title with the menu
35954 Insert\SpecialChar \menuseparator
35956 \begin_inset space ~
35962 Short titles are used as alternative for multiline section headings to
35963 keep the table of contents clearly arranged.
35964 Only the short title appears in the table of contents and therefore also
35965 in the PDF-bookmark.
35968 \begin_layout Standard
35969 When formulas should be used in the table of contents but
35973 is used, one can use the following command in TeX-mode:
35976 \begin_layout Standard
35981 texorpdfstring{part}{alternative}
35982 \begin_inset Index idx
35985 \begin_layout Plain Layout
35996 \begin_layout Standard
35997 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
35998 This can be characters, formulas, footnotes, but also cross-references.
35999 The alternative is used instead of the part for the bookmark.
36002 \begin_layout Standard
36003 Here are two example headings:
36004 \begin_inset VSpace -3mm
36011 \begin_layout Plain Layout
36023 \begin_layout Subsubsection
36024 Heading without formula in table of contents
36025 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
36029 \begin_inset Argument
36032 \begin_layout Plain Layout
36033 Heading without formula in table of contents
36041 \begin_layout Subsubsection
36042 Heading with formula in table of contents
36046 \begin_layout Plain Layout
36056 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
36063 \begin_layout Plain Layout
36073 \begin_layout Standard
36077 \begin_layout Plain Layout
36086 In the first heading a short title was used, in the second one
36095 \begin_layout Standard
36096 To get the same formatting as for the other headings, the complete heading
36105 \begin_layout Plain Layout
36107 \begin_inset CommandInset ref
36109 reference "sub:Bold-Formulas"
36121 \begin_layout Subsection
36122 Formulas in multi-column Text
36123 \begin_inset Index idx
36126 \begin_layout Plain Layout
36127 Formula ! in multi-column text
36135 \begin_layout Standard
36136 Formulas in multi-column text are often too wide to fit into a column and
36137 thus need to be set over the whole page width.
36138 This is done by using the LaTeX-package
36146 \begin_layout Plain Layout
36151 is part of every LaTeX standard installation.
36157 \begin_inset Index idx
36160 \begin_layout Plain Layout
36161 Packages ! multicol
36166 , that is loaded with the LaTeX-preamble line
36169 \begin_layout Standard
36174 usepackage{multicol}
36177 \begin_layout Standard
36178 \begin_inset Note Greyedout
36181 \begin_layout Plain Layout
36182 Note herby that the setting
36185 \begin_inset space ~
36192 Document\SpecialChar \menuseparator
36198 \begin_inset space ~
36218 \begin_layout Standard
36219 Before the multi-column text the command
36222 \begin_layout Standard
36227 begin{multicols}{column number}
36230 \begin_layout Standard
36231 is written in TeX-mode.
36232 The column number is a number in the range of 2
36233 \begin_inset space \thinspace{}
36237 \begin_inset space \thinspace{}
36241 Before the formula the multi-column text is ended by inserting the command
36244 \begin_layout Standard
36252 \begin_layout Standard
36256 \begin_layout Standard
36257 Due to the command some space is automatically added before the formula.
36259 \begin_inset space \thinspace{}
36262 mm vertical space is inserted before the formula.
36263 When the formula style
36269 \begin_layout Plain Layout
36271 \begin_inset CommandInset ref
36273 reference "sec:Formula-Styles"
36285 \begin_inset space \thinspace{}
36288 mm space is inserted instead.
36291 \begin_layout Standard
36292 As example a multi-column text with a displayed formula:
36295 \begin_layout Standard
36301 \begin_layout Plain Layout
36305 begin{multicols}{2}
36310 Das Spektrum wird fouriertransformiert.
36311 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
36312 , Lösungsmittel) zu trennen.
36313 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
36314 nun das Aussehen des Ausgangssignals.
36315 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
36316 über alle Phasen integrieren muss.
36318 \begin_inset Formula $S$
36321 unser normiertes Ausgangssignal und
36322 \begin_inset Formula $P$
36325 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
36329 \begin_layout Plain Layout
36339 \begin_inset VSpace -6mm
36343 \begin_inset Formula
36345 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
36354 \begin_layout Plain Layout
36358 begin{multicols}{2}
36364 \begin_inset Formula $S_{0}$
36367 das Signal ohne Gradient ist und die Normierungsbedingung
36368 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
36372 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
36374 \begin_inset Formula $\nicefrac{\pi}{2}$
36378 \begin_inset space \thinspace{}
36381 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
36382 das Signal zusätzlich abschwächt.
36383 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
36385 \begin_inset Formula $T_{2}$
36391 \begin_layout Standard
36397 \begin_layout Plain Layout
36409 \begin_layout Subsection
36410 Formulas with Description of Variables
36411 \begin_inset Index idx
36414 \begin_layout Plain Layout
36415 Formula ! with description of variables
36423 \begin_layout Standard
36424 To describe variables within a formula, like in formula
36425 \begin_inset CommandInset ref
36427 reference "eq:within"
36436 \begin_inset Formula $n$
36440 \begin_inset space ~
36443 matrix is used with left aligned columns for the
36444 \begin_inset Formula $n$
36451 \begin_layout Plain Layout
36453 \begin_inset CommandInset ref
36455 reference "sec:Matrices"
36464 To set the description in a smaller size, before the matrix e.
36465 \begin_inset space \thinspace{}
36469 \begin_inset space \space{}
36482 \begin_layout Plain Layout
36484 \begin_inset CommandInset ref
36486 reference "sub:Font-Sizes"
36498 \begin_layout Standard
36499 When the formula style
36505 \begin_layout Plain Layout
36507 \begin_inset CommandInset ref
36509 reference "sec:Formula-Styles"
36530 \begin_layout Plain Layout
36537 only works in formulas with the style
36542 \begin_inset CommandInset ref
36544 reference "sub:Variable-Space"
36553 is inserted before and after the matrix to have the same separation of
36554 the matrix from the equation and the side margin.
36557 \begin_layout Standard
36558 When the formula style
36562 is used, the method described in
36563 \begin_inset CommandInset ref
36565 reference "sub:Flalign-Environment"
36569 is used to indent formulas.
36571 \begin_inset CommandInset ref
36573 reference "eq:within"
36577 consists of five columns whereas in the first two columns contain the equation,
36578 the third the matrix and the last one an empty TeX-brace.
36579 \begin_inset Formula
36581 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
36582 \rho & \textrm{density}\\
36583 V & \textrm{volume}\\
36584 g & \textrm{gravitational acceleration}
36585 \end{array} & & {}\label{eq:within}
36593 \begin_layout Subsection
36594 Upright small Greek Letters
36595 \begin_inset CommandInset label
36597 name "sub:Upright-small-Greek"
36602 \begin_inset Index idx
36605 \begin_layout Plain Layout
36606 Greek letters ! upright
36614 \begin_layout Standard
36615 Most of the math fonts only provide italic small Greek letters.
36616 But for symbols of elementary particles like pions and neutrinos, upright
36617 Greek letters are needed.
36626 \begin_layout Plain Layout
36631 is part of the LaTeX-package
36636 \begin_inset Index idx
36639 \begin_layout Plain Layout
36644 \begin_layout Plain Layout
36664 \begin_inset Index idx
36667 \begin_layout Plain Layout
36673 that is loaded with the LaTeX-preamble line
36676 \begin_layout Standard
36681 usepackage{upgreek}
36684 \begin_layout Standard
36690 \begin_layout Plain Layout
36700 \begin_inset Note Note
36703 \begin_layout Plain Layout
36704 The following table will only be displayed when the LaTeX-package
36713 They are created when the command for a small Greek letters is started
36719 For example the command
36726 \begin_inset Formula $\uptau$
36732 \begin_layout Standard
36733 With these commands reactions of elementary particles can be typeset:
36734 \begin_inset Formula
36736 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
36744 \begin_layout Standard
36745 The upright letters are more bold and wider than the italic ones.
36746 They should therefore not be used for units like
36747 \begin_inset Quotes eld
36751 \begin_inset Quotes erd
36757 \begin_layout Standard
36761 \begin_layout Plain Layout
36771 \begin_inset Note Note
36774 \begin_layout Plain Layout
36775 The following will be displayed when the LaTeX-package
36787 \begin_layout Standard
36788 You need to install the LaTeX-package
36792 to see the rest of this subsection in the output.
36795 \begin_layout Standard
36799 \begin_layout Plain Layout
36811 \begin_layout Subsection
36812 Text Characters in Formulas
36813 \begin_inset CommandInset label
36815 name "sub:Text-Characters-in"
36820 \begin_inset Index idx
36823 \begin_layout Plain Layout
36832 \begin_layout Standard
36833 In some cases you might want to insert text characters directly into formulas.
36834 When for example the centered dot · is often used in formulas like
36835 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
36838 , one would have to insert the command
36848 \begin_layout Plain Layout
36850 \begin_inset CommandInset ref
36852 reference "sub:Binary-Operators"
36861 all the time, because this character is defined in all encodings as text
36863 But the encoding can be changed by this LaTeX-preamble line:
36866 \begin_layout Standard
36871 Declare Inputtext{183}{
36881 f\SpecialChar \textcompwordmark{}
36885 \begin_layout Standard
36886 The character encoding (menu
36888 Document\SpecialChar \menuseparator
36889 Settings\SpecialChar \menuseparator
36892 ) specifies what character appears when a keyboard key is pressed.
36893 When the key for the character '·' is pressed, internally the command
36900 But this command is not available in a formula so that you would get LaTeX-erro
36902 With the changed encoding the right command is chosen automatically, depending
36903 on if the character was inserted into a formula or not.
36906 \begin_layout Standard
36907 The encoding of several characters is saved in definition files.
36908 Fore example the encoding
36912 is defined in the file
36916 that is in the installation folder of LaTeX.
36917 Encodings should only be changed via the LaTeX-preamble and not in the
36919 Otherwise own documents could not be edited by other LyX users working
36920 on other computers.
36923 \begin_layout Standard
36924 \begin_inset VSpace medskip
36927 Besides the centered dot, in this document the degree sign ° is defined
36928 with the following LaTeX-preamble line so that it can directly be inserted
36932 \begin_layout Standard
36937 DeclareInputtext{176}{
36947 f\SpecialChar \textcompwordmark{}
36951 \begin_layout Standard
36952 \begin_inset Newpage newpage
36958 \begin_layout Section
36961 \begin_inset Index idx
36964 \begin_layout Plain Layout
36973 \begin_layout Standard
36974 This section is a summary of the most important typographic rules, listed
36979 \begin_layout Plain Layout
36980 This collection was partly taken from the German semi-official dictionary
36982 \begin_inset Quotes eld
36986 \begin_inset Quotes erd
36990 \begin_inset CommandInset citation
36996 that lists some of the ISO rules.
36997 More rules are listed in
36998 \begin_inset CommandInset citation
37012 \begin_layout Itemize
37021 \begin_layout Plain Layout
37022 done with font styles, see
37023 \begin_inset CommandInset ref
37025 reference "sub:Font-Styles"
37034 , no matter if they appear in italic text: 30
37035 \begin_inset space \thinspace{}
37039 \begin_inset Newline newline
37042 Between the value and the unit is the smallest space, see
37043 \begin_inset CommandInset ref
37045 reference "sub:Predefined-Space"
37050 \begin_inset Newline newline
37053 This convention is automatically fulfilled when the command
37060 When it is entered to a formula, two boxes appear.
37061 In the first one the value is inserted, in the second one the unit, and
37063 \begin_inset Formula $\unit[30]{km/h}$
37067 \begin_inset space \thinspace{}
37077 is not a real LaTeX command but the command
37083 , therefore you cannot use it in TeX code.
37086 \begin_layout Itemize
37087 Percent and perthousand signs are set like physical units:
37088 \begin_inset Newline newline
37092 \begin_inset space \thinspace{}
37098 \begin_layout Itemize
37099 The degree sign follows directly on the value: 15°, but not when it is used
37101 \begin_inset space \thinspace{}
37107 \begin_layout Itemize
37108 In numbers with more than four digits the smallest space is inserted before
37109 every third digit to group them:
37119 \begin_inset space \thinspace{}
37123 \begin_inset space \thinspace{}
37129 \begin_layout Itemize
37130 For dimensions like 120×90×40
37131 \begin_inset space \thinspace{}
37134 cm the multiplication sign
37135 \begin_inset Quotes eld
37139 \begin_inset Quotes erd
37143 It is available either via the command
37151 Insert\SpecialChar \menuseparator
37152 Special Character\SpecialChar \menuseparator
37158 \begin_layout Itemize
37159 Functions with names consisting of several letters are set upright to avoid
37161 \begin_inset CommandInset ref
37163 reference "sub:Predefined-Functions"
37170 \begin_layout Itemize
37171 Indices consisting of several letters, are set upright:
37172 \begin_inset Formula $E_{\mathrm{kin}}$
37176 \begin_inset Newline newline
37179 Components of matrices are set italic:
37180 \begin_inset Formula $\hat{H}_{kl}$
37186 \begin_layout Itemize
37187 The differentiation/integration operator 'd', the Euler's number 'e' and
37188 the imaginary unit 'i' should be set upright, to avoid mixing them up with
37192 \begin_layout Itemize
37193 The character that denotes a
37197 transformation is inserted either by the command
37205 \begin_layout Plain Layout
37218 Insert\SpecialChar \menuseparator
37219 Special Character\SpecialChar \menuseparator
37220 Symbols\SpecialChar \menuseparator
37222 \begin_inset space ~
37228 \begin_inset Formula $\mathscr{F}$
37234 \begin_layout Standard
37235 \begin_inset Newpage newpage
37241 \begin_layout Section
37243 \begin_inset Index idx
37246 \begin_layout Plain Layout
37255 \begin_layout Standard
37256 Some characters and symbols can be created with several commands.
37257 Here is a list of the synonym commands:
37260 \begin_layout Standard
37261 \begin_inset VSpace bigskip
37265 \begin_inset space \hfill{}
37269 \begin_inset Tabular
37270 <lyxtabular version="3" rows="12" columns="2">
37271 <features tabularvalignment="middle">
37272 <column alignment="center" valignment="top" width="0pt">
37273 <column alignment="center" valignment="top" width="0pt">
37275 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37278 \begin_layout Plain Layout
37284 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37287 \begin_layout Plain Layout
37289 \begin_inset Note Note
37292 \begin_layout Plain Layout
37299 is only used as spacer.
37311 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37314 \begin_layout Plain Layout
37322 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37325 \begin_layout Plain Layout
37329 \begin_layout Plain Layout
37342 \begin_layout Plain Layout
37356 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37359 \begin_layout Plain Layout
37367 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37370 \begin_layout Plain Layout
37380 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37383 \begin_layout Plain Layout
37391 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37394 \begin_layout Plain Layout
37404 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37407 \begin_layout Plain Layout
37415 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37418 \begin_layout Plain Layout
37426 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37429 \begin_layout Plain Layout
37437 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37440 \begin_layout Plain Layout
37448 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37451 \begin_layout Plain Layout
37459 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37462 \begin_layout Plain Layout
37472 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37475 \begin_layout Plain Layout
37483 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37486 \begin_layout Plain Layout
37496 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37499 \begin_layout Plain Layout
37507 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37510 \begin_layout Plain Layout
37520 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37523 \begin_layout Plain Layout
37531 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37534 \begin_layout Plain Layout
37544 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37547 \begin_layout Plain Layout
37555 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37558 \begin_layout Plain Layout
37566 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37569 \begin_layout Plain Layout
37577 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37580 \begin_layout Plain Layout
37592 \begin_inset space \hfill{}
37596 \begin_inset Tabular
37597 <lyxtabular version="3" rows="12" columns="2">
37598 <features tabularvalignment="middle">
37599 <column alignment="center" valignment="top" width="0pt">
37600 <column alignment="center" valignment="top" width="0pt">
37602 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37605 \begin_layout Plain Layout
37611 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37614 \begin_layout Plain Layout
37622 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37625 \begin_layout Plain Layout
37633 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37636 \begin_layout Plain Layout
37648 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37651 \begin_layout Plain Layout
37659 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37662 \begin_layout Plain Layout
37672 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37675 \begin_layout Plain Layout
37683 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37686 \begin_layout Plain Layout
37696 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37699 \begin_layout Plain Layout
37707 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37710 \begin_layout Plain Layout
37718 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37721 \begin_layout Plain Layout
37729 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37732 \begin_layout Plain Layout
37740 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37743 \begin_layout Plain Layout
37751 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37754 \begin_layout Plain Layout
37764 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37767 \begin_layout Plain Layout
37775 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37778 \begin_layout Plain Layout
37788 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37791 \begin_layout Plain Layout
37799 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37802 \begin_layout Plain Layout
37812 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37815 \begin_layout Plain Layout
37823 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37826 \begin_layout Plain Layout
37836 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37839 \begin_layout Plain Layout
37847 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37850 \begin_layout Plain Layout
37860 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37863 \begin_layout Plain Layout
37871 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37874 \begin_layout Plain Layout
37888 \begin_inset space \hfill{}
37894 \begin_layout Standard
37895 \begin_inset Newpage newpage
37901 \begin_layout Bibliography
37902 \labelwidthstring References
37903 \begin_inset CommandInset bibitem
37904 LatexCommand bibitem
37916 The LaTeX Companion
37919 Addison Wesley, 2004
37922 \begin_layout Bibliography
37923 \labelwidthstring References
37924 \begin_inset CommandInset bibitem
37925 LatexCommand bibitem
37931 \begin_inset CommandInset href
37934 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
37938 of LaTeX's math abilities
37941 \begin_layout Bibliography
37942 \labelwidthstring References
37943 \begin_inset CommandInset bibitem
37944 LatexCommand bibitem
37950 \begin_inset CommandInset href
37953 target "ftp://ftp.ams.org/pub/tex/doc/amsmath/amsldoc.pdf"
37961 \begin_layout Plain Layout
37973 \begin_layout Bibliography
37974 \labelwidthstring References
37975 \begin_inset CommandInset bibitem
37976 LatexCommand bibitem
37982 \begin_inset CommandInset href
37985 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
37989 of all symbols available with LaTeX-packages
37992 \begin_layout Bibliography
37993 \labelwidthstring References
37994 \begin_inset CommandInset bibitem
37995 LatexCommand bibitem
38001 \begin_inset CommandInset href
38003 name "Documentation"
38004 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
38008 of the LaTeX-package
38013 \begin_inset Index idx
38016 \begin_layout Plain Layout
38017 Packages ! hyperref
38025 \begin_layout Bibliography
38026 \labelwidthstring References
38027 \begin_inset CommandInset bibitem
38028 LatexCommand bibitem
38034 \begin_inset CommandInset href
38036 name "Documentation"
38037 target "http://www.ctan.org/tex-archive/macros/latex/contrib/mhchem/mhchem.pdf"
38041 of the LaTeX-package
38046 \begin_inset Index idx
38049 \begin_layout Plain Layout
38058 \begin_layout Bibliography
38059 \labelwidthstring References
38060 \begin_inset CommandInset bibitem
38061 LatexCommand bibitem
38067 \begin_inset CommandInset href
38070 target "http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf"
38081 \begin_inset CommandInset ref
38083 reference "sub:Operator-Limits"
38088 \begin_inset Index idx
38091 \begin_layout Plain Layout
38102 \begin_layout Bibliography
38103 \labelwidthstring References
38104 \begin_inset CommandInset bibitem
38105 LatexCommand bibitem
38116 Auflage, Duden 2001
38119 \begin_layout Bibliography
38120 \labelwidthstring References
38121 \begin_inset CommandInset bibitem
38122 LatexCommand bibitem
38128 \begin_inset CommandInset href
38131 target "http://physics.nist.gov/Document/checklist.pdf"
38135 for reviewing manuscripts
38138 \begin_layout Standard
38139 \begin_inset CommandInset index_print
38140 LatexCommand printindex