1 #LyX 2.0.0svn created this file. For more info see http://www.lyx.org/
7 % DO NOT ALTER THIS PREAMBLE!!!
9 % This preamble is designed to ensure that the file prints
10 % out as advertised. If you mess with this preamble,
11 % parts of this document may not print out as expected. If you
12 % have problems LaTeXing this file, please contact
13 % the documentation team
14 % email: lyx-docs@lists.lyx.org
20 % set fonts for nicer pdf view
21 \IfFileExists{lmodern.sty}
22 {\usepackage{lmodern}}{}
24 \fi % end if pdflatex is used
26 % Folgendes Problem lösen:
27 % Besteht die Kapitelnummer aus zu vielen Ziffern, wird die
28 % Kapitelüberschrift im Inhaltsverzeichnis direkt an oder über
29 % die Kapitelnummer geschrieben.
30 % Als Lösung wird mehr Platz zwischen Nummer und
31 % Überschrift eingefügt.
32 \renewcommand{\l@subsection}{\@dottedtocline{2}{1.5em}{2.8em}}
33 \renewcommand{\l@subsubsection}{\@dottedtocline{3}{4.3em}{3.6em}}
35 % To be able to enter the character ° and · directly in LyX,
37 \DeclareInputText{176}{\ifmmode^\circ\else\textdegree\fi}
38 \DeclareInputText{183}{\ifmmode\cdot\else\textperiodcentered\fi}
40 % increase link area for cross-references and autoname them,
41 \AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}}
43 \settowidth{\abc}{\space}
45 \renewcommand{\equationautorefname}{\hspace{-\abc}}
46 \renewcommand{\sectionautorefname}{sec.\negthinspace}
47 \renewcommand{\subsectionautorefname}{sec.\negthinspace}
48 \renewcommand{\subsubsectionautorefname}{sec.\negthinspace}}
50 % don't load packages twice
51 % see first footnote in sec. 9.3
52 \@ifundefined{textcolor}{\usepackage{color}}{}
54 % the pages of the TOC are numbered roman
55 % and a PDF-bookmark for the TOC is added
57 \let\myTOC\tableofcontents
58 \renewcommand{\tableofcontents}{%
60 \pdfbookmark[1]{\contentsname}{}
63 \pagenumbering{arabic}}
65 % insert additional vertical space of 1.5 mm between footnotes,
67 \renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
69 % provides caption formatting
70 \setkomafont{captionlabel}{\bfseries}
73 \usepackage[samesize]{cancel}
75 % enables calculation of values,
78 % for multiple table row and column cells
85 % for the Fourier transformation symbol
88 % center multirows (e.g. in sec. 13.3)
89 \renewcommand{\multirowsetup}{\centering}
91 % define a color, used in sec.9.3
92 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
94 % declare operators (see sec. 10.4 and sec. 15.2)
95 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
96 \DeclareMathOperator{\sgn}{sgn}
98 \newcommand{\spce}{\textvisiblespace}
100 % example definitions for sec. 20.1
101 \newcommand{\gr}{\Longrightarrow}
102 \newcommand{\us}[1]{\underline{#1}}
103 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
104 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
105 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
107 % example macro from sec. 19.4
108 %\def\tagform@#1{\maketag@@@{|#1|}}
110 % macro from sec. 10.2
111 \def\clap#1{\hbox to 0pt{\hss #1\hss}}
112 \def\mathclap {\mathpalette \mathclapinternal}
113 \def\mathclapinternal #1#2{\clap{$\mathsurround =0pt #1{#2}$}}
116 % ------------------------------------
117 % used to check for needed LaTeX packages
120 % check for package eurosym
121 % used for the Euro symbol
123 \IfFileExists{eurosym.sty}
124 {\usepackage[gennarrow]{eurosym}
125 \setboolean{eurosym}{true}}
126 {\setboolean{eurosym}{false}}
128 % check for package braket
129 % used for physical vectors
131 \IfFileExists{braket.sty}
133 \setboolean{braket}{true}}
134 {\setboolean{braket}{false}}
136 % check for package cancel
138 \IfFileExists{cancel.sty}
140 \setboolean{cancel}{true}}
141 {\setboolean{cancel}{false}}
143 % check for package upgreek
145 \IfFileExists{upgreek.sty}
146 {\usepackage{upgreek}
147 \setboolean{upgreek}{true}}
148 {\setboolean{upgreek}{false}}
150 \options bibliography=totoc,index=totoc,BCOR7.5mm,titlepage,captions=tableheading
151 \use_default_options false
152 \maintain_unincluded_children false
158 \font_typewriter default
159 \font_default_family default
167 \default_output_format default
169 \bibtex_command default
170 \index_command default
174 \pdf_title "LyX's Math Manual"
175 \pdf_author "LyX Team, Uwe Stöhr"
176 \pdf_subject "LyX-documentation about math"
177 \pdf_keywords "LyX, Mathed"
179 \pdf_bookmarksnumbered true
180 \pdf_bookmarksopen true
181 \pdf_bookmarksopenlevel 1
182 \pdf_breaklinks false
186 \pdf_pdfusetitle false
187 \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false"
197 \paperorientation portrait
200 \notefontcolor #0000ff
207 \paragraph_separation skip
209 \quotes_language english
212 \paperpagestyle plain
216 \tracking_changes false
217 \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 \begin{align*}
2077 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
2078 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}
2086 \begin_layout Standard
2087 The command for the example above is:
2090 \begin_layout Standard
2099 \begin_layout Plain Layout
2109 \begin_inset Formula $\downarrow$
2118 \begin_layout Plain Layout
2133 \begin_layout Plain Layout
2143 \begin_inset Formula $\downarrow$
2147 \begin_inset Formula $\downarrow$
2153 \begin_layout Standard
2154 \begin_inset VSpace medskip
2160 \begin_layout Standard
2167 sets the fraction always in the size of a displayed formula, also when
2168 it is part of another fraction.
2171 \begin_layout Standard
2172 It is possible to specify the alignment of the numerator.
2179 is used to left align it, the command
2192 centers the numerator.
2193 These fractions demonstrate the different alignments:
2196 \begin_layout Standard
2197 \begin_inset Formula $\cfrac[l]{A}{B+C}$
2201 \begin_inset Formula $\cfrac{A}{B+C}$
2205 \begin_inset Formula $\cfrac[r]{A}{B+C}$
2211 \begin_layout Standard
2212 \begin_inset Note Greyedout
2215 \begin_layout Plain Layout
2232 are no real LaTeX commands but represent the command
2236 cfrac[alignment]{numerator}{denominator}
2239 Therefore you cannot use them in TeX code.
2247 \begin_layout Standard
2248 \begin_inset VSpace medskip
2251 It is often advantageous to combine
2264 \begin_inset Formula \[
2265 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}\]
2272 \begin_layout Standard
2273 For inline fractions with a sloped fraction stroke you can use the command
2281 \begin_inset Index idx
2284 \begin_layout Plain Layout
2293 \begin_inset Formula $\nicefrac{5}{31}$
2303 \begin_inset Index idx
2306 \begin_layout Plain Layout
2315 \begin_inset Formula $\unitfrac{5}{31}$
2318 There is furthermore the command
2324 that offers to write a fraction in combination with a number:
2325 \begin_inset Formula $\unitfrac[2]{1}{3}$
2331 \begin_layout Standard
2332 \begin_inset Note Greyedout
2335 \begin_layout Plain Layout
2346 is not a real LaTeX command but the command
2347 \begin_inset Newline newline
2354 unitfrac[number]{numerator}{denominator}
2357 Therefore you cannot use it in TeX code.
2365 \begin_layout Standard
2366 How to define own fractions where the fraction stroke can be changed, is
2368 \begin_inset CommandInset ref
2370 reference "sub:Self-defined-Fractions"
2377 \begin_layout Subsection
2379 \begin_inset Index idx
2382 \begin_layout Plain Layout
2391 \begin_layout Standard
2392 Square roots are created with
2399 \begin_inset Index idx
2402 \begin_layout Plain Layout
2410 or the math toolbar button
2411 \begin_inset Graphics
2412 filename ../images/math/sqrt.png
2417 , all other roots with the command
2424 \begin_inset Index idx
2427 \begin_layout Plain Layout
2435 or with the math toolbar button
2436 \begin_inset Graphics
2437 filename ../images/math/root.png
2445 \begin_layout Standard
2447 \begin_inset Tabular
2448 <lyxtabular version="3" rows="3" columns="2">
2449 <features tabularvalignment="middle">
2450 <column alignment="center" valignment="top" width="0pt">
2451 <column alignment="center" valignment="top" width="0pt">
2453 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2456 \begin_layout Plain Layout
2462 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2465 \begin_layout Plain Layout
2467 \begin_inset Note Note
2470 \begin_layout Plain Layout
2477 is only used as spacer.
2489 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2492 \begin_layout Plain Layout
2499 \begin_layout Plain Layout
2513 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2516 \begin_layout Plain Layout
2517 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$
2527 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
2530 \begin_layout Plain Layout
2537 \begin_layout Plain Layout
2547 \begin_inset Formula $\downarrow$
2555 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
2558 \begin_layout Plain Layout
2559 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$
2575 \begin_layout Standard
2576 A square root can also be created with
2582 when the root index field is left empty.
2585 \begin_layout Standard
2586 With certain indices the distance to the root is too small, like in this
2588 \begin_inset Formula $\sqrt[\beta]{B}$
2592 \begin_inset Newline newline
2596 \begin_inset Formula $\beta$
2600 To avoid this, the commands
2607 \begin_inset Index idx
2610 \begin_layout Plain Layout
2625 \begin_inset Index idx
2628 \begin_layout Plain Layout
2636 are used with the following scheme:
2639 \begin_layout Standard
2653 \begin_layout Standard
2654 Distance is the number of Big Points (unit bp;
2655 \begin_inset Formula $\mathrm{72\, bp=1\, inch}$
2658 ), that the index should be moved to the left or top, resp..
2659 The commands are written to the index.
2660 This way the command
2661 \begin_inset Newline newline
2671 \begin_inset Formula $\to$
2677 \begin_inset Formula $\to$
2686 \begin_layout Plain Layout
2696 \begin_inset Formula $\to$
2700 \begin_inset Newline newline
2705 produces a correct typeset formula:
2706 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2712 \begin_layout Subsection
2713 Binomial Coefficients
2714 \begin_inset Index idx
2717 \begin_layout Plain Layout
2718 Binomial coefficients
2726 \begin_layout Standard
2727 Binomial coefficients are inserted with the command
2734 \begin_inset Index idx
2737 \begin_layout Plain Layout
2745 or with the submenu of the math toolbar button
2746 \begin_inset Graphics
2747 filename ../images/math/frac-square.png
2753 Analog to fractions (
2772 \begin_inset Index idx
2775 \begin_layout Plain Layout
2790 \begin_inset Index idx
2793 \begin_layout Plain Layout
2802 For other brackets around binomial coeficients there are the commands
2809 \begin_inset Index idx
2812 \begin_layout Plain Layout
2827 \begin_inset Index idx
2830 \begin_layout Plain Layout
2841 \begin_layout Standard
2843 \begin_inset Tabular
2844 <lyxtabular version="3" rows="6" columns="2">
2845 <features tabularvalignment="middle">
2846 <column alignment="center" valignment="top" width="0pt">
2847 <column alignment="center" valignment="top" width="0pt">
2849 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2852 \begin_layout Plain Layout
2858 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2861 \begin_layout Plain Layout
2863 \begin_inset Note Note
2866 \begin_layout Plain Layout
2873 is only used as spacer.
2885 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2888 \begin_layout Plain Layout
2895 \begin_layout Plain Layout
2905 \begin_inset Formula $\downarrow$
2913 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2916 \begin_layout Plain Layout
2917 \begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$
2927 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2930 \begin_layout Plain Layout
2937 \begin_layout Plain Layout
2947 \begin_inset Formula $\downarrow$
2955 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2958 \begin_layout Plain Layout
2959 \begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$
2969 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2972 \begin_layout Plain Layout
2979 \begin_layout Plain Layout
2989 \begin_inset Formula $\downarrow$
2997 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3000 \begin_layout Plain Layout
3001 \begin_inset Formula $\raisebox{5mm}{}\tbinom{A}{B}\raisebox{-2.5mm}{}$
3011 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3014 \begin_layout Plain Layout
3021 \begin_layout Plain Layout
3031 \begin_inset Formula $\downarrow$
3039 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3042 \begin_layout Plain Layout
3043 \begin_inset Formula $\raisebox{5mm}{}{A \brack B}\raisebox{-2.5mm}{}$
3053 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3056 \begin_layout Plain Layout
3063 \begin_layout Plain Layout
3073 \begin_inset Formula $\downarrow$
3081 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3084 \begin_layout Plain Layout
3085 \begin_inset Formula $\raisebox{5mm}{}{A \brace B}\raisebox{-2.5mm}{}$
3101 \begin_layout Subsection
3102 Case Differentiations
3103 \begin_inset Index idx
3106 \begin_layout Plain Layout
3107 Case differentiations
3115 \begin_layout Standard
3117 \begin_inset Tabular
3118 <lyxtabular version="3" rows="3" columns="2">
3119 <features tabularvalignment="middle">
3120 <column alignment="center" valignment="top" width="0pt">
3121 <column alignment="center" valignment="top" width="0pt">
3123 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3126 \begin_layout Plain Layout
3132 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3135 \begin_layout Plain Layout
3143 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3146 \begin_layout Plain Layout
3153 \begin_layout Plain Layout
3163 \begin_inset Formula $\to$
3167 \begin_inset Index idx
3170 \begin_layout Plain Layout
3183 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3186 \begin_layout Plain Layout
3187 \begin_inset Formula $\begin{cases}
3198 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3201 \begin_layout Plain Layout
3208 \begin_layout Plain Layout
3220 arg "newline-insert newline"
3228 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3231 \begin_layout Plain Layout
3232 \begin_inset Formula $\begin{cases}
3233 A & \textrm{for }x>0\\
3234 B & \textrm{for }x=0
3251 \begin_layout Standard
3258 or the usage of the math toolbar button
3259 \begin_inset Graphics
3260 filename ../images/math/cases.png
3265 you can create new lines with the shortcut
3268 arg "newline-insert newline"
3271 or the table toolbar button
3272 \begin_inset Graphics
3273 filename ../images/tabular-feature_append-row.png
3281 \begin_layout Standard
3288 is also available via the menu
3290 Insert\SpecialChar \menuseparator
3291 Math\SpecialChar \menuseparator
3297 \begin_layout Subsection
3299 \begin_inset Index idx
3302 \begin_layout Plain Layout
3311 \begin_layout Standard
3319 \begin_inset Index idx
3322 \begin_layout Plain Layout
3330 every character can be displayed canceled.
3331 The characters are quasi accentuated by a slash.
3334 \begin_layout Standard
3336 \begin_inset Tabular
3337 <lyxtabular version="3" rows="4" columns="2">
3338 <features tabularvalignment="middle">
3339 <column alignment="center" valignment="top" width="0pt">
3340 <column alignment="center" valignment="top" width="0pt">
3342 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3345 \begin_layout Plain Layout
3351 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3354 \begin_layout Plain Layout
3362 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3365 \begin_layout Plain Layout
3373 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3376 \begin_layout Plain Layout
3377 \begin_inset Formula $\not=$
3387 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3390 \begin_layout Plain Layout
3400 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3403 \begin_layout Plain Layout
3404 \begin_inset Formula $\not\le$
3414 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3417 \begin_layout Plain Layout
3427 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3430 \begin_layout Plain Layout
3431 \begin_inset Formula $\not\parallel$
3447 \begin_layout Standard
3448 The last example shows, that not all negations look good.
3449 Therefore there are for some negations special commands (see
3450 \begin_inset CommandInset ref
3452 reference "sub:Mathematical-Symbols"
3457 \begin_inset CommandInset ref
3459 reference "sec:Relations"
3466 \begin_layout Subsection
3468 \begin_inset CommandInset label
3470 name "sub:Placeholders"
3475 \begin_inset Index idx
3478 \begin_layout Plain Layout
3485 \begin_inset Index idx
3488 \begin_layout Plain Layout
3489 Chemical characters ! Isotopes
3495 \begin_inset Index idx
3498 \begin_layout Plain Layout
3503 \begin_layout Plain Layout
3514 \begin_layout Plain Layout
3529 \begin_layout Standard
3531 \begin_inset space \thinspace{}
3535 \begin_inset space \space{}
3542 \begin_layout Plain Layout
3543 Typesetting isotopes and chemical symbols is described in
3544 \begin_inset CommandInset ref
3546 reference "sub:Chemical-Symbols-and"
3555 the following problem occurs:
3558 \begin_layout Standard
3560 \begin_inset Tabular
3561 <lyxtabular version="3" rows="2" columns="2">
3562 <features tabularvalignment="middle">
3563 <column alignment="center" valignment="top" width="0pt">
3564 <column alignment="center" valignment="top" width="0pt">
3566 <cell alignment="center" valignment="top" usebox="none">
3569 \begin_layout Plain Layout
3570 Indices created with sub- and superscripts:
3575 <cell alignment="center" valignment="top" usebox="none">
3578 \begin_layout Plain Layout
3579 \begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
3589 <cell alignment="center" valignment="top" usebox="none">
3592 \begin_layout Plain Layout
3598 <cell alignment="center" valignment="top" usebox="none">
3601 \begin_layout Plain Layout
3602 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3616 \begin_inset Note Note
3619 \begin_layout Plain Layout
3626 is only used as spacer.
3634 \begin_layout Standard
3635 The shorter index is by default placed below or above the first character
3636 of the longer index.
3637 To avoid this there is the command
3644 \begin_inset Index idx
3647 \begin_layout Plain Layout
3655 or the math toolbar button
3656 \begin_inset space \thinspace{}
3663 \begin_layout Plain Layout
3664 can be found in the submenu of the toolbar button
3665 \begin_inset Graphics
3666 filename ../images/math/space.png
3677 \begin_inset Graphics
3678 filename ../images/math/phantom.png
3683 that creates one or more phantom characters.
3690 a small blue box appears that is superposed with two red arrows.
3691 The arrows indicate that the complete width and height of the box content
3692 will be created as placeholder.
3693 Phantom characters are accordingly placeholders with the size of the characters.
3696 \begin_layout Standard
3698 \begin_inset Tabular
3699 <lyxtabular version="3" rows="4" columns="2">
3700 <features tabularvalignment="middle">
3701 <column alignment="center" valignment="top" width="0">
3702 <column alignment="center" valignment="top" width="0">
3704 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3707 \begin_layout Plain Layout
3713 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3716 \begin_layout Plain Layout
3718 \begin_inset Note Note
3721 \begin_layout Plain Layout
3728 is only used as spacer.
3740 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3743 \begin_layout Plain Layout
3748 \begin_layout Plain Layout
3763 \begin_layout Plain Layout
3773 \begin_inset Formula $\to$
3780 \begin_layout Plain Layout
3794 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3797 \begin_layout Plain Layout
3798 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
3808 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3811 \begin_layout Plain Layout
3816 \begin_layout Plain Layout
3831 \begin_layout Plain Layout
3841 \begin_inset Formula $\to$
3848 \begin_layout Plain Layout
3862 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3865 \begin_layout Plain Layout
3866 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
3876 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3879 \begin_layout Plain Layout
3886 \begin_layout Plain Layout
3901 \begin_layout Plain Layout
3911 \begin_inset Formula $\to$
3918 \begin_layout Plain Layout
3932 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3935 \begin_layout Plain Layout
3936 \begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
3952 \begin_layout Standard
3953 Furthermore there are the commands
3960 \begin_inset Index idx
3963 \begin_layout Plain Layout
3972 \begin_inset space ~
3976 \begin_inset Graphics
3977 filename ../images/math/vphantom.png
3989 \begin_inset Index idx
3992 \begin_layout Plain Layout
4001 \begin_inset space ~
4005 \begin_inset Graphics
4006 filename ../images/math/hphantom.png
4018 creates only space for the maximal height of the characters in the box
4019 but not for its width.
4026 creates only space for the width of the box content.
4027 Therefore the boxes of both commands have only one red arrow.
4030 \begin_layout Standard
4041 \begin_layout Plain Layout
4056 space for the height of the integral sign,
4060 \begin_layout Plain Layout
4067 creates an integral sign, see
4068 \begin_inset CommandInset ref
4070 reference "sub:Big-Operators"
4079 because this is the larger character.
4080 An example application is in
4081 \begin_inset CommandInset ref
4083 reference "sub:Multiline-Brackets"
4090 \begin_layout Standard
4091 Placeholders can also be used for text when it is inserted via the menu
4094 Insert\SpecialChar \menuseparator
4095 Formatting\SpecialChar \menuseparator
4101 \begin_layout Standard
4103 \begin_inset Newline newline
4107 \begin_inset Phantom Phantom
4110 \begin_layout Plain Layout
4119 \begin_layout Subsection
4121 \begin_inset Index idx
4124 \begin_layout Plain Layout
4131 \begin_inset Index idx
4134 \begin_layout Plain Layout
4135 Formula ! underlined
4143 \begin_layout Standard
4145 \begin_inset Tabular
4146 <lyxtabular version="3" rows="4" columns="2">
4147 <features tabularvalignment="middle">
4148 <column alignment="center" valignment="top" width="0pt">
4149 <column alignment="center" valignment="top" width="0pt">
4151 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4154 \begin_layout Plain Layout
4160 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4163 \begin_layout Plain Layout
4165 \begin_inset Note Note
4168 \begin_layout Plain Layout
4175 is only used as spacer.
4187 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4190 \begin_layout Plain Layout
4197 \begin_layout Plain Layout
4207 \begin_inset Index idx
4210 \begin_layout Plain Layout
4223 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4226 \begin_layout Plain Layout
4227 \begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
4237 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
4240 \begin_layout Plain Layout
4247 \begin_layout Plain Layout
4257 \begin_inset Index idx
4260 \begin_layout Plain Layout
4273 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
4276 \begin_layout Plain Layout
4277 \begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
4287 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4290 \begin_layout Plain Layout
4297 \begin_layout Plain Layout
4312 \begin_layout Plain Layout
4326 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4329 \begin_layout Plain Layout
4330 \begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
4346 \begin_layout Standard
4347 In the last example it doesn't matter if first
4362 \begin_layout Standard
4363 To double underline e.
4364 \begin_inset space \thinspace{}
4368 \begin_inset space \space{}
4380 \begin_layout Standard
4381 It is possible to place up to 6 lines above or below characters.
4384 \begin_layout Standard
4385 \begin_inset VSpace bigskip
4388 Custom lines can be created using the command
4395 \begin_inset Index idx
4398 \begin_layout Plain Layout
4406 which has the following scheme:
4409 \begin_layout Standard
4414 rule[vertical offset]{length}{thickness}
4417 \begin_layout Standard
4418 The optional vertical offset shifts the line upwards (or downwards, when
4419 the value is negative).
4421 \begin_inset CommandInset ref
4423 reference "tab:Available-units"
4427 can be used for the values.
4428 Here are two example lines created with the commands
4429 \begin_inset Newline newline
4436 rule[-2ex]{3cm}{2pt}
4447 \begin_layout Standard
4449 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4455 \begin_layout Standard
4462 can also be used for text when a line is inserted via the menu
4464 Insert\SpecialChar \menuseparator
4465 Formatting\SpecialChar \menuseparator
4467 \begin_inset space ~
4475 \begin_layout Standard
4477 \begin_inset CommandInset line
4488 \begin_layout Subsection
4490 \begin_inset CommandInset label
4497 \begin_inset Index idx
4500 \begin_layout Plain Layout
4509 \begin_layout Standard
4510 There are different types of ellipses available.
4514 \begin_layout Plain Layout
4515 In the math toolbar in the submenu of the button
4516 \begin_inset Graphics
4517 filename ../images/math/ldots.png
4527 For listings dots at the baseline are used (
4534 \begin_inset Index idx
4537 \begin_layout Plain Layout
4545 ), while for operations dots are needed that are on the same height as the
4553 \begin_inset Index idx
4556 \begin_layout Plain Layout
4565 When using the command
4572 \begin_inset Index idx
4575 \begin_layout Plain Layout
4583 , LaTeX decides on the basis of the next character what type is used.
4586 \begin_layout Standard
4588 \begin_inset Tabular
4589 <lyxtabular version="3" rows="9" columns="2">
4590 <features tabularvalignment="middle">
4591 <column alignment="center" valignment="top" width="0pt">
4592 <column alignment="center" valignment="top" width="0pt">
4594 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4597 \begin_layout Plain Layout
4603 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4606 \begin_layout Plain Layout
4614 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4617 \begin_layout Plain Layout
4622 \begin_layout Plain Layout
4637 \begin_layout Plain Layout
4651 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4654 \begin_layout Plain Layout
4655 \begin_inset Formula $A_{1},\dots,A_{n}$
4665 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4668 \begin_layout Plain Layout
4673 \begin_layout Plain Layout
4688 \begin_layout Plain Layout
4702 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4705 \begin_layout Plain Layout
4706 \begin_inset Formula $A_{1}+\dots+A_{n}$
4716 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4719 \begin_layout Plain Layout
4724 \begin_layout Plain Layout
4739 \begin_layout Plain Layout
4753 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4756 \begin_layout Plain Layout
4757 \begin_inset Formula $A_{1},\ldots,A_{n}$
4767 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4770 \begin_layout Plain Layout
4775 \begin_layout Plain Layout
4790 \begin_layout Plain Layout
4804 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4807 \begin_layout Plain Layout
4808 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4818 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4821 \begin_layout Plain Layout
4829 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4832 \begin_layout Plain Layout
4833 \begin_inset Formula $\vdots$
4843 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4846 \begin_layout Plain Layout
4854 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4857 \begin_layout Plain Layout
4858 \begin_inset Formula $\ddots$
4868 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4871 \begin_layout Plain Layout
4879 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4882 \begin_layout Plain Layout
4883 \begin_inset Formula $\iddots$
4893 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4896 \begin_layout Plain Layout
4898 \begin_inset space \thinspace{}
4901 matrix with the different dots
4906 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4909 \begin_layout Plain Layout
4910 \begin_inset Formula $\begin{array}{ccc}
4911 A_{11} & \cdots & A_{1m}\\
4912 \vdots & \ddots & \vdots\\
4913 A_{n1} & \cdots & A_{nm}
4930 \begin_layout Standard
4931 The ellipses available in menu
4933 Insert\SpecialChar \menuseparator
4935 \begin_inset space ~
4949 \begin_layout Standard
4950 \begin_inset VSpace medskip
4959 , one of the options
4961 Use mathdots package (automatically)
4963 must be set in the document settings under
4966 \begin_inset space ~
4972 \begin_inset Newline newline
4977 Use mathdots package
4979 will improve the appearance of all dots in the documents if their font
4980 style or size is not the default.
4983 \begin_layout Standard
4984 \begin_inset VSpace medskip
4987 Specially for matrices there are ellipses that span over several columns.
4988 They are created with the command
4995 \begin_inset Index idx
4998 \begin_layout Plain Layout
5006 , that has the following scheme:
5009 \begin_layout Standard
5014 hdotsfor[distance]{number of columns}
5017 \begin_layout Standard
5018 The number of columns specifies how many columns should be spanned.
5019 Distance is a factor for the distance between the dots.
5022 \begin_layout Standard
5023 In the following matrix the command
5029 was inserted in the first box of the second line, to get an ellipsis with
5030 a dot distance twice as long as with the command
5037 \begin_inset Formula \[
5038 \left(\begin{array}{cccc}
5042 \end{array}\right)\]
5046 Note that the matrix fields that should be spanned must be empty, otherwise
5047 you get LaTeX-errors.
5050 \begin_layout Standard
5051 \begin_inset VSpace bigskip
5054 Furthermore you can fill with the command
5061 \begin_inset Index idx
5064 \begin_layout Plain Layout
5072 the rest of a line with dots.
5073 The effect of these commands is the same like with
5080 \begin_inset CommandInset ref
5082 reference "sub:Variable-Space"
5089 \begin_layout Standard
5090 For example the command
5098 \begin_layout Plain Layout
5112 \begin_layout Standard
5113 \begin_inset Formula $A\dotfill B$
5119 \begin_layout Standard
5126 there is for a line the command
5133 \begin_inset Index idx
5136 \begin_layout Plain Layout
5147 \begin_layout Standard
5148 \begin_inset Formula $A\hrulefill B$
5154 \begin_layout Standard
5155 To use the commands for text, they have to be inserted in TeX-mode.
5158 \begin_layout Section
5160 \begin_inset CommandInset label
5167 \begin_inset Index idx
5170 \begin_layout Plain Layout
5179 \begin_layout Standard
5180 Matrices can be inserted via the math toolbar button
5181 \begin_inset Graphics
5182 filename ../images/dialog-show_mathmatrix.png
5189 Insert\SpecialChar \menuseparator
5190 Math\SpecialChar \menuseparator
5194 In the matrix dialog you can specify the number of columns and rows, the
5195 alignment and the decoration.
5196 The vertical alignment is hereby only of importance for matrices in inline
5200 \begin_layout Standard
5201 The first matrix is top
5202 \begin_inset Formula $\begin{array}[t]{cccc}
5210 \begin_inset Formula $\begin{array}{cccc}
5217 and the third bottom
5218 \begin_inset Formula $\begin{array}[b]{cccc}
5228 \begin_layout Standard
5229 The horizontal alignment specifies how the column entries should be aligned.
5230 It is set by entering a letter for every column.
5235 denotes left aligned,
5244 To create for example a 4
5249 \begin_inset space ~
5252 matrix where the first column is left aligned, the second and third are
5253 centered and the last one is right aligned, one enters for the horizontal
5259 Normally are in a matrix all columns centered, therefore the default is
5260 for every column is a
5267 \begin_layout Standard
5268 Horizontal alignment:
5271 \begin_layout Standard
5277 \begin_inset Formula $\begin{array}{lll}
5289 \begin_inset Formula $\begin{array}{ccc}
5301 \begin_inset Formula $\begin{array}{rrr}
5311 \begin_layout Standard
5312 To add or delete rows and columns subsequently, the math toolbar buttons
5314 \begin_inset Graphics
5315 filename ../images/tabular-feature_append-row.png
5321 \begin_inset Graphics
5322 filename ../images/tabular-feature_delete-row.png
5328 \begin_inset space \thinspace{}
5333 Edit\SpecialChar \menuseparator
5337 New rows can also be created with
5340 arg "newline-insert newline"
5346 \begin_layout Standard
5347 \begin_inset VSpace bigskip
5354 adds parentheses in the selected style around the matrix.
5355 Alternatively, parentheses can can either be created with the commands
5363 \begin_inset Index idx
5366 \begin_layout Plain Layout
5381 \begin_inset Index idx
5384 \begin_layout Plain Layout
5395 \begin_inset space ~
5401 \begin_inset CommandInset ref
5403 reference "sub:Automatic-Bracket-Size"
5407 , or by using the following commands:
5408 \begin_inset VSpace medskip
5414 \begin_layout Standard
5415 \begin_inset space \hfill{}
5419 \begin_inset Tabular
5420 <lyxtabular version="3" rows="4" columns="2">
5421 <features tabularvalignment="middle">
5422 <column alignment="center" valignment="top" width="0">
5423 <column alignment="center" valignment="top" width="0">
5425 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5428 \begin_layout Plain Layout
5434 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5437 \begin_layout Plain Layout
5439 \begin_inset Note Note
5442 \begin_layout Plain Layout
5449 is only used as spacer.
5461 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5464 \begin_layout Plain Layout
5471 \begin_layout Plain Layout
5485 \begin_inset space \thinspace{}
5493 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5496 \begin_layout Plain Layout
5497 \begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
5498 0 & \textrm{-}\mathrm{i}\\
5500 \end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
5510 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5513 \begin_layout Plain Layout
5520 \begin_layout Plain Layout
5534 \begin_inset space \thinspace{}
5542 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5545 \begin_layout Plain Layout
5546 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
5547 0 & \textrm{-}\mathrm{i}\\
5549 \end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
5559 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5562 \begin_layout Plain Layout
5569 \begin_layout Plain Layout
5583 \begin_inset space \thinspace{}
5591 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5594 \begin_layout Plain Layout
5595 \begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
5596 0 & \textrm{-}\mathrm{i}\\
5598 \end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
5612 \begin_inset space \hfill{}
5616 \begin_inset Tabular
5617 <lyxtabular version="3" rows="4" columns="2">
5618 <features tabularvalignment="middle">
5619 <column alignment="center" valignment="top" width="0">
5620 <column alignment="center" valignment="top" width="0">
5622 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5625 \begin_layout Plain Layout
5631 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5634 \begin_layout Plain Layout
5642 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5645 \begin_layout Plain Layout
5652 \begin_layout Plain Layout
5666 \begin_inset space \thinspace{}
5674 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5677 \begin_layout Plain Layout
5678 \begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
5679 0 & \textrm{-}\mathrm{i}\\
5681 \end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
5691 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5694 \begin_layout Plain Layout
5701 \begin_layout Plain Layout
5715 \begin_inset space \thinspace{}
5723 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5726 \begin_layout Plain Layout
5727 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
5728 0 & \textrm{-}\mathrm{i}\\
5730 \end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
5740 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5743 \begin_layout Plain Layout
5750 \begin_layout Plain Layout
5764 \begin_inset space \thinspace{}
5772 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5775 \begin_layout Plain Layout
5776 \begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
5777 0 & \textrm{-}\mathrm{i}\\
5779 \end{array}\end{matrix}\raisebox{-5.3mm}{}$
5793 \begin_inset space \hfill{}
5799 \begin_layout Standard
5800 \begin_inset VSpace medskip
5804 \begin_inset space \thinspace{}
5808 \begin_inset space \space{}
5817 is inserted, a blue box appears between two vertical lines where the matrix
5819 \begin_inset Newline newline
5822 Note that decorated matrices ignore the vertical alignment.
5825 \begin_layout Standard
5826 \begin_inset VSpace bigskip
5829 As all multiline formulas are matrices, the length
5836 \begin_inset Index idx
5839 \begin_layout Plain Layout
5847 that is described in
5848 \begin_inset CommandInset ref
5850 reference "sub:Column-Separation"
5854 can also be used to change the column separation of matrices.
5857 \begin_layout Standard
5858 To change the row separation, the command
5865 \begin_inset Index idx
5868 \begin_layout Plain Layout
5877 It is used as follows:
5880 \begin_layout Standard
5887 arraystretch}{stretch factor}
5888 \begin_inset Index idx
5891 \begin_layout Plain Layout
5902 \begin_layout Standard
5909 assigns the stretch factor to the predefined command
5917 \begin_inset space \thinspace{}
5921 \begin_inset space \space{}
5924 the row separation, use the factor 2.
5925 This is then used for all following matrices.
5926 To go back to the original separation, assign the factor 1 to
5935 \begin_layout Standard
5936 To set matrices into a text line, the command
5943 \begin_inset Index idx
5946 \begin_layout Plain Layout
5955 When it is inserted a blue box with two dashed lines appears.
5956 In this box the matrix is inserted.
5959 \begin_layout Standard
5961 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5963 \end{smallmatrix}\right)$
5969 \begin_layout Section
5970 Brackets and Delimiters
5971 \begin_inset Index idx
5974 \begin_layout Plain Layout
5981 \begin_inset Index idx
5984 \begin_layout Plain Layout
5993 \begin_layout Subsection
5994 Vertical Brackets and Delimiters
5995 \begin_inset Index idx
5998 \begin_layout Plain Layout
6007 \begin_layout Standard
6008 \begin_inset space \hfill{}
6012 \begin_inset Tabular
6013 <lyxtabular version="3" rows="9" columns="2">
6014 <features tabularvalignment="middle">
6015 <column alignment="center" valignment="top" width="0pt">
6016 <column alignment="center" valignment="top" width="0pt">
6018 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6021 \begin_layout Plain Layout
6027 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6030 \begin_layout Plain Layout
6038 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6041 \begin_layout Plain Layout
6047 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6050 \begin_layout Plain Layout
6051 \begin_inset Formula $($
6061 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6064 \begin_layout Plain Layout
6070 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6073 \begin_layout Plain Layout
6074 \begin_inset Formula $\{$
6084 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6087 \begin_layout Plain Layout
6093 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6096 \begin_layout Plain Layout
6097 \begin_inset Formula $[$
6107 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6110 \begin_layout Plain Layout
6118 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6121 \begin_layout Plain Layout
6122 \begin_inset Formula $\langle$
6132 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6135 \begin_layout Plain Layout
6143 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6146 \begin_layout Plain Layout
6147 \begin_inset Formula $\lceil$
6157 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6160 \begin_layout Plain Layout
6168 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6171 \begin_layout Plain Layout
6172 \begin_inset Formula $\lfloor$
6182 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6185 \begin_layout Plain Layout
6191 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6194 \begin_layout Plain Layout
6195 \begin_inset Formula $/$
6205 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6208 \begin_layout Plain Layout
6214 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6217 \begin_layout Plain Layout
6218 \begin_inset Formula $|$
6232 \begin_inset space \hfill{}
6236 \begin_inset Tabular
6237 <lyxtabular version="3" rows="9" columns="2">
6238 <features tabularvalignment="middle">
6239 <column alignment="center" valignment="top" width="0pt">
6240 <column alignment="center" valignment="top" width="0pt">
6242 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6245 \begin_layout Plain Layout
6251 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6254 \begin_layout Plain Layout
6262 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6265 \begin_layout Plain Layout
6271 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6274 \begin_layout Plain Layout
6275 \begin_inset Formula $)$
6285 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6288 \begin_layout Plain Layout
6294 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6297 \begin_layout Plain Layout
6298 \begin_inset Formula $\}$
6308 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6311 \begin_layout Plain Layout
6317 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6320 \begin_layout Plain Layout
6321 \begin_inset Formula $]$
6331 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6334 \begin_layout Plain Layout
6342 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6345 \begin_layout Plain Layout
6346 \begin_inset Formula $\rangle$
6356 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6359 \begin_layout Plain Layout
6367 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6370 \begin_layout Plain Layout
6371 \begin_inset Formula $\rceil$
6381 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6384 \begin_layout Plain Layout
6392 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6395 \begin_layout Plain Layout
6396 \begin_inset Formula $\rfloor$
6406 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6409 \begin_layout Plain Layout
6419 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6422 \begin_layout Plain Layout
6423 \begin_inset Formula $\backslash$
6433 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6436 \begin_layout Plain Layout
6444 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6447 \begin_layout Plain Layout
6448 \begin_inset Formula $\|$
6462 \begin_inset space \hfill{}
6468 \begin_layout Standard
6471 \begin_inset Note Greyedout
6474 \begin_layout Plain Layout
6479 In TeX-mode the command
6486 \begin_inset Index idx
6489 \begin_layout Plain Layout
6497 must be used for the backslash, because the command
6505 produces there a line break.
6513 \begin_layout Standard
6514 For all characters listed above the size can be adjusted with the commands
6515 described in the following two subsections.
6516 When using these commands, the characters < and > can directly be used
6517 instead of the commands
6532 \begin_layout Subsubsection
6534 \begin_inset CommandInset label
6536 name "sub:Manual-Bracket-Size"
6541 \begin_inset Index idx
6544 \begin_layout Plain Layout
6545 Bracket size ! manual
6553 \begin_layout Standard
6554 The bracket size can be specified manually by the LaTeX-commands
6561 \begin_inset Index idx
6564 \begin_layout Plain Layout
6597 denotes the smallest and
6603 the largest bracket size.
6606 \begin_layout Standard
6607 These commands are used to emphasize levels of brackets:
6610 \begin_layout Standard
6612 \begin_inset Tabular
6613 <lyxtabular version="3" rows="2" columns="2">
6614 <features tabularvalignment="middle">
6615 <column alignment="center" valignment="top" width="0pt">
6616 <column alignment="center" valignment="top" width="0pt">
6618 <cell alignment="center" valignment="top" usebox="none">
6621 \begin_layout Plain Layout
6622 all brackets in the same size:
6627 <cell alignment="center" valignment="top" usebox="none">
6630 \begin_layout Plain Layout
6631 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
6641 <cell alignment="center" valignment="top" usebox="none">
6644 \begin_layout Plain Layout
6650 <cell alignment="center" valignment="top" usebox="none">
6653 \begin_layout Plain Layout
6654 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6668 \begin_inset Note Note
6671 \begin_layout Plain Layout
6678 is only used as spacer.
6686 \begin_layout Standard
6687 For the second formula the command
6697 \begin_layout Plain Layout
6711 \begin_layout Standard
6712 Here is an overview about all bracket sizes:
6715 \begin_layout Standard
6735 \begin_layout Plain Layout
6752 \begin_layout Plain Layout
6765 \begin_layout Plain Layout
6781 \begin_layout Standard
6783 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6789 \begin_layout Standard
6796 -commands there is the variant
6803 \begin_inset Index idx
6806 \begin_layout Plain Layout
6814 that adds a bit more space between the bracket and its content, and the
6828 \begin_inset Index idx
6831 \begin_layout Plain Layout
6841 , that don't add additional space.
6846 at the end of the command
6852 is for a left bracket; for a right bracket this will be replaced by an
6858 A left or right bracket can each be an opening or closing bracket.
6861 \begin_layout Standard
6862 In the following table is a comparison of the variants:
6865 \begin_layout Standard
6867 \begin_inset Tabular
6868 <lyxtabular version="3" rows="5" columns="2">
6869 <features tabularvalignment="middle">
6870 <column alignment="center" valignment="middle" width="0">
6871 <column alignment="center" valignment="middle" width="0">
6873 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6876 \begin_layout Plain Layout
6882 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6885 \begin_layout Plain Layout
6887 \begin_inset Note Note
6890 \begin_layout Plain Layout
6897 is only used as spacer.
6909 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6912 \begin_layout Plain Layout
6927 \begin_layout Plain Layout
6945 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6948 \begin_layout Plain Layout
6949 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
6959 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6962 \begin_layout Plain Layout
6977 \begin_layout Plain Layout
6995 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6998 \begin_layout Plain Layout
6999 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
7009 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7012 \begin_layout Plain Layout
7027 \begin_layout Plain Layout
7045 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7048 \begin_layout Plain Layout
7049 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
7059 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7062 \begin_layout Plain Layout
7074 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7077 \begin_layout Plain Layout
7078 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
7094 \begin_layout Subsubsection
7095 Automatic Bracket Size
7096 \begin_inset CommandInset label
7098 name "sub:Automatic-Bracket-Size"
7103 \begin_inset Index idx
7106 \begin_layout Plain Layout
7107 Bracket size ! automatic
7115 \begin_layout Standard
7116 Brackets with variable size can be inserted with the commands
7123 \begin_inset Index idx
7126 \begin_layout Plain Layout
7141 \begin_inset Index idx
7144 \begin_layout Plain Layout
7152 or via the math toolbar button
7153 \begin_inset Graphics
7154 filename ../images/dialog-show_mathdelimiter.png
7172 the wanted bracket must be inserted.
7173 The bracket size will then automatically be calculated for the output.
7176 \begin_layout Standard
7178 normal bracket: The command
7188 \begin_layout Plain Layout
7198 \begin_inset Formula $\downarrow$
7205 \begin_layout Plain Layout
7217 \begin_inset Formula \[
7225 \begin_layout Standard
7227 multiline bracket: The command
7239 \begin_layout Plain Layout
7249 \begin_inset Formula $\downarrow$
7256 \begin_layout Plain Layout
7270 \begin_inset Formula \[
7271 \ln\left(\frac{A}{C}\right)\]
7278 \begin_layout Standard
7294 \begin_inset space ~
7300 This has the advantage that you can see in LyX immediately the real bracket
7301 size and that the matching right bracket will be created too.
7302 \begin_inset Newline newline
7305 The command for the last example would then be:
7319 \begin_layout Plain Layout
7329 \begin_inset Formula $\downarrow$
7335 \begin_layout Standard
7336 To omit a left or right bracket, a dot is inserted for the omitted bracket.
7337 For example the command
7347 \begin_layout Plain Layout
7357 \begin_inset Formula $\downarrow$
7364 \begin_layout Plain Layout
7380 \begin_inset Formula \[
7381 \left.\frac{A}{B}\right\} \]
7399 will be converted by LyX to brackets in the right size when the document
7400 is reloaded and an omitted bracket will appear as dashed line.
7403 \begin_layout Standard
7404 \begin_inset VSpace bigskip
7407 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
7415 \begin_inset Index idx
7418 \begin_layout Plain Layout
7426 is additionally available for all brackets and limits.
7427 With this command the height of the following character is adapted to the
7428 one of the surrounding brackets, what is e.
7429 \begin_inset space \thinspace{}
7433 \begin_inset space \space{}
7436 needed for physical vectors:
7437 \begin_inset Formula \[
7438 \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle \]
7442 For physical vectors there is a special LaTeX-package, described in
7443 \begin_inset CommandInset ref
7445 reference "sub:Physical-Vectors"
7452 \begin_layout Subsection
7454 \begin_inset Index idx
7457 \begin_layout Plain Layout
7458 Brackets ! horizontal
7466 \begin_layout Standard
7468 \begin_inset Tabular
7469 <lyxtabular version="3" rows="4" columns="2">
7470 <features tabularvalignment="middle">
7471 <column alignment="center" valignment="top" width="0pt">
7472 <column alignment="center" valignment="top" width="0pt">
7474 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7477 \begin_layout Plain Layout
7479 \begin_inset Note Note
7482 \begin_layout Plain Layout
7489 is only used as spacer.
7499 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7502 \begin_layout Plain Layout
7510 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7513 \begin_layout Plain Layout
7517 \begin_layout Plain Layout
7532 \begin_layout Plain Layout
7545 \begin_layout Plain Layout
7558 \begin_layout Plain Layout
7571 \begin_layout Plain Layout
7579 \begin_inset Index idx
7582 \begin_layout Plain Layout
7595 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7598 \begin_layout Plain Layout
7599 \begin_inset Formula $\overbrace{A+B}^{3}$
7609 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7612 \begin_layout Plain Layout
7616 \begin_layout Plain Layout
7631 \begin_layout Plain Layout
7644 \begin_layout Plain Layout
7657 \begin_layout Plain Layout
7665 \begin_inset Index idx
7668 \begin_layout Plain Layout
7681 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7684 \begin_layout Plain Layout
7685 \begin_inset Formula $\underbrace{A+B}_{5}$
7695 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7698 \begin_layout Plain Layout
7705 \begin_layout Plain Layout
7720 \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
7799 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7802 \begin_layout Plain Layout
7803 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
7819 \begin_layout Standard
7820 In the last example it doesn't matter if
7832 is inserted at first.
7835 \begin_layout Standard
7836 \begin_inset VSpace bigskip
7839 When brackets are needed that overlap each other, multiline formulas, as
7841 \begin_inset CommandInset ref
7843 reference "sec:Multiline-Formulas"
7848 \begin_inset Formula \begin{eqnarray*}
7849 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
7850 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
7855 In the first row the formula is inserted together with the first brace.
7856 It is hereby important that the space command
7860 \begin_layout Plain Layout
7861 Space commands are explained in
7862 \begin_inset CommandInset ref
7864 reference "sub:Predefined-Space"
7879 is inserted before the first
7880 \begin_inset Formula $d$
7883 , because the brace that ends behind the
7884 \begin_inset Formula $q$
7887 prevents that the following
7888 \begin_inset Quotes eld
7892 \begin_inset Quotes erd
7895 is surrounded by space.
7899 \begin_layout Plain Layout
7900 because a bracket is not handled as character, see
7901 \begin_inset CommandInset ref
7903 reference "sub:Binary-Operators"
7912 In the second row the second brace is inserted.
7913 As it should begin before the
7914 \begin_inset Formula $b$
7929 \begin_layout Plain Layout
7937 \begin_inset CommandInset ref
7939 reference "sub:Placeholders"
7948 This space is needed because the
7949 \begin_inset Quotes eld
7953 \begin_inset Quotes erd
7956 is also surrounded by space in the formula.
7957 The brace is placed under the command
7966 \begin_layout Standard
7967 It gets more complicated when brackets overlap each other, like in the following
7972 \begin_layout Plain Layout
7984 \begin_inset Formula \begin{eqnarray*}
7985 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7986 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd
7995 \begin_layout Plain Layout
8006 The first formula row is the same as the second row of the previous example,
8007 with the difference that the brace is above.
8008 The second row contains the formula together with the second brace.
8009 To avoid that there is space between the upper brace in the first row and
8010 the formula, the row spacing need to be reduced.
8011 This is not easily possible due to a bug in LyX
8015 \begin_layout Plain Layout
8016 \begin_inset CommandInset href
8018 name "LyX-bug #1505"
8019 target "http://www.lyx.org/trac/ticket/1505"
8029 As solution for the problem, the global formula row separation
8036 \begin_inset Index idx
8039 \begin_layout Plain Layout
8047 must be changed to -6
8048 \begin_inset space \thinspace{}
8051 pt before the formula with the command
8066 is set back after the formula to the standard value of 3
8067 \begin_inset space \thinspace{}
8070 pt using the same command.
8071 More about the row separation in formulas is explained in
8072 \begin_inset CommandInset ref
8074 reference "sub:Line-Separation"
8081 \begin_layout Section
8083 \begin_inset Index idx
8086 \begin_layout Plain Layout
8095 \begin_layout Standard
8096 Arrows can be inserted via the math toolbar button
8097 \begin_inset Graphics
8098 filename ../images/math/leftarrow.png
8103 or the commands listed in the following subsections.
8106 \begin_layout Standard
8107 \begin_inset Newpage newpage
8113 \begin_layout Subsection
8115 \begin_inset Index idx
8118 \begin_layout Plain Layout
8127 \begin_layout Standard
8128 \begin_inset space \hfill{}
8132 \begin_inset Tabular
8133 <lyxtabular version="3" rows="8" columns="2">
8134 <features tabularvalignment="middle">
8135 <column alignment="center" valignment="top" width="0pt">
8136 <column alignment="center" valignment="top" width="0pt">
8138 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8141 \begin_layout Plain Layout
8147 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8150 \begin_layout Plain Layout
8158 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8161 \begin_layout Plain Layout
8169 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8172 \begin_layout Plain Layout
8173 \begin_inset Formula $\gets$
8183 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8186 \begin_layout Plain Layout
8194 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8197 \begin_layout Plain Layout
8198 \begin_inset Formula $\Leftarrow$
8208 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8211 \begin_layout Plain Layout
8219 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8222 \begin_layout Plain Layout
8223 \begin_inset Formula $\longleftarrow$
8233 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8236 \begin_layout Plain Layout
8244 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8247 \begin_layout Plain Layout
8248 \begin_inset Formula $\Longleftarrow$
8258 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8261 \begin_layout Plain Layout
8269 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8272 \begin_layout Plain Layout
8273 \begin_inset Formula $\leftharpoonup$
8283 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8286 \begin_layout Plain Layout
8294 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8297 \begin_layout Plain Layout
8298 \begin_inset Formula $\leftharpoondown$
8308 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8311 \begin_layout Plain Layout
8319 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8322 \begin_layout Plain Layout
8323 \begin_inset Formula $\hookleftarrow$
8337 \begin_inset space \hfill{}
8341 \begin_inset Tabular
8342 <lyxtabular version="3" rows="8" columns="2">
8343 <features tabularvalignment="middle">
8344 <column alignment="center" valignment="top" width="0pt">
8345 <column alignment="center" valignment="top" width="0pt">
8347 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8350 \begin_layout Plain Layout
8356 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8359 \begin_layout Plain Layout
8367 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8370 \begin_layout Plain Layout
8378 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8381 \begin_layout Plain Layout
8382 \begin_inset Formula $\to$
8392 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8395 \begin_layout Plain Layout
8403 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8406 \begin_layout Plain Layout
8407 \begin_inset Formula $\Rightarrow$
8417 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8420 \begin_layout Plain Layout
8428 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8431 \begin_layout Plain Layout
8432 \begin_inset Formula $\longrightarrow$
8442 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8445 \begin_layout Plain Layout
8453 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8456 \begin_layout Plain Layout
8457 \begin_inset Formula $\Longrightarrow$
8467 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8470 \begin_layout Plain Layout
8478 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8481 \begin_layout Plain Layout
8482 \begin_inset Formula $\rightharpoonup$
8492 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8495 \begin_layout Plain Layout
8503 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8506 \begin_layout Plain Layout
8507 \begin_inset Formula $\rightharpoondown$
8517 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8520 \begin_layout Plain Layout
8528 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8531 \begin_layout Plain Layout
8532 \begin_inset Formula $\hookrightarrow$
8546 \begin_inset space \hfill{}
8552 \begin_layout Standard
8553 \begin_inset space \hfill{}
8557 \begin_inset Tabular
8558 <lyxtabular version="3" rows="6" columns="2">
8559 <features tabularvalignment="middle">
8560 <column alignment="center" valignment="top" width="0pt">
8561 <column alignment="center" valignment="top" width="0pt">
8563 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8566 \begin_layout Plain Layout
8572 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8575 \begin_layout Plain Layout
8583 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8586 \begin_layout Plain Layout
8594 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8597 \begin_layout Plain Layout
8598 \begin_inset Formula $\leftrightarrow$
8608 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8611 \begin_layout Plain Layout
8619 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8622 \begin_layout Plain Layout
8623 \begin_inset Formula $\Leftrightarrow$
8633 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8636 \begin_layout Plain Layout
8644 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8647 \begin_layout Plain Layout
8648 \begin_inset Formula $\longleftrightarrow$
8658 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8661 \begin_layout Plain Layout
8669 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8672 \begin_layout Plain Layout
8673 \begin_inset Formula $\Longleftrightarrow$
8683 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8686 \begin_layout Plain Layout
8694 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8697 \begin_layout Plain Layout
8698 \begin_inset Formula $\rightleftharpoons$
8712 \begin_inset space \hspace{}
8717 \begin_inset space \hfill{}
8721 \begin_inset Tabular
8722 <lyxtabular version="3" rows="5" columns="2">
8723 <features tabularvalignment="middle">
8724 <column alignment="center" valignment="top" width="0pt">
8725 <column alignment="center" valignment="top" width="0pt">
8727 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8730 \begin_layout Plain Layout
8736 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8739 \begin_layout Plain Layout
8747 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8750 \begin_layout Plain Layout
8758 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8761 \begin_layout Plain Layout
8762 \begin_inset Formula $\mapsto$
8772 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8775 \begin_layout Plain Layout
8783 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8786 \begin_layout Plain Layout
8787 \begin_inset Formula $\longmapsto$
8797 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8800 \begin_layout Plain Layout
8808 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8811 \begin_layout Plain Layout
8812 \begin_inset Formula $\leadsto$
8822 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8825 \begin_layout Plain Layout
8833 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8836 \begin_layout Plain Layout
8837 \begin_inset Formula $\dasharrow$
8851 \begin_inset space \hfill{}
8857 \begin_layout Standard
8858 \begin_inset VSpace medskip
8861 Arrows used as accent like e.
8862 \begin_inset space \thinspace{}
8866 \begin_inset space \space{}
8869 vector arrows are listed in
8870 \begin_inset CommandInset ref
8872 reference "sec:Accents"
8879 \begin_layout Standard
8880 \begin_inset VSpace bigskip
8883 Furthermore there are the labeled arrows
8884 \begin_inset Index idx
8887 \begin_layout Plain Layout
8900 \begin_inset Index idx
8903 \begin_layout Plain Layout
8918 \begin_inset Index idx
8921 \begin_layout Plain Layout
8928 \begin_layout Plain Layout
8943 When inserting one of these commands in a formula, an arrow with two blue
8944 boxes appear where the label can be inserted.
8945 The length of the arrow adapts to the label width.
8948 \begin_layout Standard
8950 \begin_inset Tabular
8951 <lyxtabular version="3" rows="3" columns="2">
8952 <features tabularvalignment="middle">
8953 <column alignment="center" valignment="top" width="0pt">
8954 <column alignment="center" valignment="top" width="0pt">
8956 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8959 \begin_layout Plain Layout
8965 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8968 \begin_layout Plain Layout
8970 \begin_inset Note Note
8973 \begin_layout Plain Layout
8980 is only used as spacer.
8992 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8995 \begin_layout Plain Layout
9002 \begin_layout Plain Layout
9012 \begin_inset Formula $\downarrow$
9016 \begin_inset Formula $\to$
9024 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9027 \begin_layout Plain Layout
9028 \begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
9038 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9041 \begin_layout Plain Layout
9048 \begin_layout Plain Layout
9058 \begin_inset Formula $\downarrow$
9062 \begin_inset Formula $\to$
9070 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9073 \begin_layout Plain Layout
9074 \begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
9090 \begin_layout Subsection
9091 Vertical and diagonal Arrows
9092 \begin_inset Index idx
9095 \begin_layout Plain Layout
9102 \begin_inset Index idx
9105 \begin_layout Plain Layout
9114 \begin_layout Standard
9115 \begin_inset space \hfill{}
9119 \begin_inset Tabular
9120 <lyxtabular version="3" rows="7" columns="2">
9121 <features tabularvalignment="middle">
9122 <column alignment="center" valignment="top" width="0pt">
9123 <column alignment="center" valignment="top" width="0pt">
9125 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9128 \begin_layout Plain Layout
9134 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9137 \begin_layout Plain Layout
9145 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9148 \begin_layout Plain Layout
9156 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9159 \begin_layout Plain Layout
9160 \begin_inset Formula $\uparrow$
9170 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9173 \begin_layout Plain Layout
9181 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9184 \begin_layout Plain Layout
9185 \begin_inset Formula $\Uparrow$
9195 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9198 \begin_layout Plain Layout
9206 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9209 \begin_layout Plain Layout
9210 \begin_inset Formula $\updownarrow$
9220 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9223 \begin_layout Plain Layout
9231 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9234 \begin_layout Plain Layout
9235 \begin_inset Formula $\Updownarrow$
9245 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9248 \begin_layout Plain Layout
9256 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9259 \begin_layout Plain Layout
9260 \begin_inset Formula $\Downarrow$
9270 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9273 \begin_layout Plain Layout
9281 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9284 \begin_layout Plain Layout
9285 \begin_inset Formula $\downarrow$
9299 \begin_inset space \hfill{}
9303 \begin_inset Tabular
9304 <lyxtabular version="3" rows="5" columns="2">
9305 <features tabularvalignment="middle">
9306 <column alignment="center" valignment="top" width="0pt">
9307 <column alignment="center" valignment="top" width="0pt">
9309 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9312 \begin_layout Plain Layout
9318 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9321 \begin_layout Plain Layout
9329 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9332 \begin_layout Plain Layout
9340 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9343 \begin_layout Plain Layout
9344 \begin_inset Formula $\nearrow$
9354 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9357 \begin_layout Plain Layout
9365 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9368 \begin_layout Plain Layout
9369 \begin_inset Formula $\searrow$
9379 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9382 \begin_layout Plain Layout
9390 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9393 \begin_layout Plain Layout
9394 \begin_inset Formula $\swarrow$
9404 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9407 \begin_layout Plain Layout
9415 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9418 \begin_layout Plain Layout
9419 \begin_inset Formula $\nwarrow$
9433 \begin_inset space \hfill{}
9439 \begin_layout Standard
9440 \begin_inset VSpace medskip
9443 Vertical arrows can be used also as delimiter together with the commands
9445 \begin_inset CommandInset ref
9447 reference "sub:Manual-Bracket-Size"
9452 \begin_inset CommandInset ref
9454 reference "sub:Automatic-Bracket-Size"
9461 \begin_layout Standard
9462 \begin_inset Newpage newpage
9468 \begin_layout Section
9470 \begin_inset CommandInset label
9477 \begin_inset Index idx
9480 \begin_layout Plain Layout
9489 \begin_layout Standard
9490 Accents can be inserted via the math toolbar button
9491 \begin_inset Graphics
9492 filename ../images/math/hat.png
9497 or the commands listed in the following subsections.
9500 \begin_layout Subsection
9501 Accents for one Character
9505 \begin_layout Plain Layout
9518 \begin_layout Plain Layout
9520 \begin_inset CommandInset ref
9522 reference "sub:Accents-in-Text"
9535 \begin_layout Plain Layout
9543 \begin_inset Note Note
9546 \begin_layout Plain Layout
9553 is used to avoid that the footnote appears in the PDF-bookmark.
9556 \begin_layout Plain Layout
9564 \begin_inset CommandInset ref
9566 reference "sub:Formulas-in-Section"
9576 \begin_inset CommandInset label
9578 name "sub:Accents-for-one"
9583 \begin_inset Index idx
9586 \begin_layout Plain Layout
9587 Accents ! for one character
9595 \begin_layout Standard
9596 \begin_inset space \hfill{}
9600 \begin_inset Tabular
9601 <lyxtabular version="3" rows="8" columns="2">
9602 <features tabularvalignment="middle">
9603 <column alignment="center" valignment="top" width="0pt">
9604 <column alignment="center" valignment="top" width="0pt">
9606 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9609 \begin_layout Plain Layout
9615 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9618 \begin_layout Plain Layout
9620 \begin_inset Note Note
9623 \begin_layout Plain Layout
9630 is only used as spacer.
9642 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9645 \begin_layout Plain Layout
9652 \begin_layout Plain Layout
9666 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9669 \begin_layout Plain Layout
9670 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
9680 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9683 \begin_layout Plain Layout
9690 \begin_layout Plain Layout
9704 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9707 \begin_layout Plain Layout
9708 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
9718 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9721 \begin_layout Plain Layout
9728 \begin_layout Plain Layout
9742 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9745 \begin_layout Plain Layout
9746 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
9756 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9759 \begin_layout Plain Layout
9766 \begin_layout Plain Layout
9780 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9783 \begin_layout Plain Layout
9784 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
9794 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9797 \begin_layout Plain Layout
9804 \begin_layout Plain Layout
9814 \begin_inset Index idx
9817 \begin_layout Plain Layout
9828 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9831 \begin_layout Plain Layout
9832 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
9842 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9845 \begin_layout Plain Layout
9852 \begin_layout Plain Layout
9866 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9869 \begin_layout Plain Layout
9870 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
9880 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9883 \begin_layout Plain Layout
9890 \begin_layout Plain Layout
9904 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9907 \begin_layout Plain Layout
9908 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
9922 \begin_inset space \hfill{}
9926 \begin_inset Tabular
9927 <lyxtabular version="3" rows="7" columns="2">
9928 <features tabularvalignment="middle">
9929 <column alignment="center" valignment="top" width="0pt">
9930 <column alignment="center" valignment="top" width="0pt">
9932 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9935 \begin_layout Plain Layout
9941 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9944 \begin_layout Plain Layout
9952 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9955 \begin_layout Plain Layout
9962 \begin_layout Plain Layout
9976 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9979 \begin_layout Plain Layout
9980 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
9990 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9993 \begin_layout Plain Layout
10000 \begin_layout Plain Layout
10014 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10017 \begin_layout Plain Layout
10018 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
10028 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10031 \begin_layout Plain Layout
10038 \begin_layout Plain Layout
10052 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10055 \begin_layout Plain Layout
10056 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
10066 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10069 \begin_layout Plain Layout
10076 \begin_layout Plain Layout
10090 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10093 \begin_layout Plain Layout
10094 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
10104 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10107 \begin_layout Plain Layout
10114 \begin_layout Plain Layout
10128 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10131 \begin_layout Plain Layout
10132 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
10142 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10145 \begin_layout Plain Layout
10152 \begin_layout Plain Layout
10166 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10169 \begin_layout Plain Layout
10170 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
10184 \begin_inset space \hfill{}
10190 \begin_layout Standard
10191 \begin_inset VSpace bigskip
10197 \begin_layout Standard
10198 You can directly insert accents like é to formulas.
10199 LyX will transform them to the corresponding accent command.
10201 \begin_inset Index idx
10204 \begin_layout Plain Layout
10210 it is better to insert a quotation mark before the vowel.
10211 These two characters are then treated by LaTeX as
10215 character when the formula part with the umlaut is marked as German.
10223 \begin_inset Quotes eld
10227 \begin_inset Quotes erd
10230 umlauts are created as demonstrated in the following example:
10233 \begin_layout Standard
10234 \begin_inset VSpace -2mm
10240 \begin_layout Standard
10242 \begin_inset Tabular
10243 <lyxtabular version="3" rows="3" columns="2">
10244 <features tabularvalignment="middle">
10245 <column alignment="center" valignment="top" width="0">
10246 <column alignment="center" valignment="top" width="0">
10248 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10251 \begin_layout Plain Layout
10257 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10260 \begin_layout Plain Layout
10262 \begin_inset Note Note
10265 \begin_layout Plain Layout
10273 \begin_inset space \thinspace{}
10276 pt space are only used as spacer.
10288 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10291 \begin_layout Plain Layout
10294 \begin_inset Quotes grd
10302 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10305 \begin_layout Plain Layout
10306 \begin_inset space \hspace{}
10313 \begin_inset Formula $"i$
10323 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10326 \begin_layout Plain Layout
10333 \begin_layout Plain Layout
10347 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10350 \begin_layout Plain Layout
10351 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
10367 \begin_layout Standard
10368 Another advantage to
10374 is that umlauts can directly be converted to mathematical text because
10375 the accent commands above are
10381 in mathematical text
10384 To convert an accented character to mathematical text, only the character
10385 under the accent may be converted.
10386 This applies also for all other conversions, e.
10387 \begin_inset space \thinspace{}
10391 \begin_inset space \space{}
10397 \begin_layout Standard
10398 In mathematical text, umlauts and other accented characters can directly
10402 \begin_layout Subsection
10403 Accents for Operators
10404 \begin_inset Index idx
10407 \begin_layout Plain Layout
10408 Accents ! for operators
10416 \begin_layout Standard
10424 \begin_inset Index idx
10427 \begin_layout Plain Layout
10442 \begin_inset Index idx
10445 \begin_layout Plain Layout
10453 characters can be placed above or below an operator, respectively, to accent
10462 \begin_inset Index idx
10465 \begin_layout Plain Layout
10473 characters can be set before and behind an operator.
10474 The command scheme is:
10477 \begin_layout Standard
10493 \begin_layout Standard
10500 must always be before the operator that should be accented.
10501 You can accent with several characters and even with other operators and
10509 for example only characters behind an operator, write nothing between the
10510 first braces but don't omit the braces.
10513 \begin_layout Standard
10514 For example the command
10519 \begin_inset Formula $\to$
10529 \begin_inset Formula $\to$
10538 \begin_layout Plain Layout
10554 \begin_inset Formula \[
10555 \sideset{}{'}\sum_{k=1}^{n}\]
10562 \begin_layout Standard
10571 \begin_layout Plain Layout
10586 \begin_layout Plain Layout
10598 \begin_inset Formula $\uparrow$
10606 \begin_inset Formula \[
10607 \overset{a}{\maltese}\]
10611 As seen in the last example, with
10623 also symbols and characters can be accented; with
10629 this is not possible.
10632 \begin_layout Subsection
10633 Accents for several Characters
10634 \begin_inset Index idx
10637 \begin_layout Plain Layout
10638 Accents ! for several characters
10646 \begin_layout Standard
10647 \begin_inset space \hfill{}
10651 \begin_inset Tabular
10652 <lyxtabular version="3" rows="5" columns="2">
10653 <features tabularvalignment="middle">
10654 <column alignment="center" valignment="top" width="0pt">
10655 <column alignment="center" valignment="top" width="0pt">
10657 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10660 \begin_layout Plain Layout
10666 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10669 \begin_layout Plain Layout
10671 \begin_inset Note Note
10674 \begin_layout Plain Layout
10681 is only used as spacer.
10693 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10696 \begin_layout Plain Layout
10703 \begin_layout Plain Layout
10717 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10720 \begin_layout Plain Layout
10721 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
10731 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10734 \begin_layout Plain Layout
10741 \begin_layout Plain Layout
10755 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10758 \begin_layout Plain Layout
10759 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
10769 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10772 \begin_layout Plain Layout
10779 \begin_layout Plain Layout
10793 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10796 \begin_layout Plain Layout
10797 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
10807 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10810 \begin_layout Plain Layout
10813 underleftrightarrow
10817 \begin_layout Plain Layout
10831 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10834 \begin_layout Plain Layout
10835 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
10849 \begin_inset space \hfill{}
10853 \begin_inset Tabular
10854 <lyxtabular version="3" rows="5" columns="2">
10855 <features tabularvalignment="middle">
10856 <column alignment="center" valignment="top" width="0pt">
10857 <column alignment="center" valignment="top" width="0pt">
10859 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10862 \begin_layout Plain Layout
10868 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10871 \begin_layout Plain Layout
10879 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10882 \begin_layout Plain Layout
10889 \begin_layout Plain Layout
10903 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10906 \begin_layout Plain Layout
10907 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
10917 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10920 \begin_layout Plain Layout
10927 \begin_layout Plain Layout
10941 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10944 \begin_layout Plain Layout
10945 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
10955 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10958 \begin_layout Plain Layout
10965 \begin_layout Plain Layout
10979 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10982 \begin_layout Plain Layout
10983 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
10993 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10996 \begin_layout Plain Layout
11003 \begin_layout Plain Layout
11017 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11020 \begin_layout Plain Layout
11021 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
11035 \begin_inset space \hfill{}
11041 \begin_layout Standard
11042 \begin_inset VSpace medskip
11045 With these commands as many characters as you like can be accented.
11058 will only be set in the output with a length of three characters, as shown
11059 in the following example:
11060 \begin_inset Formula \[
11061 \widetilde{A+B=C-D}\]
11068 \begin_layout Standard
11076 \begin_inset Index idx
11079 \begin_layout Plain Layout
11094 \begin_inset Index idx
11097 \begin_layout Plain Layout
11105 described in the previous subsection it is also possible to accent several
11115 \begin_layout Plain Layout
11125 \begin_inset Formula $\downarrow$
11131 \begin_inset Formula \[
11132 \underset{***}{A=B}\]
11139 \begin_layout Section
11141 \begin_inset CommandInset label
11148 \begin_inset Index idx
11151 \begin_layout Plain Layout
11160 \begin_layout Subsection
11162 \begin_inset CommandInset label
11164 name "sub:Predefined-Space"
11169 \begin_inset Index idx
11172 \begin_layout Plain Layout
11173 Space ! horizontal ! predefined
11181 \begin_layout Standard
11182 Sometimes it is necessary to insert horizontal space to a formula.
11183 This is done by inserting a protected space (shortcut
11186 arg "space-insert protected"
11191 \begin_inset Quotes eld
11200 \begin_layout Plain Layout
11212 \begin_inset Quotes erd
11215 appears and by pressing
11219 several times one can select one of eight different space sizes.
11220 The spaces can also be inserted using the math toolbar button
11221 \begin_inset Graphics
11222 filename ../images/math/space.png
11227 or special commands.
11228 Independent from the inserted command, one can select the size again by
11236 \begin_layout Standard
11239 \begin_inset VSpace -5mm
11243 \begin_inset Tabular
11244 <lyxtabular version="3" rows="3" columns="7">
11245 <features tabularvalignment="middle">
11246 <column alignment="center" valignment="middle" width="6.8cm">
11247 <column alignment="center" valignment="top" width="0">
11248 <column alignment="center" valignment="top" width="0">
11249 <column alignment="center" valignment="top" width="0">
11250 <column alignment="center" valignment="top" width="0">
11251 <column alignment="center" valignment="top" width="0">
11252 <column alignment="center" valignment="top" width="0">
11254 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11257 \begin_layout Plain Layout
11263 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11266 \begin_layout Plain Layout
11274 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11277 \begin_layout Plain Layout
11285 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11288 \begin_layout Plain Layout
11296 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11299 \begin_layout Plain Layout
11307 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11310 \begin_layout Plain Layout
11318 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11321 \begin_layout Plain Layout
11331 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11334 \begin_layout Plain Layout
11339 keystrokes after inserting the protected space
11344 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11347 \begin_layout Plain Layout
11353 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11356 \begin_layout Plain Layout
11362 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11365 \begin_layout Plain Layout
11371 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11374 \begin_layout Plain Layout
11380 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11383 \begin_layout Plain Layout
11389 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11392 \begin_layout Plain Layout
11400 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11403 \begin_layout Plain Layout
11409 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11412 \begin_layout Plain Layout
11413 \begin_inset Formula $A\, B$
11421 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11424 \begin_layout Plain Layout
11425 \begin_inset Formula $A\: B$
11433 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11436 \begin_layout Plain Layout
11437 \begin_inset Formula $A\; B$
11445 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11448 \begin_layout Plain Layout
11449 \begin_inset Formula $A\quad B$
11457 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11460 \begin_layout Plain Layout
11461 \begin_inset Formula $A\qquad B$
11469 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11472 \begin_layout Plain Layout
11473 \begin_inset Formula $A\! B$
11489 \begin_layout Standard
11490 The last size seem to produce no space.
11491 It is displayed red in LyX contrary to the other sizes, because it is a
11493 There are two more negative spaces:
11496 \begin_layout Standard
11498 \begin_inset Tabular
11499 <lyxtabular version="3" rows="3" columns="3">
11500 <features tabularvalignment="middle">
11501 <column alignment="center" valignment="middle" width="6.8cm">
11502 <column alignment="center" valignment="top" width="0pt">
11503 <column alignment="center" valignment="top" width="0pt">
11505 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11508 \begin_layout Plain Layout
11514 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11517 \begin_layout Plain Layout
11525 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11528 \begin_layout Plain Layout
11538 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11541 \begin_layout Plain Layout
11546 keystrokes after inserting the protected space
11551 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11554 \begin_layout Plain Layout
11560 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11563 \begin_layout Plain Layout
11571 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11574 \begin_layout Plain Layout
11580 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11583 \begin_layout Plain Layout
11584 \begin_inset Formula $A\negmedspace B$
11592 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11595 \begin_layout Plain Layout
11596 \begin_inset Formula $A\negthickspace B$
11612 \begin_layout Standard
11613 Negative spaces can lead to characters overlapping each other.
11614 Thus they can be used to enforce ligatures, what is e.
11615 \begin_inset space \thinspace{}
11619 \begin_inset space \space{}
11622 useful for summation operators:
11625 \begin_layout Standard
11627 \begin_inset Tabular
11628 <lyxtabular version="3" rows="3" columns="2">
11629 <features tabularvalignment="middle">
11630 <column alignment="center" valignment="top" width="0">
11631 <column alignment="center" valignment="top" width="0">
11633 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11636 \begin_layout Plain Layout
11642 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11645 \begin_layout Plain Layout
11647 \begin_inset Note Note
11650 \begin_layout Plain Layout
11657 is only used as spacer.
11669 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11672 \begin_layout Plain Layout
11681 \begin_layout Plain Layout
11695 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11698 \begin_layout Plain Layout
11699 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
11709 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11712 \begin_layout Plain Layout
11723 \begin_layout Plain Layout
11737 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11740 \begin_layout Plain Layout
11741 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
11757 \begin_layout Standard
11758 Relations like for example equal signs, are always surrounded by space.
11759 To suppress this, the equal sign is placed into a TeX-brace.
11760 The following example demonstrates this:
11763 \begin_layout Standard
11765 \begin_inset Tabular
11766 <lyxtabular version="3" rows="2" columns="2">
11767 <features tabularvalignment="middle">
11768 <column alignment="center" valignment="top" width="0pt">
11769 <column alignment="center" valignment="top" width="0pt">
11771 <cell alignment="center" valignment="top" usebox="none">
11774 \begin_layout Plain Layout
11780 <cell alignment="center" valignment="top" usebox="none">
11783 \begin_layout Plain Layout
11784 \begin_inset Formula $A=B$
11794 <cell alignment="center" valignment="top" usebox="none">
11797 \begin_layout Plain Layout
11798 \begin_inset Note Note
11801 \begin_layout Plain Layout
11808 is only used as spacer.
11814 \begin_inset Formula $\raisebox{5mm}{}$
11817 equation without space
11822 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11825 \begin_layout Plain Layout
11826 \begin_inset Formula $A{=}B$
11842 \begin_layout Standard
11844 The command for the last formula is:
11849 \begin_inset Formula $\to$
11855 \begin_layout Standard
11856 \begin_inset VSpace bigskip
11859 Spaces are needed for physical units, because the space between the value
11860 and the unit is the smallest one and not a normal space.
11861 For units in text, the smallest space is inserted via the menu
11863 Insert\SpecialChar \menuseparator
11864 Formatting\SpecialChar \menuseparator
11866 \begin_inset space ~
11874 arg "space-insert thin"
11880 \begin_layout Standard
11881 An example to visualize the difference:
11884 \begin_layout Standard
11885 \begin_inset Tabular
11886 <lyxtabular version="3" rows="2" columns="2">
11887 <features tabularvalignment="middle">
11888 <column alignment="left" valignment="top" width="0">
11889 <column alignment="left" valignment="top" width="0">
11891 <cell alignment="center" valignment="top" usebox="none">
11894 \begin_layout Plain Layout
11896 \begin_inset Formula $\cdot$
11904 <cell alignment="center" valignment="top" usebox="none">
11907 \begin_layout Plain Layout
11908 space between value and unit
11915 <cell alignment="center" valignment="top" usebox="none">
11918 \begin_layout Plain Layout
11920 \begin_inset space \thinspace{}
11924 \begin_inset Formula $\cdot$
11932 <cell alignment="center" valignment="top" usebox="none">
11935 \begin_layout Plain Layout
11936 smallest space between value and unit
11949 \begin_layout Subsection
11954 \begin_layout Plain Layout
11967 \begin_layout Plain Layout
11968 for vertical space in formulas see
11969 \begin_inset CommandInset ref
11971 reference "sub:Line-Separation"
11984 \begin_layout Plain Layout
11992 \begin_inset Note Note
11995 \begin_layout Plain Layout
11998 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
12001 \begin_layout Plain Layout
12004 texorpdfstring is in section
12005 \begin_inset CommandInset ref
12007 reference "sub:Formulas-in-Section"
12017 \begin_inset CommandInset label
12019 name "sub:Variable-Space"
12024 \begin_inset Index idx
12027 \begin_layout Plain Layout
12028 Space ! horizontal ! variable
12036 \begin_layout Standard
12037 Space with a defined length can be inserted with the command
12044 \begin_inset Index idx
12047 \begin_layout Plain Layout
12057 \begin_inset Quotes eld
12066 \begin_layout Plain Layout
12078 \begin_inset Quotes erd
12082 The length can be specified by left-clicking on the
12083 \begin_inset Quotes eld
12092 \begin_layout Plain Layout
12104 \begin_inset Quotes erd
12108 The length may also be negative.
12109 To insert so many space that the formula uses all available space, the
12117 \begin_inset Index idx
12120 \begin_layout Plain Layout
12131 \begin_layout Standard
12132 \begin_inset VSpace -1mm
12138 \begin_layout Standard
12140 \begin_inset Tabular
12141 <lyxtabular version="3" rows="4" columns="2">
12142 <features tabularvalignment="middle">
12143 <column alignment="center" valignment="top" width="0">
12144 <column alignment="center" valignment="top" width="0">
12146 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12149 \begin_layout Plain Layout
12157 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12160 \begin_layout Plain Layout
12168 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12171 \begin_layout Plain Layout
12178 \begin_layout Plain Layout
12188 \begin_inset Formula $\to$
12194 \begin_inset space \thinspace{}
12202 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12205 \begin_layout Plain Layout
12206 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
12216 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12219 \begin_layout Plain Layout
12226 \begin_layout Plain Layout
12236 \begin_inset Formula $\to$
12242 \begin_inset space \thinspace{}
12250 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12253 \begin_layout Plain Layout
12254 \begin_inset Formula $A\hspace{-1mm}A\not=A$
12264 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12267 \begin_layout Plain Layout
12274 \begin_layout Plain Layout
12288 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12291 \begin_layout Plain Layout
12292 \begin_inset Formula $A=A\hfill B=B$
12308 \begin_layout Standard
12309 In the last example the available space is given by the longest column entry
12311 In an inline formula the space depends on the length of the line in which
12319 Thus, when the line uses the full width, no space will be created.
12326 only has an effect on displayed formulas when the formula style
12331 (Formula styles are explained in
12332 \begin_inset CommandInset ref
12334 reference "sec:Formula-Styles"
12341 \begin_layout Standard
12348 , there are the commands
12360 that fill the space with a pattern, see
12361 \begin_inset CommandInset ref
12363 reference "sub:Ellipses"
12370 \begin_layout Standard
12371 For text, variable space can be inserted via the menu
12373 Insert\SpecialChar \menuseparator
12374 Formatting\SpecialChar \menuseparator
12376 \begin_inset space ~
12384 \begin_layout Standard
12385 This is a line with
12386 \begin_inset space \hspace{}
12391 \begin_inset space \thinspace{}
12397 \begin_layout Standard
12398 This is a line with
12399 \begin_inset space \hfill{}
12405 \begin_layout Subsection
12406 Space besides inline Formulas
12407 \begin_inset Index idx
12410 \begin_layout Plain Layout
12411 Space ! besides inline formulas
12419 \begin_layout Standard
12420 The space that surrounds inline formulas can be adjusted with the length
12428 \begin_inset Index idx
12431 \begin_layout Plain Layout
12440 The value of a length is set with the command
12447 \begin_inset Index idx
12450 \begin_layout Plain Layout
12458 that has the following scheme:
12461 \begin_layout Standard
12466 setlength{length name}{value}
12469 \begin_layout Standard
12477 \begin_inset space \thinspace{}
12483 \begin_layout Standard
12493 \begin_layout Standard
12494 is inserted in TeX-mode.
12496 \begin_inset space \thinspace{}
12499 mm space will now be set around all inline formulas:
12503 \begin_layout Plain Layout
12517 \begin_layout Standard
12518 This is a line with an inline formula
12519 \begin_inset Formula $A=B$
12523 \begin_inset space \thinspace{}
12526 mm surrounding space.
12530 \begin_layout Plain Layout
12544 \begin_layout Standard
12545 To return to the predefined value,
12551 is set to the value 0
12552 \begin_inset space \thinspace{}
12558 \begin_layout Section
12560 \begin_inset Index idx
12563 \begin_layout Plain Layout
12570 \begin_inset Index idx
12573 \begin_layout Plain Layout
12578 \begin_layout Plain Layout
12589 \begin_layout Plain Layout
12604 \begin_layout Standard
12605 Boxes for text are described in chapter
12612 \begin_inset space ~
12620 \begin_layout Subsection
12622 \begin_inset CommandInset label
12624 name "sub:Boxes-with-Frame"
12629 \begin_inset Index idx
12632 \begin_layout Plain Layout
12641 \begin_layout Standard
12642 It is possible to frame formulas or parts of it with the commands
12649 \begin_inset Index idx
12652 \begin_layout Plain Layout
12667 \begin_inset Index idx
12670 \begin_layout Plain Layout
12681 \begin_layout Standard
12682 When one of these commands is inserted to a formula, a blue box appears
12683 within a frame to enter formula parts.
12690 an additional formula has to be created by
12694 within this box, because the box content will otherwise be treated as mathemati
12702 is used, a new formula is automatically created inside the frame.
12705 \begin_layout Standard
12712 is not suitable to frame displayed formulas because the formula will always
12713 be set in the size of the text.
12720 is in contrary not suitable to frame inline formulas, because the formula
12721 will always be set in the size of a displayed formula.
12724 \begin_layout Standard
12731 there is the command
12738 \begin_inset Index idx
12741 \begin_layout Plain Layout
12749 where additionally the frame width and the alignment can be specified.
12756 is used in the following scheme:
12759 \begin_layout Standard
12764 framebox[frame width][position]{box content}
12767 \begin_layout Standard
12768 The position can either be
12785 right aligns the formula in the box.
12786 When no position is given, the formula will be centered.
12787 \begin_inset Newline newline
12790 Is no width given, also no position can be given.
12791 In this case the frame width is adjusted to the box content like for
12800 \begin_layout Standard
12807 is inserted, a box appears containing three blue boxes.
12808 The first two boxes are surrounded by brackets and denote the two optional
12810 The third box is for formula parts like for
12819 \begin_layout Standard
12821 \begin_inset Tabular
12822 <lyxtabular version="3" rows="5" columns="2">
12823 <features tabularvalignment="middle">
12824 <column alignment="center" valignment="top" width="0">
12825 <column alignment="center" valignment="top" width="0">
12827 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12830 \begin_layout Plain Layout
12836 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12839 \begin_layout Plain Layout
12841 \begin_inset Note Note
12844 \begin_layout Plain Layout
12851 is only used as spacer.
12863 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12866 \begin_layout Plain Layout
12873 \begin_layout Plain Layout
12892 \begin_layout Plain Layout
12906 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12909 \begin_layout Plain Layout
12910 \begin_inset Formula $\raisebox{6mm}{}\fbox{\ensuremath{\int A=B}}\raisebox{-4mm}{}$
12920 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12923 \begin_layout Plain Layout
12930 \begin_layout Plain Layout
12945 \begin_layout Plain Layout
12959 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12962 \begin_layout Plain Layout
12963 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
12973 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12976 \begin_layout Plain Layout
12983 \begin_layout Plain Layout
12997 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13000 \begin_layout Plain Layout
13001 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
13011 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13014 \begin_layout Plain Layout
13021 \begin_layout Plain Layout
13031 \begin_inset Formula $\to$
13035 \begin_inset Formula $\to$
13048 \begin_layout Plain Layout
13058 \begin_inset Formula $\downarrow$
13066 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13069 \begin_layout Plain Layout
13070 \begin_inset Formula $\raisebox{6mm}{}$
13074 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
13078 \begin_inset Formula $\raisebox{-4mm}{}$
13094 \begin_layout Standard
13095 The frame thickness can also be adjusted.
13096 To do this the following commands have to be inserted in TeX-mode before
13100 \begin_layout Standard
13110 \begin_inset Quotes eld
13114 \begin_inset Quotes erd
13128 \begin_inset Quotes eld
13132 \begin_inset Quotes erd
13138 \begin_layout Standard
13139 \begin_inset Quotes eld
13143 \begin_inset Quotes erd
13146 specifies the minimal distance between the frame and the first character
13148 An example for this is the following framed formula:
13152 \begin_layout Plain Layout
13164 \begin_inset Formula \[
13169 Before this formula the commands
13172 \begin_layout Standard
13194 \begin_layout Standard
13195 were inserted in TeX-mode.
13196 The given values are used for all following boxes.
13199 \begin_layout Standard
13200 To return to the standard frame size, the command
13203 \begin_layout Standard
13228 \begin_layout Plain Layout
13242 \begin_layout Standard
13243 is inserted in TeX-mode before the next formula.
13246 \begin_layout Subsection
13247 Boxes without Frame
13248 \begin_inset CommandInset label
13250 name "sub:Boxes-without-Frame"
13255 \begin_inset Index idx
13258 \begin_layout Plain Layout
13259 Boxes ! without frame
13267 \begin_layout Standard
13268 For boxes without a frame there are the following box commands:
13275 \begin_inset Index idx
13278 \begin_layout Plain Layout
13293 \begin_inset Index idx
13296 \begin_layout Plain Layout
13311 \begin_inset Index idx
13314 \begin_layout Plain Layout
13325 \begin_layout Standard
13332 a box can be super- or subscripted.
13333 But in contrary to normal super- and subscripting, the characters in the
13334 box keep their font size.
13341 is used in the following scheme:
13344 \begin_layout Standard
13349 raisebox{height}{box content}
13352 \begin_layout Standard
13353 When the box should contain a formula, an extra formula is needed like for
13364 \begin_inset Note Greyedout
13367 \begin_layout Plain Layout
13378 this extra formula is created by pressing
13382 twice instead of once because LyX doesn't yet support
13396 \begin_layout Standard
13398 \begin_inset Tabular
13399 <lyxtabular version="3" rows="4" columns="2">
13400 <features tabularvalignment="middle">
13401 <column alignment="center" valignment="top" width="0">
13402 <column alignment="center" valignment="top" width="0">
13404 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13407 \begin_layout Plain Layout
13413 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13416 \begin_layout Plain Layout
13424 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13427 \begin_layout Plain Layout
13431 \begin_inset Formula $\to$
13437 \begin_inset Formula $\to$
13445 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13448 \begin_layout Plain Layout
13449 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13459 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13462 \begin_layout Plain Layout
13466 \begin_inset Formula $\to$
13472 \begin_inset Formula $\to$
13480 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13483 \begin_layout Plain Layout
13484 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13494 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13497 \begin_layout Plain Layout
13501 \begin_inset Formula $\to$
13520 \begin_layout Plain Layout
13534 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13537 \begin_layout Plain Layout
13538 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
13554 \begin_layout Standard
13579 , with the difference that there is no frame.
13582 \begin_layout Subsection
13584 \begin_inset CommandInset label
13586 name "sub:Colored-Boxes"
13591 \begin_inset Index idx
13594 \begin_layout Plain Layout
13603 \begin_layout Standard
13604 To be able to use all commands explained in this section, the LaTeX-package
13613 \begin_layout Plain Layout
13618 is part of every LaTeX standard installation.
13624 \begin_inset Index idx
13627 \begin_layout Plain Layout
13633 has to be loaded in the LaTeX-preamble with the line
13637 \begin_layout Plain Layout
13638 When text is colored somewhere in the document with a predefined color,
13639 LyX loads the LaTeX-package
13644 Thus it is possible that the package is loaded twice, but this doesn't
13651 \begin_inset Note Note
13654 \begin_layout Plain Layout
13655 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
13664 \begin_layout Standard
13672 \begin_layout Standard
13673 \begin_inset VSpace medskip
13676 To color boxes, the command
13683 \begin_inset Index idx
13686 \begin_layout Plain Layout
13694 is used in the following scheme:
13697 \begin_layout Standard
13702 colorbox{color}{box content}
13705 \begin_layout Standard
13706 The box content can also be a box and a
13712 can also be part of another box (see the 2nd and 3rd example).
13713 When the box should contain a formula, an extra formula has to be created,
13714 the same way as for
13724 \begin_layout Plain Layout
13725 This also applies for the command
13739 \begin_layout Standard
13740 One of the following predefined colors can be chosen:
13743 \begin_layout Standard
13777 \begin_layout Standard
13779 \begin_inset Tabular
13780 <lyxtabular version="3" rows="4" columns="2">
13781 <features tabularvalignment="middle">
13782 <column alignment="center" valignment="top" width="0">
13783 <column alignment="center" valignment="top" width="0">
13785 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13788 \begin_layout Plain Layout
13794 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13797 \begin_layout Plain Layout
13799 \begin_inset Note Note
13802 \begin_layout Plain Layout
13809 is only used as spacer.
13821 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13824 \begin_layout Plain Layout
13828 \begin_inset Formula $\to$
13838 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13841 \begin_layout Plain Layout
13842 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
13852 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13855 \begin_layout Plain Layout
13859 \begin_inset Formula $\to$
13870 \begin_layout Plain Layout
13884 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13887 \begin_layout Plain Layout
13888 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
13898 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13901 \begin_layout Plain Layout
13908 \begin_layout Plain Layout
13920 \begin_inset Formula $\to$
13939 \begin_layout Plain Layout
13953 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13956 \begin_layout Plain Layout
13957 \begin_inset Formula $\raisebox{7mm}{}\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}\raisebox{-5mm}{}$
13973 \begin_layout Standard
13980 only colors the box but not the characters in the box.
13981 To color all characters, the whole formula is highlighted and the wanted
13982 color is chosen in the
13985 \begin_inset space ~
13991 The dialog can be called with the toolbar button
13992 \begin_inset Graphics
13993 filename ../images/dialog-show_character.png
14000 Edit\SpecialChar \menuseparator
14002 \begin_inset space ~
14005 Style\SpecialChar \menuseparator
14009 The formula number has then the same color as the formula.
14010 When the formula number should get another color than the formula characters,
14011 the color must be changed within the formula.
14014 \begin_layout Standard
14018 \begin_layout Standard
14021 \begin_inset Formula \begin{equation}
14022 \int A=B\label{eq:red}\end{equation}
14029 \begin_inset Formula \begin{equation}
14030 \textcolor{red}{\int A=B}\label{eq:redgreen}\end{equation}
14037 \begin_layout Standard
14039 \begin_inset CommandInset ref
14045 is completely colored red.
14046 \begin_inset Newline newline
14050 \begin_inset CommandInset ref
14052 reference "eq:redgreen"
14056 was first completely colored green to set the color for the formula number.
14057 Subsequently the formula characters were colored red.
14060 \begin_layout Standard
14061 \begin_inset VSpace bigskip
14064 To color the frame different than the rest of the box, the command
14071 \begin_inset Index idx
14074 \begin_layout Plain Layout
14082 is used in the following scheme:
14085 \begin_layout Standard
14090 fcolorbox{frame color}{color}{box content}
14093 \begin_layout Standard
14100 is an extension of the command
14107 The frame width is set, like for
14130 \begin_layout Plain Layout
14142 \begin_inset Formula \[
14143 \fcolorbox{cyan}{magenta}{A=B}\]
14151 \begin_layout Plain Layout
14165 \begin_layout Standard
14166 This formula was created with the command
14167 \begin_inset Newline newline
14175 \begin_inset Formula $\to$
14181 \begin_inset Formula $\to$
14191 \begin_layout Standard
14192 \begin_inset VSpace bigskip
14195 To use other colors than the predefined ones, they have to be defined first.
14198 \begin_layout Standard
14199 One can for example define the color
14200 \begin_inset Quotes eld
14208 \begin_inset Quotes erd
14211 with the LaTeX-preamble line:
14214 \begin_layout Standard
14219 definecolor{darkgreen}{cmyk}{0.5,
14234 \begin_inset Index idx
14237 \begin_layout Plain Layout
14248 \begin_layout Standard
14253 is the color space that denotes the colors
14270 The four comma separated numbers are the portion factor for the corresponding
14271 colors of the color space.
14272 The factors can be in the range of 0
14273 \begin_inset space \thinspace{}
14277 \begin_inset space \thinspace{}
14285 also the color space
14289 can be used for definitions.
14306 , so that there are in this case three portion factors for the corresponding
14308 Furthermore there is the color space
14312 with one portion factor for the gray value.
14315 \begin_layout Standard
14316 As example a framed box with the new defined color
14320 where the characters have been colored
14325 \begin_inset Formula \begin{equation}
14326 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}\end{equation}
14333 \begin_layout Standard
14334 Self-defined colors can also be used for text with the help of the command
14342 \begin_inset Index idx
14345 \begin_layout Plain Layout
14354 \begin_layout Standard
14358 \begin_layout Plain Layout
14362 textcolor{darkgreen}{
14368 \begin_inset Quotes eld
14372 \begin_inset Quotes erd
14379 \begin_layout Plain Layout
14389 \begin_layout Standard
14397 \begin_inset Index idx
14400 \begin_layout Plain Layout
14408 is used in the scheme
14412 textcolor{color}{characters to color}
14417 \begin_layout Subsection
14419 \begin_inset CommandInset label
14421 name "sub:Paragraph-Boxes"
14426 \begin_inset Index idx
14429 \begin_layout Plain Layout
14430 Boxes ! as paragraph
14438 \begin_layout Standard
14439 A box that can contain several lines and paragraphs, a so called paragraph
14440 box (parbox), can be created with the menu
14442 Insert\SpecialChar \menuseparator
14445 or the toolbar button
14446 \begin_inset Graphics
14447 filename ../images/box-insert.png
14455 \begin_layout Standard
14456 The following example shows a framed parbox in a line:
14459 \begin_layout Standard
14460 \begin_inset VSpace medskip
14464 \begin_inset Box Boxed
14474 height_special "totalheight"
14477 \begin_layout Plain Layout
14478 This is a paragraph box.
14480 \begin_inset space \thinspace{}
14483 cm long and can also contain formulas:
14484 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14495 \begin_layout Standard
14496 \begin_inset VSpace medskip
14502 \begin_layout Standard
14503 Such a box is created by right-clicking on the gray box inset.
14504 A dialog pops up showing the box properties.
14518 \begin_inset space \thinspace{}
14523 Vertical Box Alignment
14528 \begin_layout Standard
14529 \begin_inset VSpace medskip
14532 In LaTeX a parbox is created with the command
14539 \begin_inset Index idx
14542 \begin_layout Plain Layout
14550 that has the following scheme:
14553 \begin_layout Standard
14558 parbox[position]{width}{box content}
14561 \begin_layout Standard
14575 for bottom means that the box is aligned within the surrounding text with
14581 for top this is done with the first line.
14582 When no position is given, the box will be vertically centered, see section
14590 \begin_inset space ~
14595 manual for examples.
14598 \begin_layout Standard
14599 \begin_inset VSpace bigskip
14602 To frame formulas completely, including the formula number, the formula
14603 must be set into a parbox.
14604 To do this, the command
14618 is inserted in TeX-mode before the formula.
14626 \begin_inset Index idx
14629 \begin_layout Plain Layout
14637 is hereby the line width set for the document.
14638 Because the frame is outside the parbox, 2
14639 \begin_inset space \thinspace{}
14642 times the frame separation and the frame thickness must be subtracted from
14644 As this is not automatically done by LyX due to a bug
14648 \begin_layout Plain Layout
14649 \begin_inset CommandInset href
14651 name "LyX-bug #4483"
14652 target "http://www.lyx.org/trac/ticket/4483"
14661 , TeX-mode has to be used.
14662 To be able to multiply and subtract in arguments, the LaTeX-package
14670 \begin_layout Plain Layout
14675 is part of every LaTeX standard installation.
14681 \begin_inset Index idx
14684 \begin_layout Plain Layout
14690 must be loaded in the LaTeX-preamble with the line
14693 \begin_layout Standard
14701 \begin_layout Standard
14702 Behind the formula both boxes are closed by entering
14707 Here is an example:
14711 \begin_layout Plain Layout
14725 \begin_layout Standard
14729 \begin_layout Plain Layout
14747 \begin_inset Formula \begin{equation}
14748 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}\end{equation}
14756 \begin_layout Plain Layout
14767 \begin_layout Plain Layout
14781 \begin_layout Standard
14782 \begin_inset VSpace medskip
14785 As a parbox is used as argument of
14791 , there is in this case no difference between
14806 \begin_layout Standard
14807 \begin_inset VSpace bigskip
14810 Paragraph boxes are very useful to comment formulas directly.
14817 is used in combination with the command
14831 \begin_inset CommandInset ref
14833 reference "sub:User-defined-Numbering"
14840 \begin_layout Standard
14841 An example of a formula commented with
14850 \begin_layout Standard
14854 \begin_layout Plain Layout
14867 This is a description.
14868 It is distinctly separated from the formula and multiline.
14872 \begin_layout Plain Layout
14884 \begin_layout Standard
14885 Such a formula must be inserted completely in TeX-mode because LyX does
14886 not yet support the command
14893 The formula is created with the following command sequence:
14896 \begin_layout Standard
14909 is inserted in TeX-mode.
14913 \begin_layout Plain Layout
14914 When the formula style
14926 can also be replaced by
14933 (formula styles see
14934 \begin_inset CommandInset ref
14936 reference "sec:Formula-Styles"
14945 Then the description follows as normal text and finally
14951 is inserted in TeX-mode.
14964 hereby create a displayed formula.
14967 \begin_layout Standard
14974 can be seen in this example that was
14975 \begin_inset Quotes eld
14979 \begin_inset Quotes erd
14982 using the mathematical textmode:
14983 \begin_inset Formula \[
14984 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}\]
14991 \begin_layout Section
14993 \begin_inset Index idx
14996 \begin_layout Plain Layout
15005 \begin_layout Subsection
15007 \begin_inset CommandInset label
15009 name "sub:Big-Operators"
15014 \begin_inset Index idx
15017 \begin_layout Plain Layout
15024 \begin_inset Index idx
15027 \begin_layout Plain Layout
15034 \begin_inset Index idx
15037 \begin_layout Plain Layout
15046 \begin_layout Standard
15047 To be able to use all integral operators listed here, the option
15049 Use esint package automatically
15051 must be set in the document settings under
15054 \begin_inset space ~
15062 \begin_layout Standard
15063 \begin_inset space \hfill{}
15067 \begin_inset Tabular
15068 <lyxtabular version="3" rows="11" columns="2">
15069 <features tabularvalignment="middle">
15070 <column alignment="center" valignment="top" width="0pt">
15071 <column alignment="center" valignment="top" width="0pt">
15073 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15076 \begin_layout Plain Layout
15082 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15085 \begin_layout Plain Layout
15093 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15096 \begin_layout Plain Layout
15100 \begin_inset Index idx
15103 \begin_layout Plain Layout
15116 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15119 \begin_layout Plain Layout
15120 \begin_inset Formula $\int$
15130 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15133 \begin_layout Plain Layout
15141 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15144 \begin_layout Plain Layout
15145 \begin_inset Formula $\oint$
15155 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15158 \begin_layout Plain Layout
15166 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15169 \begin_layout Plain Layout
15170 \begin_inset Formula $\ointctrclockwise$
15180 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15183 \begin_layout Plain Layout
15191 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15194 \begin_layout Plain Layout
15195 \begin_inset Formula $\ointclockwise$
15205 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15208 \begin_layout Plain Layout
15216 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15219 \begin_layout Plain Layout
15220 \begin_inset Formula $\sqint$
15230 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15233 \begin_layout Plain Layout
15241 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15244 \begin_layout Plain Layout
15246 \begin_inset Formula $\fint$
15256 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15259 \begin_layout Plain Layout
15267 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15270 \begin_layout Plain Layout
15272 \begin_inset Formula $\landupint$
15282 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15285 \begin_layout Plain Layout
15293 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15296 \begin_layout Plain Layout
15298 \begin_inset Formula $\landdownint$
15308 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15311 \begin_layout Plain Layout
15319 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15322 \begin_layout Plain Layout
15323 \begin_inset Formula $\bigcap$
15333 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15336 \begin_layout Plain Layout
15344 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15347 \begin_layout Plain Layout
15348 \begin_inset Formula $\bigcup$
15362 \begin_inset space \hfill{}
15366 \begin_inset Tabular
15367 <lyxtabular version="3" rows="11" columns="2">
15368 <features tabularvalignment="middle">
15369 <column alignment="center" valignment="top" width="0pt">
15370 <column alignment="center" valignment="top" width="0pt">
15372 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15375 \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
15392 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15395 \begin_layout Plain Layout
15399 \begin_inset Index idx
15402 \begin_layout Plain Layout
15415 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15418 \begin_layout Plain Layout
15419 \begin_inset Formula $\sum$
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" leftline="true" rightline="true" usebox="none">
15455 \begin_layout Plain Layout
15456 \begin_inset Formula $\prod$
15466 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15469 \begin_layout Plain Layout
15477 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15480 \begin_layout Plain Layout
15481 \begin_inset Formula $\coprod$
15491 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15494 \begin_layout Plain Layout
15502 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15505 \begin_layout Plain Layout
15506 \begin_inset Formula $\bigodot$
15516 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15519 \begin_layout Plain Layout
15527 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15530 \begin_layout Plain Layout
15531 \begin_inset Formula $\bigotimes$
15541 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15544 \begin_layout Plain Layout
15552 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15555 \begin_layout Plain Layout
15556 \begin_inset Formula $\bigoplus$
15566 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15569 \begin_layout Plain Layout
15577 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15580 \begin_layout Plain Layout
15581 \begin_inset Formula $\bigwedge$
15591 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15594 \begin_layout Plain Layout
15602 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15605 \begin_layout Plain Layout
15606 \begin_inset Formula $\bigvee$
15616 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15619 \begin_layout Plain Layout
15627 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15630 \begin_layout Plain Layout
15631 \begin_inset Formula $\bigsqcup$
15641 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15644 \begin_layout Plain Layout
15652 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15655 \begin_layout Plain Layout
15656 \begin_inset Formula $\biguplus$
15670 \begin_inset space \hfill{}
15676 \begin_layout Standard
15677 All big operators can also be inserted via the math toolbar button
15678 \begin_inset Graphics
15679 filename ../images/math/intop.png
15687 \begin_layout Standard
15688 The operators are called big because they are bigger than the sometimes
15689 equal looking binary operators.
15690 All big operators can have limits as described in the next subsection.
15693 \begin_layout Standard
15694 For all integral operators there is a second version available, ending on
15712 These operators are different from
15719 \begin_inset space \space{}
15722 in the style the operator limits are displayed, see
15723 \begin_inset CommandInset ref
15725 reference "sub:Operator-Limits"
15733 \begin_layout Subsubsection*
15734 Advice for Integrals
15737 \begin_layout Standard
15742 in an integral is an operator, that therefore has to be set upright.
15743 This is done by highlighting the
15747 and using the keyboard shortcut
15757 \begin_layout Plain Layout
15763 \begin_inset CommandInset ref
15765 reference "sub:Font-Styles"
15775 Finally the smallest space is inserted before the
15779 , as this is usual for operators.
15783 \begin_layout Standard
15785 \begin_inset Formula $\int A(x)dx$
15789 \begin_inset Newline newline
15793 \begin_inset Phantom HPhantom
15796 \begin_layout Plain Layout
15803 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15809 \begin_layout Standard
15810 For multiple integrals there are the following commands:
15811 \begin_inset VSpace medskip
15817 \begin_layout Standard
15818 \begin_inset space \hfill{}
15822 \begin_inset Tabular
15823 <lyxtabular version="3" rows="4" columns="2">
15824 <features tabularvalignment="middle">
15825 <column alignment="center" valignment="top" width="0">
15826 <column alignment="center" valignment="top" width="0">
15828 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15831 \begin_layout Plain Layout
15837 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15840 \begin_layout Plain Layout
15842 \begin_inset Note Note
15845 \begin_layout Plain Layout
15852 is only used as spacer.
15864 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15867 \begin_layout Plain Layout
15875 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15878 \begin_layout Plain Layout
15879 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
15889 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15892 \begin_layout Plain Layout
15900 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15903 \begin_layout Plain Layout
15904 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
15914 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15917 \begin_layout Plain Layout
15925 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15928 \begin_layout Plain Layout
15929 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
15943 \begin_inset space \hfill{}
15947 \begin_inset Tabular
15948 <lyxtabular version="3" rows="4" columns="2">
15949 <features tabularvalignment="middle">
15950 <column alignment="center" valignment="top" width="0">
15951 <column alignment="center" valignment="top" width="0">
15953 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15956 \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
15973 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15976 \begin_layout Plain Layout
15984 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15987 \begin_layout Plain Layout
15988 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
15998 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16001 \begin_layout Plain Layout
16009 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16012 \begin_layout Plain Layout
16013 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
16023 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16026 \begin_layout Plain Layout
16034 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16037 \begin_layout Plain Layout
16038 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
16052 \begin_inset space \hfill{}
16058 \begin_layout Subsection
16060 \begin_inset CommandInset label
16062 name "sub:Operator-Limits"
16067 \begin_inset Index idx
16070 \begin_layout Plain Layout
16079 \begin_layout Standard
16080 Limits are created by super- and subscripts:
16083 \begin_layout Standard
16085 \begin_inset Tabular
16086 <lyxtabular version="3" rows="2" columns="2">
16087 <features tabularvalignment="middle">
16088 <column alignment="center" valignment="top" width="0pt">
16089 <column alignment="center" valignment="top" width="0pt">
16091 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16094 \begin_layout Plain Layout
16100 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16103 \begin_layout Plain Layout
16105 \begin_inset Note Note
16108 \begin_layout Plain Layout
16115 is only used as spacer.
16127 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16130 \begin_layout Plain Layout
16139 \begin_layout Plain Layout
16149 \begin_inset Formula $\to$
16153 \begin_inset Formula $\to$
16161 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16164 \begin_layout Plain Layout
16165 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
16181 \begin_layout Standard
16182 Limits of inline formulas are set right beside the operator.
16183 Limits in displayed formulas are set above or below the operator, except
16184 for integral limits.
16187 \begin_layout Standard
16188 To force that the limits are set beside the operator, the cursor is set
16189 directly behind the operator and the limits type is changed with the menu
16192 Edit\SpecialChar \menuseparator
16193 Math\SpecialChar \menuseparator
16212 \begin_layout Standard
16213 The default limits type is this:
16214 \begin_inset Formula \[
16215 \sum_{x=0}^{\infty}\frac{1}{x^{2}}\]
16219 This is how it looks when the limits type was changed to
16226 \begin_inset Formula \[
16227 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}\]
16231 For integrals, except those ending with
16247 etc., the limits are by default set beside the operator.
16248 But for multiple integrals the limits are often set below the operator.
16249 In the following example the limits type was therefore set to
16253 and so set below the integrals:
16254 \begin_inset Formula \begin{equation}
16255 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}\end{equation}
16262 \begin_layout Standard
16263 \begin_inset VSpace medskip
16266 To specify conditions for limits, the commands
16273 \begin_inset Index idx
16276 \begin_layout Plain Layout
16291 \begin_inset Index idx
16294 \begin_layout Plain Layout
16303 To create for example this expression
16304 \begin_inset Formula \begin{equation}
16305 \sum_{\begin{subarray}{c}
16309 \end{subarray}}^{n}k^{-2}\label{eq:substack}\end{equation}
16316 \begin_layout Standard
16317 the following has to be done:
16318 \begin_inset Newline newline
16333 \begin_layout Plain Layout
16345 One is now in a blue box under the summation operator and insert there
16354 \begin_layout Plain Layout
16366 The blue box is now within a purple box and now several lines can be written
16368 A new line is created by inserting a line break (
16371 arg "newline-insert newline"
16376 \begin_inset Newline newline
16381 0<k<1000 Ctrl+Return
16382 \begin_inset Newline newline
16387 is typed in, a new box appears below for the new line.
16390 \begin_layout Standard
16391 The alignment of the lines can be changed to left aligned with the
16401 Edit\SpecialChar \menuseparator
16405 To get right alignment,
16413 \begin_layout Plain Layout
16424 is inserted at the beginning of the line.
16427 \begin_layout Standard
16440 with the difference that the lines are always centered.
16443 \begin_layout Standard
16444 \begin_inset VSpace bigskip
16448 \begin_inset CommandInset ref
16450 reference "eq:substack"
16454 there can be too much space beside an operator, because the characters
16455 following the operator are set beside the limits.
16458 \begin_layout Standard
16459 To avoid this, the following macro can be used in the LaTeX-preamble:
16462 \begin_layout Standard
16476 \begin_inset Newline newline
16488 \begin_inset Newline newline
16495 mathclapinternal #1#2{
16499 mathsurround =0pt #1{#2}$}}
16502 \begin_layout Standard
16503 This defines the command
16510 \begin_inset Index idx
16513 \begin_layout Plain Layout
16521 that sets the width of the limit to 0
16522 \begin_inset space \thinspace{}
16526 The command scheme is
16529 \begin_layout Standard
16537 \begin_layout Standard
16538 where the limit can consist of several conditions.
16541 \begin_layout Standard
16543 \begin_inset CommandInset ref
16545 reference "eq:substack"
16549 , one uses the command
16552 \begin_layout Standard
16565 \begin_layout Plain Layout
16574 0<k<1000 Ctrl+Return
16577 \begin_layout Standard
16578 to create the lower limit.
16579 The summand is now directly behind the summation operator:
16580 \begin_inset Formula \[
16581 \sum_{\mathclap{\substack{0<k<1000\\
16592 \begin_layout Standard
16593 \begin_inset VSpace bigskip
16596 How to use one limit for several operators is described in
16597 \begin_inset CommandInset ref
16599 reference "sub:Self-defined-Operators"
16606 \begin_layout Subsection
16608 \begin_inset CommandInset label
16610 name "sub:Binary-Operators"
16615 \begin_inset Index idx
16618 \begin_layout Plain Layout
16627 \begin_layout Standard
16628 Binary operators are surrounded by space when there is a character before
16630 \begin_inset VSpace medskip
16636 \begin_layout Standard
16637 \begin_inset space \hfill{}
16641 \begin_inset Tabular
16642 <lyxtabular version="3" rows="13" columns="2">
16643 <features tabularvalignment="middle">
16644 <column alignment="center" valignment="top" width="0pt">
16645 <column alignment="center" valignment="top" width="0pt">
16647 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16650 \begin_layout Plain Layout
16652 \begin_inset Note Note
16655 \begin_layout Plain Layout
16662 is only used as spacer.
16672 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16675 \begin_layout Plain Layout
16683 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16686 \begin_layout Plain Layout
16692 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16695 \begin_layout Plain Layout
16696 \begin_inset Formula $+$
16706 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16709 \begin_layout Plain Layout
16715 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16718 \begin_layout Plain Layout
16719 \begin_inset Formula $-$
16729 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16732 \begin_layout Plain Layout
16740 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16743 \begin_layout Plain Layout
16744 \begin_inset Formula $\pm$
16754 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16757 \begin_layout Plain Layout
16765 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16768 \begin_layout Plain Layout
16769 \begin_inset Formula $\mp$
16779 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16782 \begin_layout Plain Layout
16790 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16793 \begin_layout Plain Layout
16794 \begin_inset Formula $\cdot$
16804 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16807 \begin_layout Plain Layout
16815 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16818 \begin_layout Plain Layout
16819 \begin_inset Formula $\times$
16829 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16832 \begin_layout Plain Layout
16840 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16843 \begin_layout Plain Layout
16844 \begin_inset Formula $\div$
16854 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16857 \begin_layout Plain Layout
16861 \begin_layout Plain Layout
16874 \begin_layout Plain Layout
16886 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16889 \begin_layout Plain Layout
16890 \begin_inset Formula $*$
16900 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16903 \begin_layout Plain Layout
16911 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16914 \begin_layout Plain Layout
16915 \begin_inset Formula $\star$
16925 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16928 \begin_layout Plain Layout
16936 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16939 \begin_layout Plain Layout
16940 \begin_inset Formula $\circ$
16950 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16953 \begin_layout Plain Layout
16961 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16964 \begin_layout Plain Layout
16965 \begin_inset Formula $\diamond$
16975 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16978 \begin_layout Plain Layout
16986 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16989 \begin_layout Plain Layout
16990 \begin_inset Formula $\bullet$
17004 \begin_inset space \hfill{}
17008 \begin_inset Tabular
17009 <lyxtabular version="3" rows="13" columns="2">
17010 <features tabularvalignment="middle">
17011 <column alignment="center" valignment="top" width="0pt">
17012 <column alignment="center" valignment="top" width="0pt">
17014 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17017 \begin_layout Plain Layout
17023 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17026 \begin_layout Plain Layout
17034 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17037 \begin_layout Plain Layout
17045 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17048 \begin_layout Plain Layout
17049 \begin_inset Formula $\nabla$
17059 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17062 \begin_layout Plain Layout
17070 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17073 \begin_layout Plain Layout
17074 \begin_inset Formula $\bigtriangledown$
17084 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17087 \begin_layout Plain Layout
17095 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17098 \begin_layout Plain Layout
17099 \begin_inset Formula $\bigtriangleup$
17109 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17112 \begin_layout Plain Layout
17120 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17123 \begin_layout Plain Layout
17124 \begin_inset Formula $\Box$
17134 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17137 \begin_layout Plain Layout
17145 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17148 \begin_layout Plain Layout
17149 \begin_inset Formula $\cap$
17159 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17162 \begin_layout Plain Layout
17170 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17173 \begin_layout Plain Layout
17174 \begin_inset Formula $\cup$
17184 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17187 \begin_layout Plain Layout
17195 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17198 \begin_layout Plain Layout
17199 \begin_inset Formula $\dagger$
17209 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17212 \begin_layout Plain Layout
17220 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17223 \begin_layout Plain Layout
17224 \begin_inset Formula $\ddagger$
17234 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17237 \begin_layout Plain Layout
17245 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17248 \begin_layout Plain Layout
17249 \begin_inset Formula $\wr$
17259 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17262 \begin_layout Plain Layout
17270 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17273 \begin_layout Plain Layout
17274 \begin_inset Formula $\bigcirc$
17284 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17287 \begin_layout Plain Layout
17295 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17298 \begin_layout Plain Layout
17299 \begin_inset Formula $\wedge$
17309 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17312 \begin_layout Plain Layout
17320 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17323 \begin_layout Plain Layout
17324 \begin_inset Formula $\vee$
17338 \begin_inset space \hfill{}
17342 \begin_inset Tabular
17343 <lyxtabular version="3" rows="13" columns="2">
17344 <features tabularvalignment="middle">
17345 <column alignment="center" valignment="top" width="0pt">
17346 <column alignment="center" valignment="top" width="0pt">
17348 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17351 \begin_layout Plain Layout
17357 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17360 \begin_layout Plain Layout
17368 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17371 \begin_layout Plain Layout
17379 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17382 \begin_layout Plain Layout
17383 \begin_inset Formula $\oplus$
17393 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17396 \begin_layout Plain Layout
17404 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17407 \begin_layout Plain Layout
17408 \begin_inset Formula $\ominus$
17418 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17421 \begin_layout Plain Layout
17429 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17432 \begin_layout Plain Layout
17433 \begin_inset Formula $\otimes$
17443 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17446 \begin_layout Plain Layout
17454 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17457 \begin_layout Plain Layout
17458 \begin_inset Formula $\oslash$
17468 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17471 \begin_layout Plain Layout
17479 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17482 \begin_layout Plain Layout
17483 \begin_inset Formula $\odot$
17493 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17496 \begin_layout Plain Layout
17504 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17507 \begin_layout Plain Layout
17508 \begin_inset Formula $\amalg$
17518 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17521 \begin_layout Plain Layout
17529 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17532 \begin_layout Plain Layout
17533 \begin_inset Formula $\uplus$
17543 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17546 \begin_layout Plain Layout
17554 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17557 \begin_layout Plain Layout
17558 \begin_inset Formula $\setminus$
17568 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17571 \begin_layout Plain Layout
17579 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17582 \begin_layout Plain Layout
17583 \begin_inset Formula $\sqcap$
17593 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17596 \begin_layout Plain Layout
17604 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17607 \begin_layout Plain Layout
17608 \begin_inset Formula $\sqcup$
17618 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17621 \begin_layout Plain Layout
17629 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17632 \begin_layout Plain Layout
17633 \begin_inset Formula $\triangleleft$
17643 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17646 \begin_layout Plain Layout
17654 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17657 \begin_layout Plain Layout
17658 \begin_inset Formula $\triangleright$
17672 \begin_inset space \hfill{}
17678 \begin_layout Standard
17679 All binary operators can also be inserted via the math toolbar button
17680 \begin_inset Graphics
17681 filename ../images/math/pm.png
17689 \begin_layout Standard
17690 To typeset the Laplace operator also
17707 \begin_inset Formula $\nabla^{2}$
17710 ) can be used instead of
17719 \begin_layout Standard
17726 Insert\SpecialChar \menuseparator
17738 \begin_layout Subsection
17739 Self-defined Operators
17740 \begin_inset CommandInset label
17742 name "sub:Self-defined-Operators"
17747 \begin_inset Index idx
17750 \begin_layout Plain Layout
17751 Operators ! self-defined
17759 \begin_layout Standard
17760 With the help of the command
17764 DeclareMathOperator
17767 \begin_inset Index idx
17770 \begin_layout Plain Layout
17775 DeclareMathOperator
17780 custom operators can be defined in the LaTeX-preamble.
17781 Its command scheme is:
17784 \begin_layout Standard
17789 DeclareMathOperator{new command}{display}
17792 \begin_layout Standard
17793 Display can be characters or symbols that define how the operator looks
17795 To define a big operator a * is set behind the command.
17796 All self-defined big operators can have limits as described in
17797 \begin_inset CommandInset ref
17799 reference "sub:Operator-Limits"
17806 \begin_layout Standard
17807 For example the LaTeX-preamble line
17810 \begin_layout Standard
17815 DeclareMathOperator*{
17822 \begin_layout Standard
17823 defines the command
17829 , that inserts a big operator consisting of the lozenge symbol from
17830 \begin_inset CommandInset ref
17832 reference "sub:Miscellaneous-Symbols"
17837 \begin_inset Formula \[
17838 \Lozenge_{n=1}^{\infty}\]
17842 The command for this formula is:
17853 \begin_inset Formula $\to$
17859 \begin_layout Standard
17860 \begin_inset VSpace bigskip
17863 When self-defined operators are not used several times in the document,
17864 they can also be defined with the commands
17871 \begin_inset Index idx
17874 \begin_layout Plain Layout
17889 \begin_inset Index idx
17892 \begin_layout Plain Layout
17900 , which have the following scheme:
17903 \begin_layout Standard
17917 \begin_layout Standard
17924 defines big operators,
17933 \begin_layout Standard
17941 \begin_inset space \thinspace{}
17945 \begin_inset space \space{}
17948 be used to use one limit for several operators:
17951 \begin_layout Standard
17952 \begin_inset Formula \[
17953 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}\]
17960 \begin_layout Standard
17961 The command for the formula above is:
17962 \begin_inset Newline newline
17981 \begin_layout Plain Layout
17993 \begin_inset Formula $\to$
18002 \begin_layout Plain Layout
18016 \begin_layout Section
18018 \begin_inset Index idx
18021 \begin_layout Plain Layout
18030 \begin_layout Subsection
18032 \begin_inset CommandInset label
18034 name "sub:Font-Styles"
18039 \begin_inset Index idx
18042 \begin_layout Plain Layout
18051 \begin_layout Standard
18052 Latin letters in formulas can be set in one of the following font styles:
18053 \begin_inset VSpace -2mm
18059 \begin_layout Standard
18061 \begin_inset Tabular
18062 <lyxtabular version="3" rows="7" columns="3">
18063 <features tabularvalignment="middle">
18064 <column alignment="center" valignment="top" width="0">
18065 <column alignment="center" valignment="top" width="0">
18066 <column alignment="center" valignment="top" width="0">
18068 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18071 \begin_layout Plain Layout
18077 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18080 \begin_layout Plain Layout
18086 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18089 \begin_layout Plain Layout
18097 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18100 \begin_layout Plain Layout
18109 \begin_layout Plain Layout
18125 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18128 \begin_layout Plain Layout
18129 \begin_inset Formula $\mathbb{ABC}$
18137 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18140 \begin_layout Plain Layout
18153 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18156 \begin_layout Plain Layout
18165 \begin_layout Plain Layout
18181 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18184 \begin_layout Plain Layout
18185 \begin_inset Formula $\mathbf{AbC}$
18193 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18196 \begin_layout Plain Layout
18209 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18212 \begin_layout Plain Layout
18221 \begin_layout Plain Layout
18237 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18240 \begin_layout Plain Layout
18241 \begin_inset Formula $\boldsymbol{AbC}$
18249 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18252 \begin_layout Plain Layout
18255 arg "font-boldsymbol"
18265 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18268 \begin_layout Plain Layout
18277 \begin_layout Plain Layout
18293 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18296 \begin_layout Plain Layout
18297 \begin_inset Formula $\mathcal{ABC}$
18305 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18308 \begin_layout Plain Layout
18321 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18324 \begin_layout Plain Layout
18333 \begin_layout Plain Layout
18349 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18352 \begin_layout Plain Layout
18353 \begin_inset Formula $\mathfrak{AbC}$
18361 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18364 \begin_layout Plain Layout
18372 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18375 \begin_layout Plain Layout
18384 \begin_layout Plain Layout
18400 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18403 \begin_layout Plain Layout
18404 \begin_inset Formula $\mathscr{AbC}$
18412 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18415 \begin_layout Plain Layout
18429 \begin_layout Standard
18431 \begin_inset Tabular
18432 <lyxtabular version="3" rows="5" columns="3">
18433 <features tabularvalignment="middle">
18434 <column alignment="center" valignment="top" width="0">
18435 <column alignment="center" valignment="top" width="0">
18436 <column alignment="center" valignment="top" width="0">
18438 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18441 \begin_layout Plain Layout
18447 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18450 \begin_layout Plain Layout
18456 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18459 \begin_layout Plain Layout
18467 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18470 \begin_layout Plain Layout
18479 \begin_layout Plain Layout
18495 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18498 \begin_layout Plain Layout
18499 \begin_inset Formula $\mathit{AbC}$
18507 <cell alignment="center" valignment="top" topline="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 $\mathrm{AbC}$
18558 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18561 \begin_layout Plain Layout
18574 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18577 \begin_layout Plain Layout
18586 \begin_layout Plain Layout
18602 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18605 \begin_layout Plain Layout
18606 \begin_inset Formula $\mathsf{AbC}$
18614 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18617 \begin_layout Plain Layout
18630 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18633 \begin_layout Plain Layout
18642 \begin_layout Plain Layout
18658 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18661 \begin_layout Plain Layout
18662 \begin_inset Formula $\mathtt{AbC}$
18670 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18673 \begin_layout Plain Layout
18676 arg "font-typewriter"
18692 \begin_layout Standard
18693 \begin_inset Note Greyedout
18696 \begin_layout Plain Layout
18713 can only be used for big letters.
18721 \begin_layout Standard
18722 Predefined is the style
18731 \begin_layout Standard
18732 The style commands work also for letters in mathematical constructs:
18733 \begin_inset Formula \[
18734 \mathfrak{A=\frac{b}{C}}\]
18741 \begin_layout Standard
18742 Characters in mathematical text don't appear in a math font style but in
18743 the text font style
18750 That their style can't be set correctly via the text style dialog is a
18755 \begin_layout Plain Layout
18756 \begin_inset CommandInset href
18758 name "LyX-bug #4629"
18759 target "http://www.lyx.org/trac/ticket/4629"
18771 \begin_layout Standard
18772 Instead of the style commands the dialog
18774 Edit\SpecialChar \menuseparator
18775 Math\SpecialChar \menuseparator
18778 or the toolbar button
18779 \begin_inset Graphics
18780 filename ../images/math/font.png
18788 \begin_layout Subsection
18790 \begin_inset CommandInset label
18792 name "sub:Bold-Formulas"
18797 \begin_inset Index idx
18800 \begin_layout Plain Layout
18809 \begin_layout Standard
18810 To make a complete formula bold, the command
18816 from the previous subsection cannot be used, because it doesn't work for
18817 small Greek letters.
18818 Furthermore it prints Latin letters always upright, like in the following
18822 \begin_layout Standard
18823 \begin_inset Formula \[
18824 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}\]
18831 \begin_layout Standard
18832 To display the formula correctly, the command
18839 \begin_inset Formula \[
18840 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}\]
18844 It is also possible to set the formula in a
18846 boldmath environment
18849 This environment is created by inserting the command
18856 \begin_inset Index idx
18859 \begin_layout Plain Layout
18868 To end the environment, the command
18875 \begin_inset Index idx
18878 \begin_layout Plain Layout
18886 is inserted in TeX-mode.
18890 \begin_layout Plain Layout
18900 \begin_inset Formula \[
18901 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}\]
18909 \begin_layout Plain Layout
18921 \begin_layout Subsection
18923 \begin_inset Index idx
18926 \begin_layout Plain Layout
18935 \begin_layout Standard
18936 Formulas can be colored like normal text: Highlight a formula or a formula
18942 Here is a formula in magenta:
18943 \begin_inset Formula \[
18944 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}\]
18951 \begin_layout Standard
18952 You can also define your own colors as described in
18953 \begin_inset CommandInset ref
18955 reference "sub:Colored-Boxes"
18960 They can be used with the TeX code command
18967 \begin_inset Index idx
18970 \begin_layout Plain Layout
18981 \begin_layout Standard
18986 textcolor{color}{characters or formula}
18989 \begin_layout Standard
18990 The following example was colored completely dark green and partly red:
18993 \begin_layout Standard
18997 \begin_layout Plain Layout
19001 textcolor{darkgreen}{
19007 \begin_inset Formula \[
19008 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}\]
19016 \begin_layout Plain Layout
19026 \begin_layout Standard
19027 Due to a bug in LyX only complete formulas can be colored with self-defined
19032 \begin_layout Plain Layout
19033 \begin_inset CommandInset href
19035 name "LyX-bug #5269"
19036 target "http://www.lyx.org/trac/ticket/5269"
19048 \begin_layout Subsection
19050 \begin_inset CommandInset label
19052 name "sub:Font-Sizes"
19057 \begin_inset Index idx
19060 \begin_layout Plain Layout
19069 \begin_layout Standard
19070 For characters in formulas there are, analog to characters in text, the
19071 following size commands:
19074 \begin_layout Standard
19118 \begin_inset Newline newline
19140 \begin_layout Standard
19141 The size produced by the commands depends on the document font size, that
19142 corresponds with the command
19149 The other commands produce smaller or larger sizes than
19156 The font size can however not exceed a certain value.
19157 Is for example the document font size 12
19158 \begin_inset space \thinspace{}
19167 switches to the same size as
19177 \begin_layout Standard
19178 A size command is inserted in TeX-mode before the formula and sets the size
19179 for all following formula and text characters.
19180 To switch back to the initial size, the command
19186 is inserted behind the formula in TeX-mode.
19189 \begin_layout Standard
19190 \begin_inset Newpage newpage
19196 \begin_layout Standard
19197 Within a formula the size can be changed using the following size commands:
19200 \begin_layout Standard
19203 \begin_inset Tabular
19204 <lyxtabular version="3" rows="5" columns="2">
19205 <features tabularvalignment="middle">
19206 <column alignment="center" valignment="top" width="0">
19207 <column alignment="center" valignment="top" width="0">
19209 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19212 \begin_layout Plain Layout
19218 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19221 \begin_layout Plain Layout
19223 \begin_inset Note Note
19226 \begin_layout Plain Layout
19233 is only used as spacer.
19245 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19248 \begin_layout Plain Layout
19252 \begin_inset Index idx
19255 \begin_layout Plain Layout
19268 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19271 \begin_layout Plain Layout
19272 \begin_inset Formula $\raisebox{6.5mm}{}{\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-5.5mm}{}$
19282 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19285 \begin_layout Plain Layout
19293 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19296 \begin_layout Plain Layout
19297 \begin_inset Formula $\raisebox{4.5mm}{}{\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-4mm}{}$
19307 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19310 \begin_layout Plain Layout
19318 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19321 \begin_layout Plain Layout
19322 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
19332 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19335 \begin_layout Plain Layout
19343 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19346 \begin_layout Plain Layout
19347 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
19363 \begin_layout Standard
19364 After entering these commands, a blue box appears in which the formula parts
19368 \begin_layout Standard
19369 There is a further method to change the font size, that though only works
19370 for symbols or letters in mathematical text.
19371 To use it, one of the above text size commands is inserted in mathematical
19373 All following characters until the end of the mathematical text or until
19374 another size command will have the selected size.
19376 \begin_inset VSpace -2mm
19382 \begin_layout Standard
19386 \begin_layout Plain Layout
19396 \begin_inset Formula \[
19397 A=\frac{B}{c}\cdot\maltese\]
19402 \begin_inset Formula \[
19403 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}\]
19411 \begin_layout Plain Layout
19423 \begin_layout Standard
19424 \begin_inset VSpace medskip
19427 Before both formulas the command
19434 The command for the second formula is:
19435 \begin_inset Newline newline
19446 \begin_layout Plain Layout
19461 \begin_layout Plain Layout
19476 \begin_layout Plain Layout
19491 \begin_layout Plain Layout
19501 \begin_inset Formula $\to$
19505 \begin_inset Formula $\to$
19509 \begin_inset Newline newline
19513 \begin_inset space \hspace*{}
19527 \begin_layout Plain Layout
19542 \begin_layout Plain Layout
19557 \begin_layout Plain Layout
19569 \begin_layout Standard
19570 If a symbol cannot be displayed in different sizes, it will always be displayed
19571 in the default size.
19574 \begin_layout Standard
19575 \begin_inset Newpage newpage
19581 \begin_layout Section
19583 \begin_inset Index idx
19586 \begin_layout Plain Layout
19595 \begin_layout Standard
19596 All Greek letters can also be inserted via the toolbar button
19597 \begin_inset Graphics
19598 filename ../images/math/alpha.png
19606 \begin_layout Subsection
19608 \begin_inset Index idx
19611 \begin_layout Plain Layout
19612 Greek letters ! small
19620 \begin_layout Standard
19621 \begin_inset space \hfill{}
19625 \begin_inset Tabular
19626 <lyxtabular version="3" rows="11" columns="2">
19627 <features tabularvalignment="middle">
19628 <column alignment="center" valignment="top" width="0pt">
19629 <column alignment="center" valignment="top" width="0pt">
19631 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19634 \begin_layout Plain Layout
19640 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19643 \begin_layout Plain Layout
19651 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19654 \begin_layout Plain Layout
19662 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19665 \begin_layout Plain Layout
19666 \begin_inset Formula $\alpha$
19676 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19679 \begin_layout Plain Layout
19687 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19690 \begin_layout Plain Layout
19691 \begin_inset Formula $\beta$
19701 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19704 \begin_layout Plain Layout
19712 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19715 \begin_layout Plain Layout
19716 \begin_inset Formula $\gamma$
19726 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19729 \begin_layout Plain Layout
19737 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19740 \begin_layout Plain Layout
19741 \begin_inset Formula $\delta$
19751 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19754 \begin_layout Plain Layout
19762 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19765 \begin_layout Plain Layout
19766 \begin_inset Formula $\epsilon$
19776 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19779 \begin_layout Plain Layout
19787 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19790 \begin_layout Plain Layout
19791 \begin_inset Formula $\varepsilon$
19801 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19804 \begin_layout Plain Layout
19812 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19815 \begin_layout Plain Layout
19816 \begin_inset Formula $\zeta$
19826 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19829 \begin_layout Plain Layout
19837 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19840 \begin_layout Plain Layout
19841 \begin_inset Formula $\eta$
19851 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19854 \begin_layout Plain Layout
19862 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19865 \begin_layout Plain Layout
19866 \begin_inset Formula $\theta$
19876 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19879 \begin_layout Plain Layout
19887 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19890 \begin_layout Plain Layout
19891 \begin_inset Formula $\vartheta$
19905 \begin_inset space \hfill{}
19909 \begin_inset Tabular
19910 <lyxtabular version="3" rows="12" columns="2">
19911 <features tabularvalignment="middle">
19912 <column alignment="center" valignment="top" width="0pt">
19913 <column alignment="center" valignment="top" width="0pt">
19915 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19918 \begin_layout Plain Layout
19924 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19927 \begin_layout Plain Layout
19935 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19938 \begin_layout Plain Layout
19946 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19949 \begin_layout Plain Layout
19950 \begin_inset Formula $\iota$
19960 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19963 \begin_layout Plain Layout
19971 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19974 \begin_layout Plain Layout
19975 \begin_inset Formula $\kappa$
19985 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19988 \begin_layout Plain Layout
19996 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19999 \begin_layout Plain Layout
20000 \begin_inset Formula $\varkappa$
20010 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20013 \begin_layout Plain Layout
20021 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20024 \begin_layout Plain Layout
20025 \begin_inset Formula $\lambda$
20035 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20038 \begin_layout Plain Layout
20046 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20049 \begin_layout Plain Layout
20050 \begin_inset Formula $\mu$
20060 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20063 \begin_layout Plain Layout
20071 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20074 \begin_layout Plain Layout
20075 \begin_inset Formula $\nu$
20085 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20088 \begin_layout Plain Layout
20096 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20099 \begin_layout Plain Layout
20100 \begin_inset Formula $\xi$
20110 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20113 \begin_layout Plain Layout
20119 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20122 \begin_layout Plain Layout
20123 \begin_inset Formula $o$
20133 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20136 \begin_layout Plain Layout
20144 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20147 \begin_layout Plain Layout
20148 \begin_inset Formula $\pi$
20158 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20161 \begin_layout Plain Layout
20169 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20172 \begin_layout Plain Layout
20173 \begin_inset Formula $\varpi$
20183 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20186 \begin_layout Plain Layout
20194 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20197 \begin_layout Plain Layout
20198 \begin_inset Formula $\rho$
20212 \begin_inset space \hfill{}
20216 \begin_inset Tabular
20217 <lyxtabular version="3" rows="11" columns="2">
20218 <features tabularvalignment="middle">
20219 <column alignment="center" valignment="top" width="0pt">
20220 <column alignment="center" valignment="top" width="0pt">
20222 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20225 \begin_layout Plain Layout
20231 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20234 \begin_layout Plain Layout
20242 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20245 \begin_layout Plain Layout
20253 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20256 \begin_layout Plain Layout
20257 \begin_inset Formula $\varrho$
20267 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20270 \begin_layout Plain Layout
20278 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20281 \begin_layout Plain Layout
20282 \begin_inset Formula $\sigma$
20292 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20295 \begin_layout Plain Layout
20303 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20306 \begin_layout Plain Layout
20307 \begin_inset Formula $\varsigma$
20317 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20320 \begin_layout Plain Layout
20328 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20331 \begin_layout Plain Layout
20332 \begin_inset Formula $\tau$
20342 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20345 \begin_layout Plain Layout
20353 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20356 \begin_layout Plain Layout
20357 \begin_inset Formula $\upsilon$
20367 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20370 \begin_layout Plain Layout
20378 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20381 \begin_layout Plain Layout
20382 \begin_inset Formula $\phi$
20392 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20395 \begin_layout Plain Layout
20403 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20406 \begin_layout Plain Layout
20407 \begin_inset Formula $\varphi$
20417 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20420 \begin_layout Plain Layout
20428 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20431 \begin_layout Plain Layout
20432 \begin_inset Formula $\chi$
20442 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20445 \begin_layout Plain Layout
20453 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20456 \begin_layout Plain Layout
20457 \begin_inset Formula $\psi$
20467 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20470 \begin_layout Plain Layout
20478 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20481 \begin_layout Plain Layout
20482 \begin_inset Formula $\omega$
20496 \begin_inset space \hfill{}
20502 \begin_layout Standard
20503 \begin_inset VSpace medskip
20509 \begin_layout Standard
20510 How to create upright Greek letters is explained in
20511 \begin_inset CommandInset ref
20513 reference "sub:Upright-small-Greek"
20520 \begin_layout Subsection
20522 \begin_inset Index idx
20525 \begin_layout Plain Layout
20526 Greek letters ! big
20534 \begin_layout Standard
20535 \begin_inset space \hfill{}
20539 \begin_inset Tabular
20540 <lyxtabular version="3" rows="7" columns="2">
20541 <features tabularvalignment="middle">
20542 <column alignment="center" valignment="top" width="0pt">
20543 <column alignment="center" valignment="top" width="0pt">
20545 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20548 \begin_layout Plain Layout
20554 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20557 \begin_layout Plain Layout
20565 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20568 \begin_layout Plain Layout
20576 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20579 \begin_layout Plain Layout
20580 \begin_inset Formula $\Gamma$
20590 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20593 \begin_layout Plain Layout
20601 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20604 \begin_layout Plain Layout
20605 \begin_inset Formula $\Delta$
20615 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20618 \begin_layout Plain Layout
20626 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20629 \begin_layout Plain Layout
20630 \begin_inset Formula $\Theta$
20640 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20643 \begin_layout Plain Layout
20651 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20654 \begin_layout Plain Layout
20655 \begin_inset Formula $\Lambda$
20665 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20668 \begin_layout Plain Layout
20676 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20679 \begin_layout Plain Layout
20680 \begin_inset Formula $\Xi$
20690 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20693 \begin_layout Plain Layout
20701 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20704 \begin_layout Plain Layout
20705 \begin_inset Formula $\Pi$
20719 \begin_inset space \hfill{}
20723 \begin_inset Tabular
20724 <lyxtabular version="3" rows="6" columns="2">
20725 <features tabularvalignment="middle">
20726 <column alignment="center" valignment="top" width="0pt">
20727 <column alignment="center" valignment="top" width="0pt">
20729 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20732 \begin_layout Plain Layout
20738 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20741 \begin_layout Plain Layout
20749 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20752 \begin_layout Plain Layout
20760 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20763 \begin_layout Plain Layout
20764 \begin_inset Formula $\Sigma$
20774 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20777 \begin_layout Plain Layout
20785 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20788 \begin_layout Plain Layout
20789 \begin_inset Formula $\Upsilon$
20799 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20802 \begin_layout Plain Layout
20810 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20813 \begin_layout Plain Layout
20814 \begin_inset Formula $\Phi$
20824 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20827 \begin_layout Plain Layout
20835 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20838 \begin_layout Plain Layout
20839 \begin_inset Formula $\Psi$
20849 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20852 \begin_layout Plain Layout
20860 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20863 \begin_layout Plain Layout
20864 \begin_inset Formula $\Omega$
20878 \begin_inset space \hfill{}
20884 \begin_layout Standard
20885 \begin_inset VSpace medskip
20888 That the big Greek letters appear upright is caused by a design bug when
20890 To get correct italic big letters, begin every command with
20895 For example the command
20902 \begin_inset Formula $\varGamma$
20908 \begin_layout Subsection
20910 \begin_inset Index idx
20913 \begin_layout Plain Layout
20914 Greek letters ! bold
20922 \begin_layout Standard
20923 Greek letters cannot be set with different font styles like Latin letters.
20924 They can only be made bold with the command
20931 \begin_inset Index idx
20934 \begin_layout Plain Layout
20945 \begin_layout Standard
20947 \begin_inset Tabular
20948 <lyxtabular version="3" rows="3" columns="2">
20949 <features tabularvalignment="middle">
20950 <column alignment="center" valignment="top" width="0">
20951 <column alignment="center" valignment="top" width="0">
20953 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20956 \begin_layout Plain Layout
20962 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20965 \begin_layout Plain Layout
20973 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20976 \begin_layout Plain Layout
20988 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20991 \begin_layout Plain Layout
20992 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
21002 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21005 \begin_layout Plain Layout
21017 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21020 \begin_layout Plain Layout
21021 \begin_inset Formula $\theta\boldsymbol{\theta}$
21037 \begin_layout Section
21042 \begin_layout Plain Layout
21055 \begin_layout Plain Layout
21056 A list with all symbols of most of the LaTeX-packages can be found in
21057 \begin_inset CommandInset citation
21072 \begin_layout Plain Layout
21080 \begin_inset Note Note
21083 \begin_layout Plain Layout
21086 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
21089 \begin_layout Plain Layout
21092 texorpdfstring is in section
21093 \begin_inset CommandInset ref
21095 reference "sub:Formulas-in-Section"
21105 \begin_inset Index idx
21108 \begin_layout Plain Layout
21117 \begin_layout Standard
21118 Many of the symbols listed in this section can also be inserted via the
21120 \begin_inset Graphics
21121 filename ../images/math/nabla.png
21127 \begin_inset Graphics
21128 filename ../images/math/digamma.png
21136 \begin_layout Subsection
21137 Mathematical Symbols
21138 \begin_inset CommandInset label
21140 name "sub:Mathematical-Symbols"
21145 \begin_inset Index idx
21148 \begin_layout Plain Layout
21149 Symbols ! mathematical
21157 \begin_layout Standard
21158 \begin_inset space \hfill{}
21162 \begin_inset Tabular
21163 <lyxtabular version="3" rows="10" columns="2">
21164 <features tabularvalignment="middle">
21165 <column alignment="center" valignment="top" width="0pt">
21166 <column alignment="center" valignment="top" width="0pt">
21168 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21171 \begin_layout Plain Layout
21177 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21180 \begin_layout Plain Layout
21188 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21191 \begin_layout Plain Layout
21199 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21202 \begin_layout Plain Layout
21203 \begin_inset Formula $\neg$
21213 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21216 \begin_layout Plain Layout
21224 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21227 \begin_layout Plain Layout
21228 \begin_inset Formula $\Im$
21238 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21241 \begin_layout Plain Layout
21249 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21252 \begin_layout Plain Layout
21253 \begin_inset Formula $\Re$
21263 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21266 \begin_layout Plain Layout
21274 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21277 \begin_layout Plain Layout
21278 \begin_inset Formula $\aleph$
21288 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21291 \begin_layout Plain Layout
21299 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21302 \begin_layout Plain Layout
21303 \begin_inset Formula $\partial$
21313 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21316 \begin_layout Plain Layout
21324 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21327 \begin_layout Plain Layout
21328 \begin_inset Formula $\infty$
21338 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21341 \begin_layout Plain Layout
21349 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21352 \begin_layout Plain Layout
21353 \begin_inset Formula $\wp$
21363 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21366 \begin_layout Plain Layout
21374 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21377 \begin_layout Plain Layout
21378 \begin_inset Formula $\imath$
21388 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21391 \begin_layout Plain Layout
21399 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21402 \begin_layout Plain Layout
21403 \begin_inset Formula $\jmath$
21417 \begin_inset space \hfill{}
21421 \begin_inset Tabular
21422 <lyxtabular version="3" rows="10" columns="2">
21423 <features tabularvalignment="middle">
21424 <column alignment="center" valignment="top" width="0pt">
21425 <column alignment="center" valignment="top" width="0pt">
21427 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21430 \begin_layout Plain Layout
21436 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21439 \begin_layout Plain Layout
21441 \begin_inset Note Note
21444 \begin_layout Plain Layout
21451 is only used as spacer.
21463 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21466 \begin_layout Plain Layout
21474 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21477 \begin_layout Plain Layout
21478 \begin_inset Formula $\forall$
21488 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21491 \begin_layout Plain Layout
21499 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21502 \begin_layout Plain Layout
21503 \begin_inset Formula $\exists$
21513 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21516 \begin_layout Plain Layout
21524 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21527 \begin_layout Plain Layout
21528 \begin_inset Formula $\nexists$
21538 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21541 \begin_layout Plain Layout
21549 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21552 \begin_layout Plain Layout
21553 \begin_inset Formula $\emptyset$
21563 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21566 \begin_layout Plain Layout
21574 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21577 \begin_layout Plain Layout
21578 \begin_inset Formula $\varnothing$
21588 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21591 \begin_layout Plain Layout
21599 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21602 \begin_layout Plain Layout
21603 \begin_inset Formula $\dag$
21613 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21616 \begin_layout Plain Layout
21624 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21627 \begin_layout Plain Layout
21628 \begin_inset Formula $\ddag$
21638 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21641 \begin_layout Plain Layout
21649 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21652 \begin_layout Plain Layout
21656 \begin_layout Plain Layout
21666 \begin_inset Formula $\complement$
21673 \begin_layout Plain Layout
21687 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21690 \begin_layout Plain Layout
21698 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21701 \begin_layout Plain Layout
21702 \begin_inset Formula $\Bbbk$
21716 \begin_inset space \hfill{}
21720 \begin_inset Tabular
21721 <lyxtabular version="3" rows="10" columns="2">
21722 <features tabularvalignment="middle">
21723 <column alignment="center" valignment="top" width="0pt">
21724 <column alignment="center" valignment="top" width="0pt">
21726 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21729 \begin_layout Plain Layout
21735 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21738 \begin_layout Plain Layout
21746 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21749 \begin_layout Plain Layout
21757 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21760 \begin_layout Plain Layout
21761 \begin_inset Formula $\prime$
21771 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21774 \begin_layout Plain Layout
21782 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21785 \begin_layout Plain Layout
21786 \begin_inset Formula $\backprime$
21796 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21799 \begin_layout Plain Layout
21807 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21810 \begin_layout Plain Layout
21811 \begin_inset Formula $\mho$
21821 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21824 \begin_layout Plain Layout
21832 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21835 \begin_layout Plain Layout
21836 \begin_inset Formula $\triangle$
21846 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21849 \begin_layout Plain Layout
21857 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21860 \begin_layout Plain Layout
21861 \begin_inset Formula $\angle$
21871 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21874 \begin_layout Plain Layout
21882 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21885 \begin_layout Plain Layout
21886 \begin_inset Formula $\measuredangle$
21896 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21899 \begin_layout Plain Layout
21907 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21910 \begin_layout Plain Layout
21911 \begin_inset Formula $\sphericalangle$
21921 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21924 \begin_layout Plain Layout
21932 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21935 \begin_layout Plain Layout
21936 \begin_inset Formula $\top$
21946 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21949 \begin_layout Plain Layout
21957 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21960 \begin_layout Plain Layout
21961 \begin_inset Formula $\bot$
21975 \begin_inset space \hfill{}
21981 \begin_layout Subsection
21982 Miscellaneous Symbols
21983 \begin_inset CommandInset label
21985 name "sub:Miscellaneous-Symbols"
21990 \begin_inset Index idx
21993 \begin_layout Plain Layout
21994 Symbols ! miscellaneous
22002 \begin_layout Standard
22005 \begin_inset Tabular
22006 <lyxtabular version="3" rows="10" columns="2">
22007 <features tabularvalignment="middle">
22008 <column alignment="center" valignment="top" width="0pt">
22009 <column alignment="center" valignment="top" width="0pt">
22011 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22014 \begin_layout Plain Layout
22020 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22023 \begin_layout Plain Layout
22031 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22034 \begin_layout Plain Layout
22042 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22045 \begin_layout Plain Layout
22046 \begin_inset Formula $\flat$
22056 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22059 \begin_layout Plain Layout
22067 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22070 \begin_layout Plain Layout
22071 \begin_inset Formula $\natural$
22081 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22084 \begin_layout Plain Layout
22092 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22095 \begin_layout Plain Layout
22096 \begin_inset Formula $\sharp$
22106 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22109 \begin_layout Plain Layout
22117 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22120 \begin_layout Plain Layout
22121 \begin_inset Formula $\surd$
22131 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22134 \begin_layout Plain Layout
22142 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22145 \begin_layout Plain Layout
22146 \begin_inset Formula $\checkmark$
22156 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22159 \begin_layout Plain Layout
22167 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22170 \begin_layout Plain Layout
22171 \begin_inset Formula $\yen$
22181 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22184 \begin_layout Plain Layout
22192 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22195 \begin_layout Plain Layout
22196 \begin_inset Formula $\pounds$
22206 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22209 \begin_layout Plain Layout
22215 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22218 \begin_layout Plain Layout
22219 \begin_inset Formula $\$$
22229 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22232 \begin_layout Plain Layout
22238 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22241 \begin_layout Plain Layout
22242 \begin_inset Formula $§$
22256 \begin_inset Tabular
22257 <lyxtabular version="3" rows="10" columns="2">
22258 <features tabularvalignment="middle">
22259 <column alignment="center" valignment="top" width="0">
22260 <column alignment="center" valignment="top" width="0">
22262 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22265 \begin_layout Plain Layout
22271 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22274 \begin_layout Plain Layout
22282 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22285 \begin_layout Plain Layout
22293 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22296 \begin_layout Plain Layout
22297 \begin_inset Formula $\hbar$
22307 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22310 \begin_layout Plain Layout
22318 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22321 \begin_layout Plain Layout
22322 \begin_inset Formula $\hslash$
22332 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22335 \begin_layout Plain Layout
22343 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22346 \begin_layout Plain Layout
22347 \begin_inset Formula $\clubsuit$
22357 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22360 \begin_layout Plain Layout
22368 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22371 \begin_layout Plain Layout
22372 \begin_inset Formula $\spadesuit$
22382 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22385 \begin_layout Plain Layout
22393 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22396 \begin_layout Plain Layout
22397 \begin_inset Formula $\bigstar$
22407 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22410 \begin_layout Plain Layout
22418 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22421 \begin_layout Plain Layout
22422 \begin_inset Formula $\blacklozenge$
22432 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22435 \begin_layout Plain Layout
22443 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22446 \begin_layout Plain Layout
22447 \begin_inset Formula $\blacktriangle$
22457 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22460 \begin_layout Plain Layout
22468 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22471 \begin_layout Plain Layout
22472 \begin_inset Formula $\blacktriangledown$
22482 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22485 \begin_layout Plain Layout
22493 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22496 \begin_layout Plain Layout
22497 \begin_inset Formula $\bullet$
22511 \begin_inset Tabular
22512 <lyxtabular version="3" rows="10" columns="2">
22513 <features tabularvalignment="middle">
22514 <column alignment="center" valignment="top" width="0pt">
22515 <column alignment="center" valignment="top" width="0pt">
22517 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22520 \begin_layout Plain Layout
22526 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22529 \begin_layout Plain Layout
22537 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22540 \begin_layout Plain Layout
22548 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22551 \begin_layout Plain Layout
22552 \begin_inset Formula $\diamondsuit$
22562 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22565 \begin_layout Plain Layout
22573 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22576 \begin_layout Plain Layout
22577 \begin_inset Formula $\Diamond$
22587 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22590 \begin_layout Plain Layout
22598 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22601 \begin_layout Plain Layout
22602 \begin_inset Formula $\heartsuit$
22612 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22615 \begin_layout Plain Layout
22623 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22626 \begin_layout Plain Layout
22627 \begin_inset Formula $\P$
22637 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22640 \begin_layout Plain Layout
22648 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22651 \begin_layout Plain Layout
22652 \begin_inset Formula $\copyright$
22662 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22665 \begin_layout Plain Layout
22673 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22676 \begin_layout Plain Layout
22677 \begin_inset Formula $\circledR$
22687 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22690 \begin_layout Plain Layout
22698 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22701 \begin_layout Plain Layout
22702 \begin_inset Formula $\maltese$
22712 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22715 \begin_layout Plain Layout
22723 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22726 \begin_layout Plain Layout
22727 \begin_inset Formula $\diagup$
22737 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22740 \begin_layout Plain Layout
22748 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22751 \begin_layout Plain Layout
22752 \begin_inset Formula $\diagdown$
22768 \begin_layout Standard
22769 \begin_inset VSpace medskip
22772 More symbols are listed in
22773 \begin_inset CommandInset ref
22775 reference "sub:Miscellaneous-special-Characters"
22782 \begin_layout Standard
22783 Some symbols can be displayed in different sizes, see
22784 \begin_inset CommandInset ref
22786 reference "sub:Font-Sizes"
22793 \begin_layout Subsection
22795 \begin_inset Index idx
22798 \begin_layout Plain Layout
22799 Symbols ! Euro-symbol
22805 \begin_inset Index idx
22808 \begin_layout Plain Layout
22815 \begin_layout Plain Layout
22832 \begin_layout Standard
22833 To use the Euro symbol in formulas, the LaTeX-package
22838 \begin_inset Index idx
22841 \begin_layout Plain Layout
22847 must be installed and loaded with the LaTeX-preamble line
22850 \begin_layout Standard
22855 usepackage[gennarrow]{eurosym}
22858 \begin_layout Standard
22859 The Euro symbol can now be inserted with the command
22866 \begin_inset Index idx
22869 \begin_layout Plain Layout
22880 \begin_layout Standard
22881 The Euro symbol can directly be inserted with the € key in mathematical
22882 text, without having
22897 can also be inserted in TeX-mode.
22898 The official currency symbol can then be inserted with the command
22905 \begin_inset Index idx
22908 \begin_layout Plain Layout
22916 , that is only available in TeX-mode.
22919 \begin_layout Standard
22923 \begin_layout Plain Layout
22933 \begin_inset Note Note
22936 \begin_layout Plain Layout
22937 The following table will only be displayed when the LaTeX-package
22949 \begin_layout Standard
22950 An overview about the different Euro symbols:
22953 \begin_layout Standard
22955 \begin_inset Tabular
22956 <lyxtabular version="3" rows="4" columns="3">
22957 <features tabularvalignment="middle">
22958 <column alignment="center" valignment="top" width="0pt">
22959 <column alignment="center" valignment="top" width="0pt">
22960 <column alignment="center" valignment="top" width="0pt">
22962 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
22965 \begin_layout Plain Layout
22971 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22974 \begin_layout Plain Layout
22980 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22983 \begin_layout Plain Layout
22991 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22994 \begin_layout Plain Layout
23000 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23003 \begin_layout Plain Layout
23011 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23014 \begin_layout Plain Layout
23015 \begin_inset Formula $\euro$
23025 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23028 \begin_layout Plain Layout
23034 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23037 \begin_layout Plain Layout
23043 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23046 \begin_layout Plain Layout
23047 \begin_inset Formula $\mbox{€}$
23057 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23060 \begin_layout Plain Layout
23066 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23069 \begin_layout Plain Layout
23077 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23080 \begin_layout Plain Layout
23084 \begin_layout Plain Layout
23106 \begin_layout Standard
23110 \begin_layout Plain Layout
23120 \begin_inset Note Note
23123 \begin_layout Plain Layout
23124 The following will be displayed when the LaTeX-package
23136 \begin_layout Standard
23137 You need to install the LaTeX-package
23141 to see the rest of this subsection in the output.
23144 \begin_layout Standard
23148 \begin_layout Plain Layout
23160 \begin_layout Section
23162 \begin_inset CommandInset label
23164 name "sec:Relations"
23169 \begin_inset Index idx
23172 \begin_layout Plain Layout
23179 \begin_inset Index idx
23182 \begin_layout Plain Layout
23187 \begin_layout Plain Layout
23198 \begin_layout Plain Layout
23213 \begin_layout Standard
23214 All relations can also be inserted via the toolbar button
23215 \begin_inset Graphics
23216 filename ../images/math/leq.png
23224 \begin_layout Standard
23225 \begin_inset space \hfill{}
23229 \begin_inset Tabular
23230 <lyxtabular version="3" rows="17" columns="2">
23231 <features tabularvalignment="middle">
23232 <column alignment="center" valignment="top" width="0pt">
23233 <column alignment="center" valignment="top" width="0pt">
23235 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23238 \begin_layout Plain Layout
23244 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23247 \begin_layout Plain Layout
23255 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23258 \begin_layout Plain Layout
23264 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23267 \begin_layout Plain Layout
23268 \begin_inset Formula $<$
23278 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23281 \begin_layout Plain Layout
23289 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23292 \begin_layout Plain Layout
23293 \begin_inset Formula $\le$
23303 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23306 \begin_layout Plain Layout
23314 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23317 \begin_layout Plain Layout
23318 \begin_inset Formula $\ll$
23328 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23331 \begin_layout Plain Layout
23339 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23342 \begin_layout Plain Layout
23343 \begin_inset Formula $\prec$
23353 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23356 \begin_layout Plain Layout
23364 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23367 \begin_layout Plain Layout
23368 \begin_inset Formula $\preceq$
23378 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23381 \begin_layout Plain Layout
23389 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23392 \begin_layout Plain Layout
23393 \begin_inset Formula $\subset$
23403 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23406 \begin_layout Plain Layout
23414 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23417 \begin_layout Plain Layout
23418 \begin_inset Formula $\subseteq$
23428 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23431 \begin_layout Plain Layout
23439 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23442 \begin_layout Plain Layout
23443 \begin_inset Formula $\sqsubseteq$
23453 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23456 \begin_layout Plain Layout
23464 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23467 \begin_layout Plain Layout
23468 \begin_inset Formula $\in$
23478 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23481 \begin_layout Plain Layout
23489 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23492 \begin_layout Plain Layout
23493 \begin_inset Formula $\vdash$
23503 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23506 \begin_layout Plain Layout
23514 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23517 \begin_layout Plain Layout
23518 \begin_inset Formula $\smile$
23528 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23531 \begin_layout Plain Layout
23539 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23542 \begin_layout Plain Layout
23543 \begin_inset Formula $\lhd$
23553 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23556 \begin_layout Plain Layout
23564 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23567 \begin_layout Plain Layout
23568 \begin_inset Formula $\unlhd$
23578 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23581 \begin_layout Plain Layout
23589 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23592 \begin_layout Plain Layout
23593 \begin_inset Formula $\gtrless$
23603 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23606 \begin_layout Plain Layout
23614 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23617 \begin_layout Plain Layout
23618 \begin_inset Formula $\mid$
23628 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23631 \begin_layout Plain Layout
23639 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23642 \begin_layout Plain Layout
23643 \begin_inset Formula $\nmid$
23657 \begin_inset space \hfill{}
23661 \begin_inset Tabular
23662 <lyxtabular version="3" rows="17" columns="2">
23663 <features tabularvalignment="middle">
23664 <column alignment="center" valignment="top" width="0pt">
23665 <column alignment="center" valignment="top" width="0pt">
23667 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23670 \begin_layout Plain Layout
23676 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23679 \begin_layout Plain Layout
23687 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23690 \begin_layout Plain Layout
23696 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23699 \begin_layout Plain Layout
23700 \begin_inset Formula $=$
23710 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23713 \begin_layout Plain Layout
23721 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23724 \begin_layout Plain Layout
23725 \begin_inset Formula $\not=$
23735 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23738 \begin_layout Plain Layout
23746 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23749 \begin_layout Plain Layout
23750 \begin_inset Formula $\equiv$
23760 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23763 \begin_layout Plain Layout
23771 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23774 \begin_layout Plain Layout
23775 \begin_inset Formula $\sim$
23785 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23788 \begin_layout Plain Layout
23796 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23799 \begin_layout Plain Layout
23800 \begin_inset Formula $\simeq$
23810 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23813 \begin_layout Plain Layout
23821 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23824 \begin_layout Plain Layout
23825 \begin_inset Formula $\approx$
23835 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23838 \begin_layout Plain Layout
23846 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23849 \begin_layout Plain Layout
23850 \begin_inset Formula $\cong$
23860 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23863 \begin_layout Plain Layout
23871 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23874 \begin_layout Plain Layout
23875 \begin_inset Formula $\bowtie$
23885 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23888 \begin_layout Plain Layout
23896 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23899 \begin_layout Plain Layout
23900 \begin_inset Formula $\notin$
23910 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23913 \begin_layout Plain Layout
23921 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23924 \begin_layout Plain Layout
23925 \begin_inset Formula $\perp$
23935 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23938 \begin_layout Plain Layout
23946 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23949 \begin_layout Plain Layout
23950 \begin_inset Formula $\propto$
23960 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23963 \begin_layout Plain Layout
23971 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23974 \begin_layout Plain Layout
23975 \begin_inset Formula $\asymp$
23985 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23988 \begin_layout Plain Layout
23996 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23999 \begin_layout Plain Layout
24000 \begin_inset Formula $\doteq$
24010 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24013 \begin_layout Plain Layout
24021 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24024 \begin_layout Plain Layout
24025 \begin_inset Formula $\circeq$
24035 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24038 \begin_layout Plain Layout
24046 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24049 \begin_layout Plain Layout
24050 \begin_inset Formula $\models$
24060 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24063 \begin_layout Plain Layout
24071 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24074 \begin_layout Plain Layout
24075 \begin_inset Formula $\widehat{=}$
24089 \begin_inset space \hfill{}
24093 \begin_inset Tabular
24094 <lyxtabular version="3" rows="17" columns="2">
24095 <features tabularvalignment="middle">
24096 <column alignment="center" valignment="top" width="0pt">
24097 <column alignment="center" valignment="top" width="0pt">
24099 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24102 \begin_layout Plain Layout
24108 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24111 \begin_layout Plain Layout
24119 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24122 \begin_layout Plain Layout
24128 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24131 \begin_layout Plain Layout
24132 \begin_inset Formula $>$
24142 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24145 \begin_layout Plain Layout
24153 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24156 \begin_layout Plain Layout
24157 \begin_inset Formula $\ge$
24167 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24170 \begin_layout Plain Layout
24178 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24181 \begin_layout Plain Layout
24182 \begin_inset Formula $\gg$
24192 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24195 \begin_layout Plain Layout
24203 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24206 \begin_layout Plain Layout
24207 \begin_inset Formula $\succ$
24217 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24220 \begin_layout Plain Layout
24228 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24231 \begin_layout Plain Layout
24232 \begin_inset Formula $\succeq$
24242 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24245 \begin_layout Plain Layout
24253 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24256 \begin_layout Plain Layout
24257 \begin_inset Formula $\supset$
24267 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24270 \begin_layout Plain Layout
24278 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24281 \begin_layout Plain Layout
24282 \begin_inset Formula $\supseteq$
24292 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24295 \begin_layout Plain Layout
24303 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24306 \begin_layout Plain Layout
24307 \begin_inset Formula $\sqsupseteq$
24317 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24320 \begin_layout Plain Layout
24328 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24331 \begin_layout Plain Layout
24332 \begin_inset Formula $\ni$
24342 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24345 \begin_layout Plain Layout
24353 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24356 \begin_layout Plain Layout
24357 \begin_inset Formula $\dashv$
24367 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24370 \begin_layout Plain Layout
24378 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24381 \begin_layout Plain Layout
24382 \begin_inset Formula $\frown$
24392 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24395 \begin_layout Plain Layout
24403 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24406 \begin_layout Plain Layout
24407 \begin_inset Formula $\rhd$
24417 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24420 \begin_layout Plain Layout
24428 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24431 \begin_layout Plain Layout
24432 \begin_inset Formula $\unrhd$
24442 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24445 \begin_layout Plain Layout
24453 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24456 \begin_layout Plain Layout
24457 \begin_inset Formula $\lessgtr$
24467 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24470 \begin_layout Plain Layout
24478 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24481 \begin_layout Plain Layout
24482 \begin_inset Formula $\parallel$
24492 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24495 \begin_layout Plain Layout
24503 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24506 \begin_layout Plain Layout
24507 \begin_inset Formula $\nparallel$
24521 \begin_inset space \hfill{}
24527 \begin_layout Standard
24528 \begin_inset VSpace medskip
24543 are bigger than the equal looking operators
24558 \begin_layout Standard
24559 Relations are, in contrary to symbols, always surrounded by space.
24562 \begin_layout Standard
24563 Relations with labels can be created with the command
24570 \begin_inset Index idx
24573 \begin_layout Plain Layout
24584 \begin_layout Standard
24586 \begin_inset Tabular
24587 <lyxtabular version="3" rows="2" columns="2">
24588 <features tabularvalignment="middle">
24589 <column alignment="center" valignment="top" width="0">
24590 <column alignment="center" valignment="top" width="0">
24592 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24595 \begin_layout Plain Layout
24601 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24604 \begin_layout Plain Layout
24606 \begin_inset Note Note
24609 \begin_layout Plain Layout
24616 is only used as spacer.
24628 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24631 \begin_layout Plain Layout
24638 \begin_layout Plain Layout
24655 \begin_layout Plain Layout
24665 \begin_inset Formula $\downarrow$
24674 \begin_layout Plain Layout
24687 \begin_layout Plain Layout
24701 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24704 \begin_layout Plain Layout
24705 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
24721 \begin_layout Section
24725 \begin_layout Subsection
24726 Predefined Functions
24727 \begin_inset CommandInset label
24729 name "sub:Predefined-Functions"
24734 \begin_inset Index idx
24737 \begin_layout Plain Layout
24738 Functions ! predefined
24746 \begin_layout Standard
24747 In general, variables are set
24751 in mathematical expressions, but not function names, because
24752 \begin_inset Formula $sin$
24755 could be misunderstood as
24756 \begin_inset Formula $s\cdot i\cdot n$
24760 Therefore there are predefined functions, that are additionally a bit separated
24762 They are inserted as commands starting with a backslash before their name.
24765 \begin_layout Standard
24767 \begin_inset Tabular
24768 <lyxtabular version="3" rows="2" columns="4">
24769 <features tabularvalignment="middle">
24770 <column alignment="center" valignment="top" width="0pt">
24771 <column alignment="center" valignment="top" width="0pt">
24772 <column alignment="center" valignment="top" width="0pt">
24773 <column alignment="center" valignment="top" width="0pt">
24775 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24778 \begin_layout Plain Layout
24784 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24787 \begin_layout Plain Layout
24793 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24796 \begin_layout Plain Layout
24802 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24805 \begin_layout Plain Layout
24813 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24816 \begin_layout Plain Layout
24822 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24825 \begin_layout Plain Layout
24826 \begin_inset Formula $Asin(x)+B$
24834 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24837 \begin_layout Plain Layout
24845 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24848 \begin_layout Plain Layout
24849 \begin_inset Formula $A\sin(x)+B$
24865 \begin_layout Standard
24866 The following functions are predefined:
24869 \begin_layout Standard
24870 \begin_inset VSpace -2mm
24876 \begin_layout Standard
24878 \begin_inset Tabular
24879 <lyxtabular version="3" rows="9" columns="4">
24880 <features tabularvalignment="middle">
24881 <column alignment="center" valignment="top" width="0pt">
24882 <column alignment="center" valignment="top" width="0pt">
24883 <column alignment="center" valignment="top" width="0pt">
24884 <column alignment="center" valignment="top" width="0pt">
24886 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24889 \begin_layout Plain Layout
24895 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24898 \begin_layout Plain Layout
24904 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24907 \begin_layout Plain Layout
24913 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24916 \begin_layout Plain Layout
24924 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24927 \begin_layout Plain Layout
24935 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24938 \begin_layout Plain Layout
24946 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24949 \begin_layout Plain Layout
24957 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24960 \begin_layout Plain Layout
24970 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24973 \begin_layout Plain Layout
24981 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24984 \begin_layout Plain Layout
24992 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24995 \begin_layout Plain Layout
25003 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25006 \begin_layout Plain Layout
25016 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25019 \begin_layout Plain Layout
25027 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25030 \begin_layout Plain Layout
25038 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25041 \begin_layout Plain Layout
25049 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25052 \begin_layout Plain Layout
25062 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25065 \begin_layout Plain Layout
25073 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25076 \begin_layout Plain Layout
25084 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25087 \begin_layout Plain Layout
25095 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25098 \begin_layout Plain Layout
25108 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25111 \begin_layout Plain Layout
25119 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25122 \begin_layout Plain Layout
25130 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25133 \begin_layout Plain Layout
25141 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25144 \begin_layout Plain Layout
25154 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25157 \begin_layout Plain Layout
25165 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25168 \begin_layout Plain Layout
25176 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25179 \begin_layout Plain Layout
25187 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25190 \begin_layout Plain Layout
25200 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25203 \begin_layout Plain Layout
25211 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25214 \begin_layout Plain Layout
25222 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25225 \begin_layout Plain Layout
25233 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25236 \begin_layout Plain Layout
25246 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25249 \begin_layout Plain Layout
25257 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25260 \begin_layout Plain Layout
25268 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25271 \begin_layout Plain Layout
25279 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25282 \begin_layout Plain Layout
25298 \begin_layout Standard
25299 They can also be inserted with the math toolbar button
25300 \begin_inset Graphics
25301 filename ../images/math/functions.png
25309 \begin_layout Subsection
25310 Self-defined Functions
25311 \begin_inset Index idx
25314 \begin_layout Plain Layout
25315 Functions ! self-defined
25323 \begin_layout Standard
25324 To use a function that is not predefined, like for example the sign function
25325 sgn(x), there are two possibilities:
25328 \begin_layout Itemize
25329 Define the function by inserting the following line to the LaTeX-preamble
25333 \begin_layout Plain Layout
25338 DeclareMathOperator
25341 \begin_inset CommandInset ref
25343 reference "sub:Self-defined-Operators"
25353 \begin_inset Newline newline
25357 \begin_inset VSpace -3mm
25361 \begin_inset Newline newline
25368 DeclareMathOperator{
25373 \begin_inset Index idx
25376 \begin_layout Plain Layout
25381 DeclareMathOperator
25387 \begin_inset Newline newline
25391 \begin_inset VSpace -2mm
25395 \begin_inset Newline newline
25398 Now the new defined function can be called with the command
25407 \begin_layout Itemize
25408 Write the formula as usual, mark the formula name, in our example the letters
25413 , and change it to mathematical text.
25414 At last a space is inserted between prefactor and function.
25417 \begin_layout Standard
25418 The result is the same with both methods as with a predefined function
25422 \begin_layout Plain Layout
25423 In LyX self-defined functions are displayed red, predefined ones black.
25431 \begin_layout Standard
25433 \begin_inset Tabular
25434 <lyxtabular version="3" rows="3" columns="2">
25435 <features tabularvalignment="middle">
25436 <column alignment="center" valignment="top" width="0pt">
25437 <column alignment="center" valignment="top" width="0pt">
25439 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25442 \begin_layout Plain Layout
25448 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25451 \begin_layout Plain Layout
25459 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25462 \begin_layout Plain Layout
25470 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25473 \begin_layout Plain Layout
25474 \begin_inset Formula $A\sgn(x)+B$
25484 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25487 \begin_layout Plain Layout
25491 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
25499 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25502 \begin_layout Plain Layout
25503 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
25519 \begin_layout Standard
25520 The first method is more suitable when the self-defined function should
25521 be used several times.
25524 \begin_layout Subsection
25526 \begin_inset Index idx
25529 \begin_layout Plain Layout
25538 \begin_layout Standard
25539 For limits there are defined besides
25546 \begin_inset Index idx
25549 \begin_layout Plain Layout
25569 furthermore the following functions:
25572 \begin_layout Standard
25574 \begin_inset Tabular
25575 <lyxtabular version="3" rows="5" columns="2">
25576 <features tabularvalignment="middle">
25577 <column alignment="center" valignment="top" width="0">
25578 <column alignment="center" valignment="top" width="0">
25580 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25583 \begin_layout Plain Layout
25589 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25592 \begin_layout Plain Layout
25594 \begin_inset Note Note
25597 \begin_layout Plain Layout
25604 is only used as spacer.
25616 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25619 \begin_layout Plain Layout
25627 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25630 \begin_layout Plain Layout
25631 \begin_inset Formula $\varliminf$
25641 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25644 \begin_layout Plain Layout
25652 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25655 \begin_layout Plain Layout
25656 \begin_inset Formula $\varlimsup$
25666 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25669 \begin_layout Plain Layout
25677 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25680 \begin_layout Plain Layout
25681 \begin_inset Formula $\varprojlim$
25691 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25694 \begin_layout Plain Layout
25702 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25705 \begin_layout Plain Layout
25706 \begin_inset Formula $\varinjlim$
25710 \begin_inset Formula $\raisebox{-2.5mm}{}$
25726 \begin_layout Standard
25727 \begin_inset VSpace medskip
25730 The limit is created by inserting a subscript.
25731 It is set right beside the function in an inline formula:
25734 \begin_layout Standard
25736 \begin_inset Tabular
25737 <lyxtabular version="3" rows="2" columns="2">
25738 <features tabularvalignment="middle">
25739 <column alignment="center" valignment="top" width="0pt">
25740 <column alignment="center" valignment="top" width="0pt">
25742 <cell alignment="center" valignment="top" usebox="none">
25745 \begin_layout Plain Layout
25751 <cell alignment="center" valignment="top" usebox="none">
25754 \begin_layout Plain Layout
25755 \begin_inset space \hspace{}
25760 \begin_inset Note Note
25763 \begin_layout Plain Layout
25770 are used here as spacer.
25782 <cell alignment="center" valignment="top" usebox="none">
25785 \begin_layout Plain Layout
25794 \begin_layout Plain Layout
25807 \begin_layout Plain Layout
25821 <cell alignment="center" valignment="top" usebox="none">
25824 \begin_layout Plain Layout
25825 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
25841 \begin_layout Standard
25842 In a displayed formula the limit is set below the formula, as usual:
25843 \begin_inset Formula \[
25851 \begin_layout Subsection
25853 \begin_inset Index idx
25856 \begin_layout Plain Layout
25857 Functions ! modulo-
25865 \begin_layout Standard
25866 The modulo-function is special, because it exists in four variants.
25869 \begin_layout Standard
25870 The variants in a displayed formula:
25871 \begin_inset Formula \begin{align*}
25872 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25873 \mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
25874 \mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
25875 \mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
25876 \mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b
25884 \begin_layout Standard
25885 In an inline formula less space is set before the function names for all
25889 \begin_layout Section
25891 \begin_inset Index idx
25894 \begin_layout Plain Layout
25903 \begin_layout Subsection
25904 Special Characters in Mathematical Text
25907 \begin_layout Standard
25908 The following commands can only be used in mathematical text or in TeX-mode:
25911 \begin_layout Standard
25912 \begin_inset space \hfill{}
25916 \begin_inset Tabular
25917 <lyxtabular version="3" rows="8" columns="2">
25918 <features tabularvalignment="middle">
25919 <column alignment="block" valignment="top" width="0">
25920 <column alignment="block" valignment="top" width="0">
25922 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25925 \begin_layout Plain Layout
25931 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25934 \begin_layout Plain Layout
25942 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25945 \begin_layout Plain Layout
25953 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25956 \begin_layout Plain Layout
25957 \begin_inset Formula $\textrm{œ}$
25967 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25970 \begin_layout Plain Layout
25978 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25981 \begin_layout Plain Layout
25982 \begin_inset Formula $\textrm{Œ}$
25992 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25995 \begin_layout Plain Layout
26003 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26006 \begin_layout Plain Layout
26007 \begin_inset Formula $\textrm{æ}$
26017 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26020 \begin_layout Plain Layout
26028 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26031 \begin_layout Plain Layout
26032 \begin_inset Formula $\textrm{Æ}$
26042 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26045 \begin_layout Plain Layout
26053 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26056 \begin_layout Plain Layout
26057 \begin_inset Formula $\textrm{\aa}$
26067 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26070 \begin_layout Plain Layout
26074 \begin_inset Index idx
26077 \begin_layout Plain Layout
26084 \begin_layout Plain Layout
26105 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26108 \begin_layout Plain Layout
26109 \begin_inset Formula $\textrm{Å}$
26119 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26122 \begin_layout Plain Layout
26130 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26133 \begin_layout Plain Layout
26134 \begin_inset Formula $\textrm{ı}$
26148 \begin_inset space \hfill{}
26152 \begin_inset Tabular
26153 <lyxtabular version="3" rows="8" columns="2">
26154 <features tabularvalignment="middle">
26155 <column alignment="block" valignment="top" width="0">
26156 <column alignment="center" valignment="top" width="0">
26158 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26161 \begin_layout Plain Layout
26163 \begin_inset Note Note
26166 \begin_layout Plain Layout
26168 \begin_inset space \thinspace{}
26171 mm is used for separation, because otherwise the output will be ¡ and ¿
26182 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26185 \begin_layout Plain Layout
26193 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26196 \begin_layout Plain Layout
26204 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26207 \begin_layout Plain Layout
26208 \begin_inset Formula $\textrm{ø}$
26218 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26221 \begin_layout Plain Layout
26229 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26232 \begin_layout Plain Layout
26233 \begin_inset Formula $\textrm{Ø}$
26243 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26246 \begin_layout Plain Layout
26254 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26257 \begin_layout Plain Layout
26258 \begin_inset Formula $\textrm{ł}$
26268 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26271 \begin_layout Plain Layout
26279 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26282 \begin_layout Plain Layout
26283 \begin_inset Formula $\textrm{Ł}$
26293 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26296 \begin_layout Plain Layout
26298 \begin_inset space \hspace{}
26306 \begin_layout Plain Layout
26320 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26323 \begin_layout Plain Layout
26324 \begin_inset Formula $\textrm{!`}$
26334 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26337 \begin_layout Plain Layout
26339 \begin_inset space \hspace{}
26347 \begin_layout Plain Layout
26361 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26364 \begin_layout Plain Layout
26365 \begin_inset Formula $\textrm{?`}$
26375 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26378 \begin_layout Plain Layout
26386 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26389 \begin_layout Plain Layout
26390 \begin_inset Formula $\textrm{ȷ}$
26404 \begin_inset space \hfill{}
26410 \begin_layout Standard
26412 \begin_inset Formula $\textrm{\textrm{Å}}$
26416 \begin_inset Formula $\textrm{\textrm{Ø}}$
26419 can also be inserted via the math toolbar button
26420 \begin_inset Graphics
26421 filename ../images/math/digamma.png
26429 \begin_layout Standard
26430 An exception are the commands
26433 \begin_inset space \hspace{}
26442 \begin_inset space \hspace{}
26448 , because they can be inserted in LyX directly to text.
26451 \begin_layout Subsection
26453 \begin_inset CommandInset label
26455 name "sub:Accents-in-Text"
26460 \begin_inset Index idx
26463 \begin_layout Plain Layout
26472 \begin_layout Standard
26473 With the following commands all letters can be accented.
26474 The commands must be inserted in TeX-mode.
26477 \begin_layout Standard
26478 \begin_inset space \hfill{}
26482 \begin_inset Tabular
26483 <lyxtabular version="3" rows="8" columns="2">
26484 <features tabularvalignment="middle">
26485 <column alignment="block" valignment="top" width="0">
26486 <column alignment="block" valignment="top" width="0">
26488 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26491 \begin_layout Plain Layout
26497 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26500 \begin_layout Plain Layout
26508 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26511 \begin_layout Plain Layout
26515 \begin_inset Quotes grd
26523 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26526 \begin_layout Plain Layout
26530 \begin_layout Plain Layout
26546 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26549 \begin_layout Plain Layout
26557 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26560 \begin_layout Plain Layout
26564 \begin_layout Plain Layout
26580 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26583 \begin_layout Plain Layout
26590 \begin_layout Plain Layout
26604 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26607 \begin_layout Plain Layout
26611 \begin_layout Plain Layout
26627 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26630 \begin_layout Plain Layout
26638 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26641 \begin_layout Plain Layout
26645 \begin_layout Plain Layout
26661 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26664 \begin_layout Plain Layout
26671 \begin_layout Plain Layout
26685 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26688 \begin_layout Plain Layout
26692 \begin_layout Plain Layout
26708 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26711 \begin_layout Plain Layout
26718 \begin_layout Plain Layout
26732 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26735 \begin_layout Plain Layout
26739 \begin_layout Plain Layout
26755 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26758 \begin_layout Plain Layout
26765 \begin_layout Plain Layout
26779 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26782 \begin_layout Plain Layout
26786 \begin_layout Plain Layout
26806 \begin_inset space \hfill{}
26810 \begin_inset Tabular
26811 <lyxtabular version="3" rows="8" columns="2">
26812 <features tabularvalignment="middle">
26813 <column alignment="block" valignment="top" width="0">
26814 <column alignment="center" valignment="top" width="0">
26816 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26819 \begin_layout Plain Layout
26825 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26828 \begin_layout Plain Layout
26836 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26839 \begin_layout Plain Layout
26846 \begin_layout Plain Layout
26860 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26863 \begin_layout Plain Layout
26867 \begin_layout Plain Layout
26883 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26886 \begin_layout Plain Layout
26894 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26897 \begin_layout Plain Layout
26901 \begin_layout Plain Layout
26917 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26920 \begin_layout Plain Layout
26924 \begin_inset Index idx
26927 \begin_layout Plain Layout
26938 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26941 \begin_layout Plain Layout
26945 \begin_layout Plain Layout
26961 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26964 \begin_layout Plain Layout
26972 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26975 \begin_layout Plain Layout
26979 \begin_layout Plain Layout
26995 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26998 \begin_layout Plain Layout
27005 \begin_layout Plain Layout
27019 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27022 \begin_layout Plain Layout
27026 \begin_layout Plain Layout
27042 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27045 \begin_layout Plain Layout
27052 \begin_layout Plain Layout
27066 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27069 \begin_layout Plain Layout
27073 \begin_layout Plain Layout
27089 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27092 \begin_layout Plain Layout
27099 \begin_layout Plain Layout
27113 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27116 \begin_layout Plain Layout
27120 \begin_layout Plain Layout
27140 \begin_inset space \hfill{}
27146 \begin_layout Standard
27147 \begin_inset VSpace medskip
27156 also two different characters can be accented.
27165 \begin_layout Plain Layout
27180 \begin_layout Plain Layout
27192 \begin_layout Standard
27205 can in combination with vowels directly be inserted with the keyboard without
27207 The same applies for the tilde
27211 \begin_layout Plain Layout
27212 This only applies for keyboards where the tilde is defined as accent.
27221 in combination with
27236 \begin_layout Standard
27279 and accents that are inserted directly with the keyboard are also available
27280 in mathematical text.
27281 For the other accents there are special math commands to be used in formulas,
27283 \begin_inset CommandInset ref
27285 reference "sub:Accents-for-one"
27292 \begin_layout Standard
27293 \begin_inset VSpace bigskip
27296 Furthermore, with the command
27303 \begin_inset Index idx
27306 \begin_layout Plain Layout
27314 all numbers and letters can be set into a circle, quasi accented with a
27315 circle, similar to the copyright symbol.
27318 \begin_layout Standard
27320 \begin_inset Tabular
27321 <lyxtabular version="3" rows="3" columns="2">
27322 <features tabularvalignment="middle">
27323 <column alignment="center" valignment="top" width="0">
27324 <column alignment="center" valignment="top" width="0">
27326 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27329 \begin_layout Plain Layout
27335 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27338 \begin_layout Plain Layout
27340 \begin_inset Note Note
27343 \begin_layout Plain Layout
27350 is only used as spacer.
27362 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27365 \begin_layout Plain Layout
27373 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27376 \begin_layout Plain Layout
27380 \begin_layout Plain Layout
27396 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27399 \begin_layout Plain Layout
27410 raisebox{-1.5pt}{W}}
27415 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27418 \begin_layout Plain Layout
27419 \begin_inset Formula $\raisebox{4.5mm}{}$
27426 \begin_layout Plain Layout
27444 \begin_inset Formula $\raisebox{-2mm}{}$
27460 \begin_layout Standard
27461 One has to take care that the character fits in the circle.
27472 \begin_layout Plain Layout
27474 \begin_inset CommandInset ref
27476 reference "sub:Font-Sizes"
27485 specifies thereby the size of the circle.
27496 \begin_layout Plain Layout
27498 \begin_inset CommandInset ref
27500 reference "sub:Boxes-without-Frame"
27509 the character can be centered.
27512 \begin_layout Subsection
27514 \begin_inset Index idx
27517 \begin_layout Plain Layout
27526 \begin_layout Standard
27527 Minuscule numbers are created with the command
27534 \begin_inset Index idx
27537 \begin_layout Plain Layout
27546 The command can be used in formulas and in TeX-mode.
27547 The command scheme is:
27550 \begin_layout Standard
27555 oldstylenums{number}
27558 \begin_layout Standard
27563 oldstylenums{0123456789
27566 \begin_inset Formula $\oldstylenums{0123456789}$
27572 \begin_layout Subsection
27573 Miscellaneous special Characters
27574 \begin_inset CommandInset label
27576 name "sub:Miscellaneous-special-Characters"
27581 \begin_inset Index idx
27584 \begin_layout Plain Layout
27585 Special characters ! miscellaneous
27593 \begin_layout Standard
27594 The following characters can only be inserted to formulas by using commands:
27597 \begin_layout Standard
27599 \begin_inset Tabular
27600 <lyxtabular version="3" rows="4" columns="2">
27601 <features tabularvalignment="middle">
27602 <column alignment="center" valignment="top" width="0">
27603 <column alignment="center" valignment="top" width="0">
27605 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27608 \begin_layout Plain Layout
27614 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27617 \begin_layout Plain Layout
27625 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27628 \begin_layout Plain Layout
27635 \begin_layout Plain Layout
27649 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27652 \begin_layout Plain Layout
27653 \begin_inset Formula $\mathcircumflex$
27663 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27666 \begin_layout Plain Layout
27674 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27677 \begin_layout Plain Layout
27678 \begin_inset Formula $\_$
27688 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27691 \begin_layout Plain Layout
27696 \begin_layout Plain Layout
27708 \begin_inset Index idx
27711 \begin_layout Plain Layout
27724 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27727 \begin_layout Plain Layout
27728 \begin_inset Formula $^{\circ}$
27744 \begin_layout Standard
27745 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
27746 contains the following line
27750 \begin_layout Plain Layout
27751 More about this is described in
27752 \begin_inset CommandInset ref
27754 reference "sub:Text-Characters-in"
27766 \begin_layout Standard
27771 DeclareInputtext{176}{
27784 \begin_layout Section
27786 \begin_inset CommandInset label
27788 name "sec:Formula-Styles"
27793 \begin_inset Index idx
27796 \begin_layout Plain Layout
27805 \begin_layout Itemize
27806 There are two different alignment styles:
27810 \begin_layout Description
27811 Centered is the predefined standard
27814 \begin_layout Description
27815 Indented for this the option
27819 must be inserted in the menu
27821 Document\SpecialChar \menuseparator
27827 \begin_inset space ~
27833 \begin_layout Standard
27838 is used, the indentation can be adjusted with the length
27845 \begin_inset Index idx
27848 \begin_layout Plain Layout
27857 Should the distance be 15
27858 \begin_inset space \thinspace{}
27861 mm, the following command line is inserted in the LaTeX-preamble
27864 \begin_layout Standard
27874 \begin_layout Standard
27875 When no length is specified, the predefined value of 30
27876 \begin_inset space \thinspace{}
27883 \begin_layout Itemize
27884 And two different numbering styles:
27888 \begin_layout Description
27889 Right is the predefined standard
27892 \begin_layout Description
27893 Left for this the option
27897 must be inserted in the menu
27899 Document\SpecialChar \menuseparator
27905 \begin_inset space ~
27912 \begin_layout Standard
27921 can also be used together.
27922 In this case both options are inserted, separated by a comma.
27925 \begin_layout Standard
27926 The chosen styles are used for all displayed formulas of the document.
27927 When both, centered and indented formulas should be created in a document,
27933 The indented formulas are then set in a flalign environment, see
27934 \begin_inset CommandInset ref
27936 reference "sub:Flalign-Environment"
27943 \begin_layout Section
27945 \begin_inset CommandInset label
27947 name "sec:Multiline-Formulas"
27952 \begin_inset Index idx
27955 \begin_layout Plain Layout
27956 Formula ! multiline
27964 \begin_layout Subsection
27968 \begin_layout Standard
27969 In LyX multiline formulas are created by pressing
27974 arg "newline-insert newline"
27980 This creates either an
27982 eqnarray environment
27984 that is described in
27985 \begin_inset CommandInset ref
27987 reference "sub:Eqnarray-Environment"
27991 or, when the option
27993 Use AMS math package
27995 in the document settings is selected, an
27999 that is described in
28000 \begin_inset CommandInset ref
28002 reference "sub:Standard-align-Environment"
28009 \begin_layout Standard
28010 There are other multiline formula environments that can be created via the
28013 Insert\SpecialChar \menuseparator
28017 These environments are described in the following sections.
28020 \begin_layout Standard
28021 In all multiline formula environments a new line is created by pressing
28025 arg "newline-insert newline"
28029 To add or delete lines, the math toolbar buttons
28030 \begin_inset Graphics
28031 filename ../images/tabular-feature_append-row.png
28037 \begin_inset Graphics
28038 filename ../images/tabular-feature_delete-row.png
28043 , respectively, or the menu
28045 Edit\SpecialChar \menuseparator
28051 \begin_layout Subsubsection
28053 \begin_inset CommandInset label
28055 name "sub:Line-Separation"
28060 \begin_inset Index idx
28063 \begin_layout Plain Layout
28064 Formula ! multiline ! Line separation
28072 \begin_layout Standard
28073 There is sometimes not enough space in multiline formulas between the lines:
28074 \begin_inset Formula \begin{eqnarray*}
28075 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}\\
28076 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
28084 \begin_layout Standard
28085 In LaTeX additional line space is specified as optional argument of the
28087 This is not yet possible in LyX
28091 \begin_layout Plain Layout
28093 \begin_inset CommandInset href
28095 name "LyX-bug #1505"
28096 target "http://www.lyx.org/trac/ticket/1505"
28105 , therefore the whole formula must be inserted in TeX-mode.
28106 To add in our example space, the command
28114 is inserted at the end of the first line.
28119 \begin_layout Plain Layout
28126 \begin_layout Plain Layout
28128 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
28131 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
28138 \begin_layout Plain Layout
28142 left(B^{2}+x_{0}^{2}
28150 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
28155 \begin_layout Plain Layout
28167 \begin_layout Standard
28168 \begin_inset VSpace bigskip
28171 To set the line separation for all lines in a formula, the length
28178 \begin_inset Index idx
28181 \begin_layout Plain Layout
28191 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
28202 \begin_inset space \thinspace{}
28207 \begin_inset space \thinspace{}
28210 mm additional line separation as in the previous example, the command
28213 \begin_layout Standard
28223 \begin_layout Standard
28224 is inserted in TeX-mode before the formula.
28225 This requires that the LaTeX-package
28233 \begin_layout Plain Layout
28238 is part of every LaTeX standard installation.
28244 \begin_inset Index idx
28247 \begin_layout Plain Layout
28253 was loaded in LaTeX-preamble with the line
28256 \begin_layout Standard
28264 \begin_layout Standard
28269 \begin_layout Plain Layout
28281 \begin_inset Formula \begin{eqnarray*}
28282 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}\\
28283 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
28291 \begin_layout Standard
28295 \begin_layout Plain Layout
28306 To get back to the predefined distance,
28312 is set to the value 3
28313 \begin_inset space \thinspace{}
28319 \begin_layout Subsubsection
28321 \begin_inset CommandInset label
28323 name "sub:Column-Separation"
28328 \begin_inset Index idx
28331 \begin_layout Plain Layout
28332 Formula ! multiline ! Column separation
28340 \begin_layout Standard
28341 Multiline formulas form a matrix.
28342 A formula in the eqnarray environment is for example a matrix with three
28344 By changing the column separation in this environment, the space beside
28345 the relation sign can be changed.
28348 \begin_layout Standard
28349 The column separation is specified with the length
28356 \begin_inset Index idx
28359 \begin_layout Plain Layout
28368 \begin_inset Newline newline
28371 column separation = 2
28372 \begin_inset space \thinspace{}
28382 \begin_inset Newline newline
28388 \begin_layout Standard
28398 \begin_layout Standard
28399 inserted in TeX-mode, sets for all following formulas a column separation
28401 \begin_inset space \thinspace{}
28405 To get back to the predefined distance,
28412 \begin_inset space \thinspace{}
28418 \begin_layout Standard
28420 \begin_inset space \thinspace{}
28423 cm column separation:
28427 \begin_layout Plain Layout
28439 \begin_inset Formula \begin{eqnarray*}
28446 A formula with the predefined column separation for matrices of 10
28447 \begin_inset space \thinspace{}
28454 \begin_layout Plain Layout
28466 \begin_inset Formula \begin{eqnarray*}
28476 \begin_layout Subsubsection
28478 \begin_inset Index idx
28481 \begin_layout Plain Layout
28490 \begin_layout Standard
28491 Long formulas can be typeset using these methods:
28494 \begin_layout Itemize
28495 When one side of the equation is much shorther than the line width, this
28496 one is chosen for the left side and the right side is typeset over two
28498 \begin_inset Formula \begin{eqnarray}
28499 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 \\
28500 & & -\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}
28505 The minus sign at the beginning of the second line does normally not appear
28506 as operator because it is the first character of the line.
28507 Thus it would not be surrounded by space and could not be distinguished
28508 from the fraction bar.
28510 \begin_inset space \thinspace{}
28513 pt space was inserted behind the minus sign with the command
28523 \begin_layout Plain Layout
28531 \begin_inset CommandInset ref
28533 reference "sub:Variable-Space"
28543 \begin_inset Index idx
28546 \begin_layout Plain Layout
28557 \begin_layout Itemize
28558 When both sides of the equation are too long, the command
28565 \begin_inset Index idx
28568 \begin_layout Plain Layout
28577 It is inserted to the first column of the first line and effects that all
28578 further insertions overwrite the following columns:
28579 \begin_inset Formula \begin{eqnarray}
28580 \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 \\
28581 & & -\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 \\
28582 & & =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}
28587 After the insertion of
28593 , the cursor is in a purple box that is a bit shifted to the left from the
28595 In this the formula is inserted.
28596 \begin_inset Newline newline
28599 The content of the further lines is inserted to the second or another formula
28601 The greater the column number where it was inserted, the larger the indentation.
28602 \begin_inset VSpace medskip
28606 \begin_inset Newline newline
28610 \begin_inset Note Greyedout
28613 \begin_layout Plain Layout
28614 Note the following when using
28623 \begin_layout Itemize
28624 The formula doesn't use the full page width.
28626 \begin_inset space \thinspace{}
28630 \begin_inset space \space{}
28634 \begin_inset Formula $-B^{2}$
28637 is added to the first line in the above example, it would have been outside
28639 To better use the width, negative space can be inserted at the beginning
28643 \begin_layout Itemize
28644 Due to a bug in LyX the cursor cannot be set with the mouse into the first
28649 \begin_layout Plain Layout
28650 \begin_inset CommandInset href
28652 name "LyX-bug #1429"
28653 target "http://www.lyx.org/trac/ticket/1429"
28662 One can only set the cursor at the beginning of the line and move it with
28671 \begin_layout Itemize
28672 Other methods to set long formulas are offered by the environments described
28674 \begin_inset CommandInset ref
28676 reference "sub:Multline-Environment"
28681 \begin_inset CommandInset ref
28683 reference "sub:Multiline-Formula-Parts"
28690 \begin_layout Subsubsection
28692 \begin_inset CommandInset label
28694 name "sub:Multiline-Brackets"
28699 \begin_inset Index idx
28702 \begin_layout Plain Layout
28703 Brackets ! for multiline expressions
28711 \begin_layout Standard
28712 For brackets spanning multiple lines the following problem occurs:
28713 \begin_inset Formula \begin{eqnarray*}
28714 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28715 & & \left.\cdots+B-D\right]
28723 \begin_layout Standard
28724 The closing bracket is smaller than the opening bracket because brackets
28725 with variable size may not span multiple lines.
28728 \begin_layout Standard
28729 To set the bracket size for the second line correctly, the first line is
28737 \begin_inset Index idx
28740 \begin_layout Plain Layout
28748 and the second line with
28756 \begin_layout Plain Layout
28770 \begin_inset CommandInset ref
28772 reference "sub:Automatic-Bracket-Size"
28784 \begin_inset Index idx
28787 \begin_layout Plain Layout
28813 \begin_layout Plain Layout
28832 \begin_layout Plain Layout
28851 \begin_layout Plain Layout
28863 \begin_inset Formula $\downarrow$
28869 \begin_inset Index idx
28872 \begin_layout Plain Layout
28880 is inserted, because the multiplication operator with its limits is the
28881 largest symbol in the first line and this should be the size for the bracket
28882 in the second line.
28885 \begin_layout Standard
28886 The result is this:
28887 \begin_inset Formula \begin{eqnarray*}
28888 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28889 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
28897 \begin_layout Subsection
28901 \begin_layout Standard
28902 Align environments can be used for every kind of multiline formulas.
28903 They are specially useful to set several formulas side by side.
28906 \begin_layout Standard
28907 Align environments consist of columns.
28908 The odd columns are right aligned, the even ones left aligned.
28909 Every line in an Align environment can be numbered.
28912 \begin_layout Standard
28913 Align environments are created via the menu
28915 Insert\SpecialChar \menuseparator
28921 Edit\SpecialChar \menuseparator
28922 Math\SpecialChar \menuseparator
28923 Change Formula Type
28925 already existing formulas can be converted to Align environments.
28928 \begin_layout Standard
28929 To add or delete columns, the math toolbar buttons
28930 \begin_inset Graphics
28931 filename ../images/tabular-feature_append-column.png
28937 \begin_inset Graphics
28938 filename ../images/tabular-feature_delete-column.png
28943 , respectively, or the menu
28945 Edit\SpecialChar \menuseparator
28951 \begin_layout Subsubsection
28952 Standard align Environment
28953 \begin_inset CommandInset label
28955 name "sub:Standard-align-Environment"
28960 \begin_inset Index idx
28963 \begin_layout Plain Layout
28964 Formula ! multiline ! align environment
28972 \begin_layout Standard
28973 This Align environment is created by presssing
28976 arg "newline-insert newline"
28979 in a formula or by the menu
28981 Insert\SpecialChar \menuseparator
28982 Math\SpecialChar \menuseparator
28983 AMS align Environment
28988 \begin_layout Standard
28989 An example for two formulas set side by side, that are created with a four
28990 column align environment:
28991 \begin_inset Formula \begin{align*}
28992 A & =\sin(B) & C & =D\\
28993 C & \ne A & B & \ne D
28998 As it can be seen, the formulas in this environment are placed so as if
29007 \begin_layout Plain Layout
29015 \begin_inset CommandInset ref
29017 reference "sub:Variable-Space"
29028 before the first and after every even column.
29029 When the formula style
29035 \begin_layout Plain Layout
29037 \begin_inset CommandInset ref
29039 reference "sec:Formula-Styles"
29050 is used, the formula is set without the
29056 before the first column.
29059 \begin_layout Subsubsection
29060 Alignat Environment
29061 \begin_inset Index idx
29064 \begin_layout Plain Layout
29065 Formula ! multiline ! alignat environment
29073 \begin_layout Standard
29074 The alignat environment has no predefined column separation.
29075 It can be inserted manually with the spaces that are described
29076 \begin_inset CommandInset ref
29078 reference "sub:Space"
29085 \begin_layout Standard
29086 The above example in the alignat environment where 1
29087 \begin_inset space \thinspace{}
29090 cm space was inserted at the beginning of the second formula:
29091 \begin_inset Formula \begin{alignat*}{2}
29092 A & =\sin(B) & \hspace{1cm}C & =D\\
29093 C & \ne A & B & \ne D
29098 Because the column separation can be set separately for every column, this
29099 environment is especially suitable to set three and more formulas side
29103 \begin_layout Subsubsection
29104 Flalign Environment
29105 \begin_inset CommandInset label
29107 name "sub:Flalign-Environment"
29112 \begin_inset Index idx
29115 \begin_layout Plain Layout
29116 Formula ! multiline ! flalign environment
29124 \begin_layout Standard
29125 In this environment the first two columns are always set as much as possible
29126 to the left and the last two ones to the right.
29128 \begin_inset Formula \begin{flalign*}
29129 A & =1 & B & =2 & C & =3\\
29130 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
29138 \begin_layout Standard
29139 By creating a flalign environment with an odd number of columns where an
29140 empty TeX-brace is inserted to the last column, several formulas in a document
29141 can be set to the left, although the formula style
29146 As example the indented formula
29147 \begin_inset CommandInset ref
29149 reference "eq:VolInt"
29154 \begin_inset Formula \begin{flalign}
29155 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}\end{flalign}
29159 The first two columns contain the formula.
29160 To indent it as with the formula style
29165 \begin_inset space \thinspace{}
29168 pt space was inserted at the beginning of the first column.
29171 \begin_layout Subsection
29172 Eqnarray Environment
29173 \begin_inset CommandInset label
29175 name "sub:Eqnarray-Environment"
29180 \begin_inset Index idx
29183 \begin_layout Plain Layout
29184 Formula ! multiline ! eqnarray environment
29192 \begin_layout Standard
29193 When this environment has been created, three blue boxes appear.
29194 The content of the first box is right aligned, the content of the last
29196 The content of the middle box appears centered and a bit smaller, because
29197 it is designed to insert there only relation characters.
29198 \begin_inset Formula \begin{eqnarray*}
29199 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
29209 \begin_layout Subsection
29211 \begin_inset Index idx
29214 \begin_layout Plain Layout
29215 Formula ! multiline ! gather environment
29223 \begin_layout Standard
29224 This environment consists of only one centered column.
29225 Every line can be numbered.
29226 \begin_inset Formula \begin{gather}
29236 \begin_layout Subsection
29237 Multline Environment
29238 \begin_inset CommandInset label
29240 name "sub:Multline-Environment"
29245 \begin_inset Index idx
29248 \begin_layout Plain Layout
29249 Formula ! multiline ! multline environment
29257 \begin_layout Standard
29258 The multline environment consists, like the gather environment, of only
29260 But the first line is left aligned, the last one right aligned.
29261 All other lines are centered.
29262 Therefore this environment is suitable for long formulas.
29264 \begin_inset CommandInset ref
29266 reference "eq:lefteqn"
29270 in the multline environment:
29271 \begin_inset Formula \begin{multline}
29272 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}\\
29273 -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}\\
29274 =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}}
29282 \begin_layout Standard
29283 In the output only the last (first) line of a multline environment appears
29284 numbered when the document numbering is right (left).
29288 \begin_layout Plain Layout
29289 numbering styles see
29290 \begin_inset CommandInset ref
29292 reference "sec:Formula-Styles"
29304 \begin_layout Standard
29312 \begin_inset Index idx
29315 \begin_layout Plain Layout
29330 \begin_inset Index idx
29333 \begin_layout Plain Layout
29341 a centered line can be right or left aligned, respectively.
29342 The commands are used as follows:
29345 \begin_layout Standard
29350 shoveright{line content}
29356 shoveleft{line content}
29359 \begin_layout Standard
29360 \begin_inset VSpace medskip
29370 \begin_inset Index idx
29373 \begin_layout Plain Layout
29381 specifies the distance of the first line from the left page margin.
29382 Predefined is the length 0
29383 \begin_inset space \thinspace{}
29389 \begin_layout Standard
29390 As example the above formula where the command
29393 \begin_layout Standard
29403 \begin_layout Standard
29404 was inserted in TeX-mode before:
29408 \begin_layout Plain Layout
29420 \begin_inset Formula \begin{multline}
29421 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}\\
29422 \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}}\\
29423 =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}}
29432 \begin_layout Plain Layout
29443 The second line was left aligned using
29452 \begin_layout Subsection
29453 Multiline Formula Parts
29454 \begin_inset CommandInset label
29456 name "sub:Multiline-Formula-Parts"
29461 \begin_inset Index idx
29464 \begin_layout Plain Layout
29465 Formula ! multiline ! formula parts
29473 \begin_layout Standard
29474 To display only parts of a formula with multiple lines, one of the following
29475 environments are used:
29492 They can be inserted via the menu
29494 Insert\SpecialChar \menuseparator
29497 or by using the commands described in this section.
29500 \begin_layout Standard
29501 The first three have the same properties as the corresponding multiline
29502 formula environments, but it is possible to set further formula parts beside
29505 \begin_inset Formula \[
29506 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29507 \Delta E\Delta t & \ge\frac{\hbar}{2}
29509 \right\} \textrm{Uncertainty relations}\]
29516 \begin_layout Standard
29517 To get this formula, a displayed formula is created where the command
29524 \begin_inset Index idx
29527 \begin_layout Plain Layout
29536 A purple box appears around the blue formula box where now columns and
29537 lines can be added.
29538 Outside the multiline environment other formula parts can be set, like
29542 \begin_layout Standard
29543 The aligned environment is also suitable for long formulas whose lines are
29544 horizontally aligned.
29545 Using aligned in a displayed formula has the advantage that the formula
29546 number is vertically centered behind the lines.
29548 \begin_inset CommandInset ref
29550 reference "eq:shortlong"
29554 in the aligned environment:
29555 \begin_inset Formula \begin{equation}
29556 \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}|}\\
29557 & -\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}|}
29566 \begin_layout Standard
29567 To use the environments
29586 \begin_inset Index idx
29589 \begin_layout Plain Layout
29604 \begin_inset Index idx
29607 \begin_layout Plain Layout
29622 \begin_inset Index idx
29625 \begin_layout Plain Layout
29633 are inserted, respectively.
29634 The split environment has the same properties as the aligned environment
29635 but it can only have two columns.
29638 \begin_layout Subsection
29639 Text in multiline Formulas
29640 \begin_inset CommandInset label
29642 name "sub:Text-in-multiline"
29647 \begin_inset Index idx
29650 \begin_layout Plain Layout
29657 \begin_inset Index idx
29660 \begin_layout Plain Layout
29661 Formula ! multiline ! text
29669 \begin_layout Standard
29670 In the Align environments, and the multline and gather environment, text
29671 can be inserted that will appear in a separate line and doesn't affect
29672 the column alignment.
29673 To do this, the command
29680 \begin_inset Index idx
29683 \begin_layout Plain Layout
29691 is used in the following scheme:
29694 \begin_layout Standard
29702 \begin_layout Standard
29703 The text should not be longer than a line because it cannot be hyphenated.
29704 As LyX doesn't yet support
29710 directly, the text is written as mathematical text.
29717 must hereby be at the beginning of a line and appears in the output above
29719 An example where the text was inserted at the beginning of the second line:
29720 \begin_inset Formula \begin{align}
29721 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29722 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29730 \begin_layout Section
29732 \begin_inset Index idx
29735 \begin_layout Plain Layout
29742 \begin_inset Index idx
29745 \begin_layout Plain Layout
29746 Formula ! numbering|see
29750 \begin_layout Plain Layout
29761 \begin_layout Plain Layout
29776 \begin_layout Subsection
29780 \begin_layout Standard
29781 Numbered formulas can be created with the menu
29783 Insert\SpecialChar \menuseparator
29784 Math\SpecialChar \menuseparator
29786 \begin_inset space ~
29794 \begin_inset space ~
29800 Existing formulas can be numbered with the menu
29802 Edit\SpecialChar \menuseparator
29803 Math\SpecialChar \menuseparator
29805 \begin_inset space ~
29813 arg "math-number-toggle"
29817 The formula number is displayed in LyX behind the formula as number sign
29819 The number sign is replaced in the output by the formula number.
29822 \begin_layout Standard
29823 When numbering is turned on in multiline formulas, all lines will be numbered.
29824 But the numbering can be controlled with the menu
29826 Edit\SpecialChar \menuseparator
29827 Math\SpecialChar \menuseparator
29829 \begin_inset space ~
29833 \begin_inset space ~
29837 \begin_inset space ~
29845 arg "math-number-line-toggle"
29851 \begin_layout Standard
29852 Except for inline formulas, all formulas can be numbered with two different
29854 \begin_inset CommandInset ref
29856 reference "sec:Formula-Styles"
29863 \begin_layout Subsection
29865 \begin_inset Index idx
29868 \begin_layout Plain Layout
29869 Cross-references ! to formulas
29877 \begin_layout Standard
29878 All labeled formulas can be cross-referenced.
29879 A label is added by the menu
29881 Insert\SpecialChar \menuseparator
29884 or the toolbar button
29885 \begin_inset Graphics
29886 filename ../images/label-insert.png
29892 The cursor must hereby be inside a displayed formula.
29893 A dialog pops up displaying the prefix
29898 The label is inserted there behind the prefix.
29899 The predefined prefix means
29900 \begin_inset Quotes eld
29904 \begin_inset Quotes erd
29907 and makes it easier to find labels in large documents because it marks
29908 it as formula label to divide it from e.
29909 \begin_inset space \thinspace{}
29913 \begin_inset space \space{}
29917 To change a label, the menu
29919 Insert\SpecialChar \menuseparator
29925 \begin_layout Standard
29926 The name of the label is displayed in LyX within two parentheses behind
29928 A formula with a label is always numbered.
29931 \begin_layout Standard
29932 Cross-references are inserted via the menu
29934 Insert\SpecialChar \menuseparator
29937 or with the toolbar button
29938 \begin_inset Graphics
29939 filename ../images/dialog-show-new-inset_ref.png
29945 A formula cross-reference appears in the output as formula number.
29946 When in the cross-reference dialog window the format
29950 is chosen, the cross-reference appears in the output as formula number
29952 \begin_inset Newline newline
29955 By right-clicking on a cross-reference in LyX, one jumps to the formula
29956 that is referenced.
29959 \begin_layout Standard
29960 Here are as examples cross-references to formulas of the following subsections:
29961 \begin_inset Note Note
29964 \begin_layout Plain Layout
29965 Note the different cross-reference types.
29973 \begin_layout Standard
29975 \begin_inset CommandInset ref
29982 \begin_inset CommandInset ref
29990 \begin_inset CommandInset ref
29996 ) big Latin letters are used for the numbering in contrary to (
29997 \begin_inset CommandInset ref
30006 \begin_layout Standard
30007 \begin_inset VSpace medskip
30010 When the argument of
30018 \begin_layout Plain Layout
30026 \begin_inset CommandInset ref
30028 reference "sub:User-defined-Numbering"
30039 contains a box like in
30040 \begin_inset CommandInset ref
30042 reference "sub:Paragraph-Boxes"
30046 , the formula cannot be referenced.
30049 \begin_layout Subsection
30051 \begin_inset Index idx
30054 \begin_layout Plain Layout
30055 Formula numbering ! subnumbering
30063 \begin_layout Standard
30064 With the help of the commands
30068 begin{subequations}
30076 formulas can be subnumbered.
30077 Both commands are inserted in TeX-mode.
30080 \begin_layout Standard
30082 \begin_inset Formula \begin{equation}
30083 A=C-B\label{eq:a}\end{equation}
30091 \begin_layout Plain Layout
30095 addtocounter{equation}{-1}
30104 \begin_layout Plain Layout
30108 begin{subequations}
30114 \begin_inset VSpace -5mm
30118 \begin_inset Formula \begin{equation}
30119 B=C-A\label{eq:b}\end{equation}
30124 \begin_inset Formula \begin{equation}
30125 C=A+B\label{eq:c}\end{equation}
30132 \begin_layout Standard
30136 \begin_layout Plain Layout
30148 \begin_layout Standard
30149 To create the example, the following is done:
30152 \begin_layout Enumerate
30153 first formula is inserted
30156 \begin_layout Enumerate
30161 addtocounter{equation}{-1}
30163 begin{subequations}
30164 \begin_inset Index idx
30167 \begin_layout Plain Layout
30176 \begin_inset Newline newline
30181 is inserted after the first formula
30184 \begin_layout Enumerate
30185 second formula is inserted
30188 \begin_layout Enumerate
30189 third formula is inserted
30192 \begin_layout Enumerate
30199 is inserted after the third formula
30202 \begin_layout Standard
30203 Every formula between the commands
30215 is subnumbered as a, b,
30216 \begin_inset Newline linebreak
30219 c, \SpecialChar \ldots{}
30220 For multiline formulas every line will be subnumbered.
30221 All subnumbered formulas are treated as
30226 But as every numbered formula increases the counter
30230 by one, the command
30236 is needed to decrease it.
30237 Otherwise the formulas
30238 \begin_inset CommandInset ref
30245 \begin_inset CommandInset ref
30252 \begin_inset CommandInset ref
30258 would be numbered as
30259 \begin_inset CommandInset ref
30266 \begin_inset CommandInset ref
30273 \begin_inset CommandInset ref
30282 \begin_layout Standard
30283 By inserting the commands in TeX-mode, a space is created between the first
30286 \begin_inset space \thinspace{}
30289 mm vertical space is inserted after the command
30293 begin{subequations}
30296 When the formula style
30302 \begin_layout Plain Layout
30304 \begin_inset CommandInset ref
30306 reference "sec:Formula-Styles"
30318 \begin_inset space \thinspace{}
30321 mm space is inserted instead.
30324 \begin_layout Standard
30325 Here is an example for a multiline formula where the numbering was turned
30326 off for the second line:
30330 \begin_layout Plain Layout
30334 begin{subequations}
30340 \begin_inset Formula \begin{eqnarray}
30341 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
30342 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
30343 & = & B^{2}-2BZ+Z^{2}\label{eq:f}
30352 \begin_layout Plain Layout
30364 \begin_layout Subsection
30365 User-defined Numbering
30366 \begin_inset CommandInset label
30368 name "sub:User-defined-Numbering"
30373 \begin_inset Index idx
30376 \begin_layout Plain Layout
30377 Formula numbering ! user-defined
30385 \begin_layout Standard
30386 \begin_inset Index idx
30389 \begin_layout Plain Layout
30390 Formula numbering ! self-defined delimiters
30395 With the standard numbering parentheses are set around the formula number.
30396 To replace the parentheses for example by vertical bars, the following
30397 line is added to the LaTeX-preamble:
30400 \begin_layout Standard
30412 \begin_inset Note Note
30415 \begin_layout Plain Layout
30416 This macro is already declared in the LaTeX-preamble for testing.
30417 To activate it, remove the percent sign at the beginning.
30425 \begin_layout Standard
30426 To use other characters, the vertical bars besides the
30430 are replaced by one ore more characters.
30431 To get only the formula number the vertical bars are omitted.
30434 \begin_layout Standard
30435 \begin_inset VSpace bigskip
30438 When there should be an expression of your choice instead of the consecutive
30439 formula number in parentheses behind the formula, the command
30446 \begin_inset Index idx
30449 \begin_layout Plain Layout
30458 \begin_inset Formula \begin{equation}
30459 A+B=C\tag{something}\label{eq:tag}\end{equation}
30463 In this example the command
30471 \begin_layout Plain Layout
30482 was inserted to the formula.
30485 \begin_layout Standard
30494 \begin_layout Plain Layout
30505 is inserted instead, the star prevents the parentheses around the expression:
30506 \begin_inset Formula \[
30507 A+B=C\tag*{something}\]
30514 \begin_layout Standard
30515 \begin_inset VSpace bigskip
30518 To restart the formula numbering with new document parts or sections, the
30519 following command is used:
30522 \begin_layout Standard
30527 @addtoreset{equation}{part}
30530 \begin_inset Index idx
30533 \begin_layout Plain Layout
30538 \begin_layout Plain Layout
30549 \begin_layout Plain Layout
30562 \begin_layout Plain Layout
30573 \begin_layout Plain Layout
30586 \begin_inset Newline newline
30590 \begin_inset Newline newline
30597 @addtoreset{equation}{section}
30600 \begin_layout Standard
30601 To be able to use these commands in TeX-mode, the
30602 \begin_inset Quotes eld
30606 \begin_inset Quotes erd
30609 character has to be made
30610 \begin_inset Quotes eld
30614 \begin_inset Quotes erd
30617 for LaTeX using the command
30631 So the command sequence in TeX-mode is:
30634 \begin_layout Standard
30640 \begin_inset Newline newline
30645 @addtoreset{equation}{section}
30646 \begin_inset Newline newline
30654 \begin_layout Standard
30655 In the LaTeX-preamble
30667 can be omitted as they are automatically internally inserted by LyX.
30670 \begin_layout Standard
30685 \begin_layout Plain Layout
30690 is part of the LaTeX-package
30695 \begin_inset Index idx
30698 \begin_layout Plain Layout
30699 Packages ! carlisle
30704 that is part of every LaTeX standard installation.
30710 \begin_inset Index idx
30713 \begin_layout Plain Layout
30714 Packages ! remreset
30719 has to be loaded in the LaTeX-preamble with the line
30722 \begin_layout Standard
30727 usepackage{remreset}
30730 \begin_layout Standard
30738 \begin_inset Index idx
30741 \begin_layout Plain Layout
30746 \begin_layout Plain Layout
30757 \begin_layout Plain Layout
30770 \begin_layout Plain Layout
30781 \begin_layout Plain Layout
30793 can be used with the same scheme as
30802 \begin_layout Standard
30803 \begin_inset VSpace bigskip
30806 Sometimes formulas should be numbered in the following form:
30809 \begin_layout Standard
30812 (section number.formula number)
30815 \begin_layout Standard
30816 The formula number should start with every section with
30817 \begin_inset Quotes eld
30821 \begin_inset Quotes erd
30827 \begin_layout Standard
30828 For this case there is the command
30835 \begin_inset Index idx
30838 \begin_layout Plain Layout
30846 , which is used with the following scheme:
30849 \begin_layout Standard
30854 numberwithin{counter}{sectioning}
30857 \begin_layout Standard
30858 Counter denotes what kind of numbering is affected, sectioning denotes what
30859 number is before the dot.
30862 \begin_layout Standard
30863 Thus in our case the following LaTeX-preamble or TeX-Code line is used:
30866 \begin_layout Standard
30871 numberwithin{equation}{section}
30874 \begin_layout Standard
30875 This is the result:
30879 \begin_layout Plain Layout
30883 numberwithin{equation}{section}
30889 \begin_inset Formula \begin{equation}
30890 A+B=C\end{equation}
30897 \begin_layout Standard
30899 \begin_inset space \thinspace{}
30903 \begin_inset space \space{}
30906 tables so that the number of the part is the sectioning,
30907 \begin_inset Newline newline
30914 numberwithin{table}{part}
30919 \begin_layout Standard
30920 To go back to the standard numbering or to prevent this kind of numbering
30921 when it is defined by the document class, the following command is inserted
30922 as TeX-Code or to the LaTeX-preamble:
30925 \begin_layout Standard
30935 \begin_inset Index idx
30938 \begin_layout Plain Layout
30952 \begin_layout Plain Layout
30968 \begin_inset Newline newline
30976 \begin_inset Newline newline
30988 \begin_layout Standard
30995 uses internally the command
31001 , described above, that also needs to be reverted.
31005 \begin_layout Plain Layout
31012 \begin_layout Plain Layout
31016 @removefromreset{equation}{section}
31019 \begin_layout Plain Layout
31031 \begin_layout Subsection
31032 Numbering with Roman Numbers and Letters
31033 \begin_inset Index idx
31036 \begin_layout Plain Layout
31037 Formula numbering ! with letters
31043 \begin_inset Index idx
31046 \begin_layout Plain Layout
31047 Formula numbering ! with Roman numbers
31055 \begin_layout Standard
31056 Formulas can also be numbered with Roman numbers and Latin letters.
31057 To number for example with small Roman numbers, the command
31060 \begin_layout Standard
31072 \begin_layout Standard
31073 is inserted before the formula in TeX-mode.
31081 \begin_inset Index idx
31084 \begin_layout Plain Layout
31092 redefines the predefined command
31108 \begin_layout Plain Layout
31115 has the same scheme like the command
31121 that is described in
31122 \begin_inset CommandInset ref
31124 reference "sub:The-Command-newcommand"
31137 is the formula counter.
31144 is used as prefix for a counter, the value of the counter is output as
31146 When a formula is numbered, LaTeX sets internally the command
31152 behind the formula.
31158 \begin_inset Index idx
31161 \begin_layout Plain Layout
31171 outputs the counter as small Roman number.
31174 \begin_layout Standard
31175 All formulas behind the command
31185 are now numbered Roman.
31186 To switch to numbering with big Roman numbers, the command is inserted
31200 \begin_inset Index idx
31203 \begin_layout Plain Layout
31215 \begin_inset Quotes eld
31219 \begin_inset Quotes erd
31222 with small Latin letters there is the command
31229 \begin_inset Index idx
31232 \begin_layout Plain Layout
31240 , for big ones there is the command
31247 \begin_inset Index idx
31250 \begin_layout Plain Layout
31263 \begin_layout Standard
31264 \begin_inset Note Greyedout
31267 \begin_layout Plain Layout
31272 Only maximal 26 formulas can be numbered with Latin letters in one document.
31280 \begin_layout Standard
31284 \begin_layout Plain Layout
31300 \begin_layout Standard
31301 \begin_inset Formula \begin{equation}
31302 A=\textrm{small roman}\end{equation}
31310 \begin_layout Plain Layout
31324 \begin_inset Formula \begin{equation}
31325 B=\textrm{big Roman}\label{eq:Rom}\end{equation}
31333 \begin_layout Plain Layout
31347 \begin_inset Formula \begin{equation}
31348 C=\textrm{small Latin}\end{equation}
31356 \begin_layout Plain Layout
31370 \begin_inset Formula \begin{equation}
31371 D=\textrm{big Latin}\label{eq:Lat}\end{equation}
31378 \begin_layout Standard
31379 To switch back to the default numbering, insert the command:
31382 \begin_layout Standard
31392 \begin_inset Index idx
31395 \begin_layout Plain Layout
31406 \begin_layout Standard
31410 \begin_layout Plain Layout
31424 \begin_inset Formula \begin{equation}
31425 E=\textrm{Arabic}\end{equation}
31432 \begin_layout Standard
31433 \begin_inset VSpace medskip
31436 As you see, formulas are numbered serially independent from the numbering
31438 When then numbering should start with
31439 \begin_inset Quotes eld
31443 \begin_inset Quotes erd
31446 when the style is changed, new equation counters have to be defined.
31447 A description about this can be found in the file
31448 \begin_inset CommandInset href
31450 name "Formula-numbering.lyx"
31451 target "run:Formula-numbering.lyx"
31458 \begin_layout Section
31459 Chemical Symbols and Equations
31460 \begin_inset CommandInset label
31462 name "sub:Chemical-Symbols-and"
31467 \begin_inset Index idx
31470 \begin_layout Plain Layout
31471 Chemical characters ! Symbols
31477 \begin_inset Index idx
31480 \begin_layout Plain Layout
31487 \begin_inset Index idx
31490 \begin_layout Plain Layout
31499 \begin_layout Standard
31500 An example text from chemistry:
31503 \begin_layout Quote
31505 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
31508 -ion reacts with two
31509 \begin_inset Formula $\mathrm{Na^{+}}$
31512 -ions to sodium sulfate
31513 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
31517 The chemical equation for this is:
31518 \begin_inset Formula \begin{equation}
31519 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}\end{equation}
31526 \begin_layout Standard
31527 This chemical equation can directly be created as formula.
31528 To avoid that the symbols appear italic, everything is highlighted and
31529 changed by the shortcut
31535 to the upright font style.
31539 \begin_layout Plain Layout
31545 \begin_inset CommandInset ref
31547 reference "sub:Font-Styles"
31559 \begin_layout Standard
31560 A more convenient way to typeset chemical formulas is to use the command
31568 \begin_inset Index idx
31571 \begin_layout Plain Layout
31579 that is available when the LaTeX-package
31584 \begin_inset Index idx
31587 \begin_layout Plain Layout
31600 to a formula a new blue box appears where chemical formulas can be inserted
31601 in an intuitive way.
31604 \begin_layout Standard
31606 \begin_inset Tabular
31607 <lyxtabular version="3" rows="9" columns="2">
31608 <features tabularvalignment="middle">
31609 <column alignment="center" valignment="top" width="0">
31610 <column alignment="center" valignment="top" width="0">
31612 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31615 \begin_layout Plain Layout
31621 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31624 \begin_layout Plain Layout
31626 \begin_inset Note Note
31629 \begin_layout Plain Layout
31636 is only used as spacer.
31648 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31651 \begin_layout Plain Layout
31658 \begin_layout Plain Layout
31672 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31675 \begin_layout Plain Layout
31676 \begin_inset Formula $\raisebox{4.5mm}{}\ce{H2CO3}\raisebox{-2mm}{}$
31686 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31689 \begin_layout Plain Layout
31696 \begin_layout Plain Layout
31710 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31713 \begin_layout Plain Layout
31714 \begin_inset Formula $\raisebox{5mm}{}\ce{SO4^{2-}}\raisebox{-2mm}{}$
31724 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31727 \begin_layout Plain Layout
31734 \begin_layout Plain Layout
31748 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31751 \begin_layout Plain Layout
31752 \begin_inset Formula $\raisebox{4.5mm}{}\ce{(NH4)2S}\raisebox{-2mm}{}$
31762 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31765 \begin_layout Plain Layout
31772 \begin_layout Plain Layout
31786 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31789 \begin_layout Plain Layout
31790 \begin_inset Formula $\raisebox{4.5mm}{}\ce{KCr(SO4)2.12H2O}\raisebox{-2mm}{}$
31800 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31803 \begin_layout Plain Layout
31810 \begin_layout Plain Layout
31825 \begin_layout Plain Layout
31840 \begin_layout Plain Layout
31854 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31857 \begin_layout Plain Layout
31858 \begin_inset Formula $\raisebox{4.5mm}{}\ce{A-B\dbond C\tbond D}\raisebox{-2mm}{}$
31868 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31871 \begin_layout Plain Layout
31878 \begin_layout Plain Layout
31888 \begin_inset Formula $\downarrow$
31892 \begin_inset Formula $\to$
31900 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31903 \begin_layout Plain Layout
31904 \begin_inset Formula $\raisebox{5mm}{}\ce{_{90}^{227}Th+}\raisebox{-2mm}{}$
31914 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31917 \begin_layout Plain Layout
31924 \begin_layout Plain Layout
31937 \begin_layout Plain Layout
31950 \begin_layout Plain Layout
31963 \begin_layout Plain Layout
31976 \begin_layout Plain Layout
31990 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31993 \begin_layout Plain Layout
31994 \begin_inset Formula $\raisebox{4.5mm}{}\ce{CO2 + C <=> 2CO}\raisebox{-2mm}{}$
32004 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32007 \begin_layout Plain Layout
32014 \begin_layout Plain Layout
32027 \begin_layout Plain Layout
32040 \begin_layout Plain Layout
32053 \begin_layout Plain Layout
32070 \begin_layout Plain Layout
32084 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32087 \begin_layout Plain Layout
32088 \begin_inset Formula $\raisebox{5mm}{}\ce{CO2 + C ->[\alpha][\beta] 2CO}\raisebox{-4mm}{}$
32104 \begin_layout Standard
32105 \begin_inset Note Greyedout
32108 \begin_layout Plain Layout
32113 Inserting a formula to a
32119 box will lead to LaTeX errors.
32120 In this case TeX code has to be used like for
32134 \begin_layout Plain Layout
32155 \begin_layout Standard
32162 the command for equation
32163 \begin_inset space ~
32167 \begin_inset CommandInset ref
32169 reference "eq:chem-reaction"
32174 \begin_inset Newline newline
32185 \begin_layout Plain Layout
32198 \begin_layout Plain Layout
32211 \begin_layout Plain Layout
32224 \begin_layout Plain Layout
32237 \begin_layout Plain Layout
32250 \begin_layout Plain Layout
32262 \begin_layout Standard
32263 To create multiline chemical equations first a multiline formula is created
32265 \begin_inset CommandInset ref
32267 reference "sec:Multiline-Formulas"
32272 Afterwards the command
32278 is used in every small blue box of the formula.
32280 \begin_inset CommandInset ref
32282 reference "eq:TEOS-reaction-1"
32287 \begin_inset CommandInset ref
32289 reference "eq:TEOS-reaction-2"
32293 are an example of a multi-stage chemical reaction where every equation
32294 has its own number.
32295 \begin_inset Formula \begin{eqnarray}
32296 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
32297 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
32305 \begin_layout Standard
32316 package provides the command
32323 \begin_inset Index idx
32326 \begin_layout Plain Layout
32334 that has to be used for special cases.
32335 For more information about
32341 and more examples have a look at the documentation of
32346 \begin_inset CommandInset citation
32355 \begin_layout Standard
32356 \begin_inset Newpage newpage
32362 \begin_layout Section
32366 \begin_layout Standard
32367 LyX supports two types of commutative diagrams:
32375 that are explained in the following.
32378 \begin_layout Subsection
32380 \begin_inset Index idx
32383 \begin_layout Plain Layout
32392 \begin_layout Standard
32393 Diagrams of this type visualize relations by vertical and horizontal lines
32395 \begin_inset Formula \[
32396 \begin{CD}A@>>>B@>>>C\\
32406 \begin_layout Standard
32407 To get them, the command
32412 \begin_inset Index idx
32415 \begin_layout Plain Layout
32425 is inserted to a formula.
32426 A blue box appears with two dashed lines where further commands can be
32431 arg "newline-insert newline"
32434 a new line is created.
32435 Horizontal relations are inserted in odd, vertical in even formula lines.
32438 \begin_layout Standard
32439 To create the relations there are the following commands:
32442 \begin_layout Itemize
32447 creates a left arrow,
32458 \begin_layout Itemize
32463 creates an up arrow,
32471 a vertical equal sign
32474 \begin_layout Itemize
32480 is a placeholder for non-existent relations
32483 \begin_layout Standard
32484 All arrows can be labeled as follows:
32487 \begin_layout Itemize
32488 Is text inserted between the first and second < or >, resp., it is placed
32490 When it is inserted between the second and third one, it appears under
32494 \begin_layout Itemize
32495 When text for vertical arrows is inserted between the first and second A
32496 or V, resp., it is placed left beside the arrow.
32497 When it is inserted between the second and third one, it appears right
32499 If the text contains an A or V, these letters must be set into a TeX-brace.
32502 \begin_layout Standard
32503 As example a diagram with all possible relations:
32506 \begin_layout Standard
32507 \begin_inset Formula \[
32508 \begin{CD}A@>j>>B@>>k>C@=F\\
32518 \begin_layout Standard
32519 The command for this is:
32520 \begin_inset Newline newline
32531 \begin_layout Plain Layout
32540 A@>j>>B@>>k>C@=F Ctrl+Return
32541 \begin_inset Newline newline
32545 \begin_inset Phantom HPhantom
32548 \begin_layout Plain Layout
32557 \begin_layout Plain Layout
32576 \begin_inset Formula $\to$
32582 \begin_inset Newline newline
32586 \begin_inset Phantom HPhantom
32589 \begin_layout Plain Layout
32598 \begin_layout Plain Layout
32615 \begin_layout Subsection
32617 \begin_inset Index idx
32620 \begin_layout Plain Layout
32621 Diagrams ! xymatrix
32629 \begin_layout Standard
32630 To be able to use xymatrices, the LaTeX-package
32635 A xymatrix is created by inserting the command
32642 Then you are able to add new matrix columns and rows like for normal matrices,
32644 \begin_inset CommandInset ref
32646 reference "sec:Matrices"
32653 \begin_layout Standard
32654 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
32656 All possibilities to create commutative diagrams and decorations are explained
32661 that you find in the menu
32663 Help\SpecialChar \menuseparator
32665 \begin_inset space ~
32673 \begin_layout Subsection
32679 \begin_inset Index idx
32682 \begin_layout Plain Layout
32691 \begin_layout Standard
32696 -diagrams, the LaTeX-package
32705 -diagram is created by inserting the command
32712 Then you are able to add new matrix columns and rows like for normal matrices,
32714 \begin_inset CommandInset ref
32716 reference "sec:Matrices"
32723 \begin_layout Standard
32724 Examples how to create
32728 diagrams in LyX is given in the
32730 Feynman-diagram manual
32732 that you find in the menu
32734 Help\SpecialChar \menuseparator
32736 \begin_inset space ~
32744 \begin_layout Section
32745 User-defined Commands
32746 \begin_inset Index idx
32749 \begin_layout Plain Layout
32750 User-defined commands
32758 \begin_layout Standard
32759 \begin_inset Note Greyedout
32762 \begin_layout Plain Layout
32767 The names of user-defined commands and macros may only consist of Latin
32776 \begin_layout Subsection
32780 \begin_inset CommandInset label
32782 name "sub:The-Command-newcommand"
32787 \begin_inset Index idx
32790 \begin_layout Plain Layout
32791 User-defined commands !
32799 \begin_inset Index idx
32802 \begin_layout Plain Layout
32813 \begin_layout Standard
32814 Many LaTeX-commands are too long to be used frequently.
32815 But it is possible to define with the command
32821 new shorter commands.
32824 \begin_layout Standard
32825 The command scheme of
32834 \begin_layout Standard
32839 newcommand{new command name}[number of arguments][optional
32844 \begin_inset Newline newline
32848 \begin_inset Phantom HPhantom
32851 \begin_layout Plain Layout
32861 {command definition}
32864 \begin_layout Standard
32865 \begin_inset Note Greyedout
32868 \begin_layout Plain Layout
32873 Assure that the name of the new command is not already used in your document
32874 or by LaTeX-packages that you use.
32875 When you for example define the command
32887 , you get an error message because
32893 is already defined as command for
32894 \begin_inset Quotes eld
32898 \begin_inset Formula $\le$
32902 \begin_inset Quotes erd
32913 \begin_layout Standard
32914 The number of arguments is an integer in the range 0
32915 \begin_inset space \thinspace{}
32919 \begin_inset space \thinspace{}
32922 9 and specifies how many arguments the new command should have.
32923 With the optional value a value for an optional argument can be predefined.
32924 When this is done, the
32932 rgument of the new command is automatically an optional one.
32935 \begin_layout Standard
32936 Here are some examples:
32939 \begin_layout Itemize
32940 To define the command
32952 , the LaTeX-preamble line is:
32953 \begin_inset VSpace medskip
32957 \begin_inset Newline newline
32971 \begin_layout Itemize
32972 To define the command
32984 , the argument (that should be underlined) must be taken into account.
32985 For this the preamble line is:
32986 \begin_inset VSpace medskip
32990 \begin_inset Newline newline
33004 \begin_inset VSpace medskip
33008 \begin_inset Newline newline
33015 acts as argument placeholder, the
33019 behind it denotes that it is the placeholder for the first argument.
33022 \begin_layout Itemize
33030 \begin_inset space \thinspace{}
33034 \begin_inset space \space{}
33044 \begin_inset VSpace medskip
33048 \begin_inset Newline newline
33059 framebox#1#2{$#3$}}
33062 \begin_inset VSpace medskip
33066 \begin_inset Newline newline
33069 The two Dollar signs creates the extra formula needed for
33076 \begin_inset CommandInset ref
33078 reference "sub:Boxes-with-Frame"
33085 \begin_layout Itemize
33086 To create a new command for
33092 where the color for the box needn't to be specified, the argument for the
33093 color is defined optional:
33094 \begin_inset VSpace medskip
33098 \begin_inset Newline newline
33109 fcolorbox{#2}{#1}{$#3$}}
33112 \begin_inset VSpace medskip
33116 \begin_inset Newline newline
33119 When the color is not specified when using
33125 , the predefined color
33132 \begin_layout Standard
33133 A test of the new defined commands:
33136 \begin_layout Standard
33138 \begin_inset Tabular
33139 <lyxtabular version="3" rows="6" columns="2">
33140 <features tabularvalignment="middle">
33141 <column alignment="center" valignment="top" width="0">
33142 <column alignment="center" valignment="top" width="0">
33144 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33147 \begin_layout Plain Layout
33153 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33156 \begin_layout Plain Layout
33158 \begin_inset Note Note
33161 \begin_layout Plain Layout
33168 is only used as spacer.
33180 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33183 \begin_layout Plain Layout
33190 \begin_layout Plain Layout
33204 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33207 \begin_layout Plain Layout
33208 \begin_inset Formula $A\gr B$
33218 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33221 \begin_layout Plain Layout
33229 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33232 \begin_layout Plain Layout
33233 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
33243 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33246 \begin_layout Plain Layout
33250 \begin_inset Formula $\to$
33256 \begin_inset Formula $\to$
33267 \begin_layout Plain Layout
33281 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33284 \begin_layout Plain Layout
33285 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
33295 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33298 \begin_layout Plain Layout
33302 \begin_inset Formula $\to$
33313 \begin_layout Plain Layout
33327 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33330 \begin_layout Plain Layout
33331 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
33341 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33344 \begin_layout Plain Layout
33350 \begin_inset Formula $\to$
33361 \begin_layout Plain Layout
33375 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33378 \begin_layout Plain Layout
33379 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
33395 \begin_layout Subsection
33397 \begin_inset Index idx
33400 \begin_layout Plain Layout
33401 User-defined commands! Math macros
33407 \begin_inset Index idx
33410 \begin_layout Plain Layout
33419 \begin_layout Standard
33420 User-defined commands are especially convenient for complex expressions.
33421 When you are for example dealing in a document with quadratic equations,
33422 the same solution type occurs several times.
33423 The general form of a quadratic equation is
33424 \begin_inset Formula \[
33425 0=\lambda^{2}+p\lambda+q\]
33429 The general form of the solution is
33430 \begin_inset Formula \[
33431 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}\]
33438 \begin_layout Standard
33439 To define a command for the solution formula where only the three parameters
33441 \begin_inset Formula $\lambda$
33445 \begin_inset Formula $p$
33449 \begin_inset Formula $q$
33452 need to be specified and the index of
33453 \begin_inset Formula $\lambda$
33456 can be given optionally, the LaTeX-preamble line is
33457 \begin_inset Newline newline
33473 \begin_inset Newline newline
33477 \begin_inset Phantom HPhantom
33480 \begin_layout Plain Layout
33494 frac{#3^{2}}{4}-#4}}
33497 \begin_layout Standard
33498 To create with this the solution formula, the command
33499 \begin_inset Newline newline
33509 \begin_inset Formula $\to$
33515 \begin_inset Formula $\to$
33522 is inserted to a formula
33527 \begin_layout Standard
33528 The definition of the new command is unintuitive because one has to know
33529 the schemes of all used LaTeX commands, e.
33530 \begin_inset space \thinspace{}
33534 \begin_inset space \space{}
33537 that a fraction is inserted in LaTeX as
33541 frac{numerator}{denominator}
33544 Furthermore one can easily forget a brace in the definition and cannot
33545 see in LyX what the new command is doing.
33546 To avoid these problems LyX offers the possibility to use math macros instead
33556 \begin_layout Standard
33557 A math macro is created by using the menu
33559 Insert\SpecialChar \menuseparator
33560 Math\SpecialChar \menuseparator
33563 or the toolbar button
33564 \begin_inset Graphics
33565 filename ../images/math-macro_newmacroname_newcommand.png
33571 The math macro toolbar appears together with the following box where the
33573 \begin_inset Newline newline
33577 \begin_inset space \hspace*{\fill}
33581 \begin_inset Graphics
33582 filename clipart/macrobox.png
33587 \begin_inset space \hspace*{\fill}
33591 \begin_inset Newline newline
33595 \begin_inset FormulaMacro
33596 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
33601 newmacroname is the default name of the macro that should be changed to
33602 something sensible.
33603 The wanted formula is inserted in the first blue box.
33604 An argument placeholder is inserted with the command
33611 \begin_inset space \thinspace{}
33615 \begin_inset space \space{}
33624 or by using the macro toolbar button
33625 \begin_inset Graphics
33626 filename ../images/math-macro-add-param.png
33632 Argument placeholders are displayed red.
33633 Maximum 9 arguments are possible.
33634 Optional arguments are created with the toolbar button
33635 \begin_inset Graphics
33636 filename ../images/math-macro-add-optional-param.png
33642 The first non-optional argument can be transformed to an optional one with
33644 \begin_inset Graphics
33645 filename ../images/math-macro-make-optional.png
33651 In the second blue box the appearance of the macro in LyX can be defined.
33652 Normally you want to see it as it is defined, so the box is kept empty.
33653 But when you have created a macro that needs lot of space on the screen,
33654 you can insert in the box for example
33655 \begin_inset Newline newline
33685 \begin_inset Newline newline
33690 For the macro only the arguments with the macro name in front of them will
33691 then be displayed in LyX, leading to a better overview.
33692 The formula appears in the output as defined in the first box.
33693 \begin_inset Newline newline
33696 The appearance of macros in formulas can furthermore be changed for single
33697 macros by setting the cursor in the macro and using the menu
33699 View\SpecialChar \menuseparator
33701 \begin_inset space ~
33705 \begin_inset space ~
33713 \begin_layout Standard
33714 To use a macro, the macro name is inserted as command to a formula, in our
33722 Our macro looks in LyX like this:
33723 \begin_inset Newline newline
33727 \begin_inset space \hspace*{\fill}
33731 \begin_inset Graphics
33732 filename clipart/macrouse.png
33737 \begin_inset space \hspace*{\fill}
33741 \begin_inset Newline newline
33744 Here is our macro example with the arguments
33745 \begin_inset Formula $x$
33749 \begin_inset Formula $\ln(x)$
33753 \begin_inset Formula $B$
33759 \begin_layout Standard
33760 \begin_inset Formula \[
33768 \begin_layout Standard
33769 LyX offers in the menu
33771 Tools\SpecialChar \menuseparator
33772 Preferences\SpecialChar \menuseparator
33773 Editing\SpecialChar \menuseparator
33776 different styles to edit macros.
33777 To find the style that suits you the most, choose a style and set the cursor
33778 in a macro formula to see the difference.
33781 \begin_layout Standard
33782 A math macro is transformed internally to a
33788 command when exporting the document.
33795 command is not placed in the LaTeX-preamble, therefore macros can only
33796 be used in formulas that are in the document below the macro definition
33800 \begin_layout Standard
33801 Math macros can also be directly be created from a
33808 When writing for example the command
33811 \begin_inset Newline newline
33820 xleftarrow[#2]{#1}}
33821 \begin_inset Newline newline
33826 in LyX as normal text, highlighting it completely and using then the shortcut
33831 , the command will be transformed to a math macro.
33832 Using this method you need to be careful that the
33838 command is typed correctly, otherwise you get a faulty macro leading to
33842 \begin_layout Standard
33843 Math macros currently yet have the problem that further formulas in macro
33844 definitions are handled wrongly.
33845 Therefore the example
33852 \begin_inset CommandInset ref
33854 reference "sub:The-Command-newcommand"
33858 cannot be created as macro.
33861 \begin_layout Standard
33862 When the cursor is in a macro definition box, you will see the macro toolbar
33866 \begin_layout Standard
33867 \begin_inset VSpace defskip
33873 \begin_layout Standard
33874 \begin_inset Graphics
33875 filename clipart/MacroToolbar.png
33880 \begin_inset Index idx
33883 \begin_layout Plain Layout
33892 \begin_layout Standard
33893 \begin_inset VSpace defskip
33899 \begin_layout Standard
33900 The macro toolbar contains from left to right the following buttons:
33903 \begin_layout Standard
33904 \begin_inset VSpace defskip
33910 \begin_layout Standard
33911 \begin_inset Tabular
33912 <lyxtabular version="3" rows="9" columns="2">
33913 <features islongtable="true" longtabularalignment="center">
33914 <column alignment="left" valignment="top" width="0">
33915 <column alignment="left" valignment="top" width="85col%">
33916 <row interlinespace="2.5mm">
33917 <cell alignment="center" valignment="top" usebox="none">
33920 \begin_layout Plain Layout
33921 \begin_inset Graphics
33922 filename ../images/math-macro-remove-param.png
33923 BoundingBox 0bp 5bp 20bp 25bp
33924 rotateOrigin center
33933 <cell alignment="center" valignment="top" usebox="none">
33936 \begin_layout Plain Layout
33939 Edit\SpecialChar \menuseparator
33940 Math\SpecialChar \menuseparator
33942 \begin_inset space ~
33945 Definition\SpecialChar \menuseparator
33946 Remove Last Argument
33952 <row interlinespace="2.5mm">
33953 <cell alignment="center" valignment="top" usebox="none">
33956 \begin_layout Plain Layout
33957 \begin_inset Graphics
33958 filename ../images/math-macro-add-param.png
33959 BoundingBox 0bp 5bp 20bp 25bp
33960 rotateOrigin center
33969 <cell alignment="center" valignment="top" usebox="none">
33972 \begin_layout Plain Layout
33975 Edit\SpecialChar \menuseparator
33976 Math\SpecialChar \menuseparator
33978 \begin_inset space ~
33981 Definition\SpecialChar \menuseparator
33988 <row interlinespace="2.5mm">
33989 <cell alignment="center" valignment="top" usebox="none">
33992 \begin_layout Plain Layout
33993 \begin_inset Graphics
33994 filename ../images/math-macro-make-optional.png
33995 BoundingBox 0bp 5bp 20bp 25bp
33996 rotateOrigin center
34005 <cell alignment="center" valignment="top" usebox="none">
34008 \begin_layout Plain Layout
34011 Edit\SpecialChar \menuseparator
34012 Math\SpecialChar \menuseparator
34014 \begin_inset space ~
34017 Definition\SpecialChar \menuseparator
34018 Make First Non-Optional into
34019 \begin_inset Newline newline
34023 \begin_inset Phantom HPhantom
34026 \begin_layout Plain Layout
34029 Edit\SpecialChar \menuseparator
34030 Math\SpecialChar \menuseparator
34032 \begin_inset space ~
34035 Definition\SpecialChar \menuseparator
34047 <row interlinespace="2.5mm">
34048 <cell alignment="center" valignment="top" usebox="none">
34051 \begin_layout Plain Layout
34052 \begin_inset Graphics
34053 filename ../images/math-macro-make-nonoptional.png
34054 BoundingBox 0bp 5bp 20bp 25bp
34055 rotateOrigin center
34064 <cell alignment="center" valignment="top" usebox="none">
34067 \begin_layout Plain Layout
34070 Edit\SpecialChar \menuseparator
34071 Math\SpecialChar \menuseparator
34073 \begin_inset space ~
34076 Definition\SpecialChar \menuseparator
34077 Make Last Optional into
34078 \begin_inset Newline newline
34082 \begin_inset Phantom HPhantom
34085 \begin_layout Plain Layout
34088 Edit\SpecialChar \menuseparator
34089 Math\SpecialChar \menuseparator
34091 \begin_inset space ~
34094 Definition\SpecialChar \menuseparator
34100 Non-Optional Argument
34106 <row interlinespace="2.5mm">
34107 <cell alignment="center" valignment="top" usebox="none">
34110 \begin_layout Plain Layout
34111 \begin_inset Graphics
34112 filename ../images/math-macro-remove-optional-param.png
34113 BoundingBox 0bp 5bp 20bp 25bp
34114 rotateOrigin center
34123 <cell alignment="center" valignment="top" usebox="none">
34126 \begin_layout Plain Layout
34129 Edit\SpecialChar \menuseparator
34130 Math\SpecialChar \menuseparator
34132 \begin_inset space ~
34135 Definition\SpecialChar \menuseparator
34136 Remove Optional Argument
34142 <row interlinespace="2.5mm">
34143 <cell alignment="center" valignment="top" usebox="none">
34146 \begin_layout Plain Layout
34147 \begin_inset Graphics
34148 filename ../images/math-macro-add-optional-param.png
34149 BoundingBox 0bp 5bp 20bp 25bp
34150 rotateOrigin center
34159 <cell alignment="center" valignment="top" usebox="none">
34162 \begin_layout Plain Layout
34165 Edit\SpecialChar \menuseparator
34166 Math\SpecialChar \menuseparator
34168 \begin_inset space ~
34171 Definition\SpecialChar \menuseparator
34172 Insert Optional Argument
34178 <row interlinespace="2.5mm">
34179 <cell alignment="center" valignment="top" usebox="none">
34182 \begin_layout Plain Layout
34183 \begin_inset Graphics
34184 filename ../images/math-macro-remove-greedy-param.png
34185 BoundingBox 0bp 5bp 20bp 25bp
34186 rotateOrigin center
34195 <cell alignment="center" valignment="top" usebox="none">
34198 \begin_layout Plain Layout
34201 Edit\SpecialChar \menuseparator
34202 Math\SpecialChar \menuseparator
34204 \begin_inset space ~
34207 Definition\SpecialChar \menuseparator
34208 Remove Last Argument
34209 \begin_inset Newline newline
34213 \begin_inset Phantom HPhantom
34216 \begin_layout Plain Layout
34219 Edit\SpecialChar \menuseparator
34220 Math\SpecialChar \menuseparator
34222 \begin_inset space ~
34225 Definition\SpecialChar \menuseparator
34231 Spitting Out To The Right
34237 <row interlinespace="2.5mm">
34238 <cell alignment="center" valignment="top" usebox="none">
34241 \begin_layout Plain Layout
34242 \begin_inset Graphics
34243 filename ../images/math-macro-append-greedy-param.png
34244 BoundingBox 0bp 5bp 20bp 25bp
34245 rotateOrigin center
34254 <cell alignment="center" valignment="top" usebox="none">
34257 \begin_layout Plain Layout
34260 Edit\SpecialChar \menuseparator
34261 Math\SpecialChar \menuseparator
34263 \begin_inset space ~
34266 Definition\SpecialChar \menuseparator
34268 \begin_inset Newline newline
34272 \begin_inset Phantom HPhantom
34275 \begin_layout Plain Layout
34278 Edit\SpecialChar \menuseparator
34279 Math\SpecialChar \menuseparator
34281 \begin_inset space ~
34284 Definition\SpecialChar \menuseparator
34290 Eating From The Right
34296 <row interlinespace="2.5mm">
34297 <cell alignment="center" valignment="top" usebox="none">
34300 \begin_layout Plain Layout
34301 \begin_inset Graphics
34302 filename ../images/math-macro-add-greedy-optional-param.png
34303 BoundingBox 0bp 5bp 20bp 25bp
34304 rotateOrigin center
34313 <cell alignment="center" valignment="top" usebox="none">
34316 \begin_layout Plain Layout
34319 Edit\SpecialChar \menuseparator
34320 Math\SpecialChar \menuseparator
34322 \begin_inset space ~
34325 Definition\SpecialChar \menuseparator
34326 Append Optional Argument
34327 \begin_inset Newline newline
34331 \begin_inset Phantom HPhantom
34334 \begin_layout Plain Layout
34337 Edit\SpecialChar \menuseparator
34338 Math\SpecialChar \menuseparator
34340 \begin_inset space ~
34343 Definition\SpecialChar \menuseparator
34349 Eating From The Right
34362 \begin_layout Standard
34363 \begin_inset Newpage newpage
34369 \begin_layout Section
34371 \begin_inset Index idx
34374 \begin_layout Plain Layout
34383 \begin_layout Subsection
34385 \begin_inset Index idx
34388 \begin_layout Plain Layout
34397 \begin_layout Standard
34398 Negative numbers often look ugly in formulas because the minus sign before
34399 the number is set with the same length as the minus operator sign.
34400 When writing the negative number in normal text, the minus sign appears
34404 \begin_layout Standard
34405 Thus, the problem disappears when converting the minus sign to mathematical
34409 \begin_layout Standard
34410 An example to visualize the problem:
34413 \begin_layout Standard
34415 \begin_inset Tabular
34416 <lyxtabular version="3" rows="3" columns="2">
34417 <features tabularvalignment="middle">
34418 <column alignment="right" valignment="top" width="0">
34419 <column alignment="left" valignment="top" width="0">
34421 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34424 \begin_layout Plain Layout
34430 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
34433 \begin_layout Plain Layout
34441 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34444 \begin_layout Plain Layout
34450 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34453 \begin_layout Plain Layout
34454 \begin_inset Formula $x=-2$
34464 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34467 \begin_layout Plain Layout
34473 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34476 \begin_layout Plain Layout
34477 \begin_inset Formula $x=\textrm{-}2$
34493 \begin_layout Subsection
34494 Comma as decimal Separator
34495 \begin_inset Index idx
34498 \begin_layout Plain Layout
34507 \begin_layout Standard
34508 In LaTeX a comma inside a formula is used, according to the English convention,
34509 as number group separator.
34510 So there will be space added behind all commas in formulas.
34513 \begin_layout Standard
34514 To avoid this, the comma is highlighted and changed to mathematical text
34524 \begin_layout Standard
34525 To use all formula commas in the document as decimal separator, the file
34534 \begin_layout Plain Layout
34539 is part of the LaTeX-package
34544 \begin_inset Index idx
34547 \begin_layout Plain Layout
34552 \begin_layout Plain Layout
34572 \begin_inset Index idx
34575 \begin_layout Plain Layout
34581 is loaded with the LaTeX-preamble line
34584 \begin_layout Standard
34592 \begin_layout Subsection
34594 \begin_inset CommandInset label
34596 name "sub:Physical-Vectors"
34601 \begin_inset Index idx
34604 \begin_layout Plain Layout
34613 \begin_layout Standard
34614 Predefined vectors are offered by the LaTeX-package
34619 \begin_inset Index idx
34622 \begin_layout Plain Layout
34628 that is loaded with the LaTeX-preamble line
34631 \begin_layout Standard
34639 \begin_layout Standard
34643 \begin_layout Plain Layout
34653 \begin_inset Note Note
34656 \begin_layout Plain Layout
34657 The following table will only be displayed when the LaTeX-package
34669 \begin_layout Standard
34670 The following commands are defined:
34673 \begin_layout Standard
34675 \begin_inset Tabular
34676 <lyxtabular version="3" rows="4" columns="2">
34677 <features tabularvalignment="middle">
34678 <column alignment="center" valignment="top" width="0">
34679 <column alignment="center" valignment="top" width="0">
34681 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34684 \begin_layout Plain Layout
34690 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34693 \begin_layout Plain Layout
34701 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34704 \begin_layout Plain Layout
34714 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34717 \begin_layout Plain Layout
34718 \begin_inset Formula $\Bra{\psi}$
34728 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34731 \begin_layout Plain Layout
34741 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34744 \begin_layout Plain Layout
34745 \begin_inset Formula $\Ket{\psi}$
34755 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34758 \begin_layout Plain Layout
34770 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34773 \begin_layout Plain Layout
34774 \begin_inset Formula $\Braket{\psi|\phi}$
34790 \begin_layout Standard
34797 assures that all vertical bars are set in the size of the surrounding brackets:
34798 \begin_inset Formula \[
34799 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}\]
34807 \begin_layout Plain Layout
34817 \begin_inset Note Note
34820 \begin_layout Plain Layout
34821 The following will be displayed when the LaTeX-package
34833 \begin_layout Standard
34834 You need to install the LaTeX-package
34838 to see the rest of this subsection in the output.
34841 \begin_layout Standard
34845 \begin_layout Plain Layout
34857 \begin_layout Standard
34864 can also be achieved using the command
34870 , that is described in
34871 \begin_inset CommandInset ref
34873 reference "sub:Automatic-Bracket-Size"
34880 \begin_layout Subsection
34881 Self-defined Fractions
34882 \begin_inset CommandInset label
34884 name "sub:Self-defined-Fractions"
34889 \begin_inset Index idx
34892 \begin_layout Plain Layout
34893 Fractions ! self-defined
34901 \begin_layout Standard
34902 To define custom commands for fractions, the command
34909 \begin_inset Index idx
34912 \begin_layout Plain Layout
34920 is used in the following scheme:
34923 \begin_layout Standard
34936 bracket}{fraction bar thickness}{style}
34937 \begin_inset Newline newline
34941 \begin_inset Phantom HPhantom
34944 \begin_layout Plain Layout
34954 {numerator}{denominator}
34957 \begin_layout Standard
34958 The style is a number in the range of 0
34959 \begin_inset space \thinspace{}
34963 \begin_inset space \thinspace{}
34969 \begin_layout Standard
34971 \begin_inset Tabular
34972 <lyxtabular version="3" rows="5" columns="2">
34973 <features tabularvalignment="middle">
34974 <column alignment="center" valignment="top" width="0">
34975 <column alignment="center" valignment="top" width="0">
34977 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34980 \begin_layout Plain Layout
34986 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34989 \begin_layout Plain Layout
34997 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35000 \begin_layout Plain Layout
35006 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35009 \begin_layout Plain Layout
35010 display style formula
35017 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35020 \begin_layout Plain Layout
35026 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35029 \begin_layout Plain Layout
35037 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35040 \begin_layout Plain Layout
35046 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35049 \begin_layout Plain Layout
35057 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35060 \begin_layout Plain Layout
35066 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35069 \begin_layout Plain Layout
35083 \begin_layout Standard
35084 When no style is given, the size is adjusted to the surrounding environment
35085 like for the command
35094 \begin_layout Standard
35095 When no fraction bar thickness is given, the predefined value of 0.4
35096 \begin_inset space \thinspace{}
35102 \begin_layout Standard
35103 \begin_inset VSpace medskip
35106 For example, the commands
35119 \begin_inset CommandInset ref
35121 reference "sub:Fractions"
35125 are defined with the commands
35128 \begin_layout Standard
35137 genfrac{}{}{}{0}{#1}{#2}}
35140 \begin_layout Standard
35144 \begin_layout Standard
35153 genfrac{(}{)}{0pt}{1}{#1}{#2}}
35156 \begin_layout Standard
35157 \begin_inset VSpace medskip
35160 To define a fraction where the fraction bar thickness can be given as optional
35161 argument, the following line is inserted to the LaTeX-preamble:
35164 \begin_layout Standard
35173 genfrac{}{}{#1}{}{#2}{#3}}
35176 \begin_layout Standard
35178 \begin_inset Formula \begin{align*}
35179 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
35180 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
35185 As one can see, the distance of the numerator and the denominator to the
35186 fraction bar is round about three times the bar thickness.
35189 \begin_layout Subsection
35191 \begin_inset Index idx
35194 \begin_layout Plain Layout
35203 \begin_layout Standard
35204 To cancel formulas or formula parts, the LaTeX-package
35209 \begin_inset Index idx
35212 \begin_layout Plain Layout
35218 has to be loaded with the LaTeX-preamble line
35221 \begin_layout Standard
35226 usepackage[samesize]{cancel}
35229 \begin_layout Standard
35233 \begin_layout Plain Layout
35243 \begin_inset Note Note
35246 \begin_layout Plain Layout
35247 The following table will only be displayed when the LaTeX-package
35259 \begin_layout Standard
35260 There are four ways to cancel formulas:
35263 \begin_layout Standard
35265 \begin_inset Tabular
35266 <lyxtabular version="3" rows="5" columns="2">
35267 <features tabularvalignment="middle">
35268 <column alignment="center" valignment="top" width="0">
35269 <column alignment="center" valignment="top" width="0">
35271 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35274 \begin_layout Plain Layout
35280 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35283 \begin_layout Plain Layout
35285 \begin_inset Note Note
35288 \begin_layout Plain Layout
35295 are used here as spacer.
35307 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35310 \begin_layout Plain Layout
35319 \begin_layout Plain Layout
35333 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35336 \begin_layout Plain Layout
35337 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
35347 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35350 \begin_layout Plain Layout
35359 \begin_layout Plain Layout
35373 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35376 \begin_layout Plain Layout
35377 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
35387 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35390 \begin_layout Plain Layout
35399 \begin_layout Plain Layout
35413 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35416 \begin_layout Plain Layout
35417 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
35427 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35430 \begin_layout Plain Layout
35434 \begin_inset Formula $\to$
35445 \begin_layout Plain Layout
35459 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35462 \begin_layout Plain Layout
35463 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
35479 \begin_layout Standard
35486 is especially suitable to visualize the reduction of fractions within formulas:
35487 \begin_inset Formula \[
35488 \frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}}\]
35495 \begin_layout Standard
35499 \begin_layout Plain Layout
35509 \begin_inset Note Note
35512 \begin_layout Plain Layout
35513 The following will be displayed when the LaTeX-package
35525 \begin_layout Standard
35526 You need to install the LaTeX-package
35530 to see the rest of this subsection in the output.
35533 \begin_layout Standard
35537 \begin_layout Plain Layout
35549 \begin_layout Subsection
35550 Formulas in Section Headings
35551 \begin_inset CommandInset label
35553 name "sub:Formulas-in-Section"
35558 \begin_inset Index idx
35561 \begin_layout Plain Layout
35562 Formula ! in section headings
35570 \begin_layout Standard
35571 When formulas are used in section headings, the following has to be taken
35575 \begin_layout Standard
35576 \begin_inset Note Greyedout
35579 \begin_layout Plain Layout
35585 \begin_inset Index idx
35588 \begin_layout Plain Layout
35589 Packages ! hyperref
35594 support is enabled in the document settings dialog under
35597 \begin_inset space ~
35602 , PDF-bookmarks are created for every section heading in the table of contents.
35603 If a section heading contains formulas, they are incorrectly displayed
35604 in the bookmark text, because formulas in bookmarks infringe the PDF convention
35613 \begin_layout Standard
35614 Both problems can be solved by inserting at the end of the section heading
35615 a short title with the menu
35617 Insert\SpecialChar \menuseparator
35619 \begin_inset space ~
35625 Short titles are used as alternative for multiline section headings to
35626 keep the table of contents clearly arranged.
35627 Only the short title appears in the table of contents and therefore also
35628 in the PDF-bookmark.
35631 \begin_layout Standard
35632 When formulas should be used in the table of contents but
35636 is used, one can use the following command in TeX-mode:
35639 \begin_layout Standard
35644 texorpdfstring{part}{alternative}
35645 \begin_inset Index idx
35648 \begin_layout Plain Layout
35659 \begin_layout Standard
35660 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
35661 This can be characters, formulas, footnotes, but also cross-references.
35662 The alternative is used instead of the part for the bookmark.
35665 \begin_layout Standard
35666 Here are two example headings:
35667 \begin_inset VSpace -3mm
35674 \begin_layout Plain Layout
35686 \begin_layout Subsubsection
35687 Heading without formula in table of contents
35688 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35692 \begin_inset Argument
35695 \begin_layout Plain Layout
35696 Heading without formula in table of contents
35704 \begin_layout Subsubsection
35705 Heading with formula in table of contents
35709 \begin_layout Plain Layout
35719 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35726 \begin_layout Plain Layout
35736 \begin_layout Standard
35740 \begin_layout Plain Layout
35749 In the first heading a short title was used, in the second one
35758 \begin_layout Standard
35759 To get the same formatting as for the other headings, the complete heading
35768 \begin_layout Plain Layout
35770 \begin_inset CommandInset ref
35772 reference "sub:Bold-Formulas"
35784 \begin_layout Subsection
35785 Formulas in multi-column Text
35786 \begin_inset Index idx
35789 \begin_layout Plain Layout
35790 Formula ! in multi-column text
35798 \begin_layout Standard
35799 Formulas in multi-column text are often too wide to fit into a column and
35800 thus need to be set over the whole page width.
35801 This is done by using the LaTeX-package
35809 \begin_layout Plain Layout
35814 is part of every LaTeX standard installation.
35820 \begin_inset Index idx
35823 \begin_layout Plain Layout
35824 Packages ! multicol
35829 , that is loaded with the LaTeX-preamble line
35832 \begin_layout Standard
35837 usepackage{multicol}
35840 \begin_layout Standard
35841 \begin_inset Note Greyedout
35844 \begin_layout Plain Layout
35845 Note herby that the setting
35848 \begin_inset space ~
35855 Document\SpecialChar \menuseparator
35861 \begin_inset space ~
35881 \begin_layout Standard
35882 Before the multi-column text the command
35885 \begin_layout Standard
35890 begin{multicols}{column number}
35893 \begin_layout Standard
35894 is written in TeX-mode.
35895 The column number is a number in the range of 2
35896 \begin_inset space \thinspace{}
35900 \begin_inset space \thinspace{}
35904 Before the formula the multi-column text is ended by inserting the command
35907 \begin_layout Standard
35915 \begin_layout Standard
35919 \begin_layout Standard
35920 Due to the command some space is automatically added before the formula.
35922 \begin_inset space \thinspace{}
35925 mm vertical space is inserted before the formula.
35926 When the formula style
35932 \begin_layout Plain Layout
35934 \begin_inset CommandInset ref
35936 reference "sec:Formula-Styles"
35948 \begin_inset space \thinspace{}
35951 mm space is inserted instead.
35954 \begin_layout Standard
35955 As example a multi-column text with a displayed formula:
35958 \begin_layout Standard
35964 \begin_layout Plain Layout
35968 begin{multicols}{2}
35973 Das Spektrum wird fouriertransformiert.
35974 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
35975 , Lösungsmittel) zu trennen.
35976 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
35977 nun das Aussehen des Ausgangssignals.
35978 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
35979 über alle Phasen integrieren muss.
35981 \begin_inset Formula $S$
35984 unser normiertes Ausgangssignal und
35985 \begin_inset Formula $P$
35988 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
35992 \begin_layout Plain Layout
36002 \begin_inset VSpace -6mm
36006 \begin_inset Formula \begin{equation}
36007 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi\end{equation}
36015 \begin_layout Plain Layout
36019 begin{multicols}{2}
36025 \begin_inset Formula $S_{0}$
36028 das Signal ohne Gradient ist und die Normierungsbedingung
36029 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
36033 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
36035 \begin_inset Formula $\nicefrac{\pi}{2}$
36039 \begin_inset space \thinspace{}
36042 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
36043 das Signal zusätzlich abschwächt.
36044 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
36046 \begin_inset Formula $T_{2}$
36052 \begin_layout Standard
36058 \begin_layout Plain Layout
36070 \begin_layout Subsection
36071 Formulas with Description of Variables
36072 \begin_inset Index idx
36075 \begin_layout Plain Layout
36076 Formula ! with description of variables
36084 \begin_layout Standard
36085 To describe variables within a formula, like in formula
36086 \begin_inset CommandInset ref
36088 reference "eq:within"
36097 \begin_inset Formula $n$
36101 \begin_inset space ~
36104 matrix is used with left aligned columns for the
36105 \begin_inset Formula $n$
36112 \begin_layout Plain Layout
36114 \begin_inset CommandInset ref
36116 reference "sec:Matrices"
36125 To set the description in a smaller size, before the matrix e.
36126 \begin_inset space \thinspace{}
36130 \begin_inset space \space{}
36143 \begin_layout Plain Layout
36145 \begin_inset CommandInset ref
36147 reference "sub:Font-Sizes"
36159 \begin_layout Standard
36160 When the formula style
36166 \begin_layout Plain Layout
36168 \begin_inset CommandInset ref
36170 reference "sec:Formula-Styles"
36191 \begin_layout Plain Layout
36198 only works in formulas with the style
36203 \begin_inset CommandInset ref
36205 reference "sub:Variable-Space"
36214 is inserted before and after the matrix to have the same separation of
36215 the matrix from the equation and the side margin.
36218 \begin_layout Standard
36219 When the formula style
36223 is used, the method described in
36224 \begin_inset CommandInset ref
36226 reference "sub:Flalign-Environment"
36230 is used to indent formulas.
36232 \begin_inset CommandInset ref
36234 reference "eq:within"
36238 consists of five columns whereas in the first two columns contain the equation,
36239 the third the matrix and the last one an empty TeX-brace.
36240 \begin_inset Formula \begin{flalign}
36241 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
36242 \rho & \textrm{density}\\
36243 V & \textrm{volume}\\
36244 g & \textrm{gravitational acceleration}
36245 \end{array} & & {}\label{eq:within}\end{flalign}
36252 \begin_layout Subsection
36253 Upright small Greek Letters
36254 \begin_inset CommandInset label
36256 name "sub:Upright-small-Greek"
36261 \begin_inset Index idx
36264 \begin_layout Plain Layout
36265 Greek letters ! upright
36273 \begin_layout Standard
36274 Most of the math fonts only provide italic small Greek letters.
36275 But for symbols of elementary particles like pions and neutrinos, upright
36276 Greek letters are needed.
36285 \begin_layout Plain Layout
36290 is part of the LaTeX-package
36295 \begin_inset Index idx
36298 \begin_layout Plain Layout
36303 \begin_layout Plain Layout
36323 \begin_inset Index idx
36326 \begin_layout Plain Layout
36332 that is loaded with the LaTeX-preamble line
36335 \begin_layout Standard
36340 usepackage{upgreek}
36343 \begin_layout Standard
36349 \begin_layout Plain Layout
36359 \begin_inset Note Note
36362 \begin_layout Plain Layout
36363 The following table will only be displayed when the LaTeX-package
36372 They are created when the command for a small Greek letters is started
36378 For example the command
36385 \begin_inset Formula $\uptau$
36391 \begin_layout Standard
36392 With these commands reactions of elementary particles can be typeset:
36393 \begin_inset Formula \[
36394 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}\]
36401 \begin_layout Standard
36402 The upright letters are more bold and wider than the italic ones.
36403 They should therefore not be used for units like
36404 \begin_inset Quotes eld
36408 \begin_inset Quotes erd
36414 \begin_layout Standard
36418 \begin_layout Plain Layout
36428 \begin_inset Note Note
36431 \begin_layout Plain Layout
36432 The following will be displayed when the LaTeX-package
36444 \begin_layout Standard
36445 You need to install the LaTeX-package
36449 to see the rest of this subsection in the output.
36452 \begin_layout Standard
36456 \begin_layout Plain Layout
36468 \begin_layout Subsection
36469 Text Characters in Formulas
36470 \begin_inset CommandInset label
36472 name "sub:Text-Characters-in"
36477 \begin_inset Index idx
36480 \begin_layout Plain Layout
36489 \begin_layout Standard
36490 In some cases you might want to insert text characters directly into formulas.
36491 When for example the centered dot · is often used in formulas like
36492 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
36495 , one would have to insert the command
36505 \begin_layout Plain Layout
36507 \begin_inset CommandInset ref
36509 reference "sub:Binary-Operators"
36518 all the time, because this character is defined in all encodings as text
36520 But the encoding can be changed by this LaTeX-preamble line:
36523 \begin_layout Standard
36528 Declare Inputtext{183}{
36538 f\SpecialChar \textcompwordmark{}
36542 \begin_layout Standard
36543 The character encoding (menu
36545 Document\SpecialChar \menuseparator
36546 Settings\SpecialChar \menuseparator
36549 ) specifies what character appears when a keyboard key is pressed.
36550 When the key for the character '·' is pressed, internally the command
36557 But this command is not available in a formula so that you would get LaTeX-erro
36559 With the changed encoding the right command is chosen automatically, depending
36560 on if the character was inserted into a formula or not.
36563 \begin_layout Standard
36564 The encoding of several characters is saved in definition files.
36565 Fore example the encoding
36569 is defined in the file
36573 that is in the installation folder of LaTeX.
36574 Encodings should only be changed via the LaTeX-preamble and not in the
36576 Otherwise own documents could not be edited by other LyX users working
36577 on other computers.
36580 \begin_layout Standard
36581 \begin_inset VSpace medskip
36584 Besides the centered dot, in this document the degree sign ° is defined
36585 with the following LaTeX-preamble line so that it can directly be inserted
36589 \begin_layout Standard
36594 DeclareInputtext{176}{
36604 f\SpecialChar \textcompwordmark{}
36608 \begin_layout Standard
36609 \begin_inset Newpage newpage
36615 \begin_layout Section
36618 \begin_inset Index idx
36621 \begin_layout Plain Layout
36630 \begin_layout Standard
36631 This section is a summary of the most important typographic rules, listed
36636 \begin_layout Plain Layout
36637 This collection was partly taken from the German semi-official dictionary
36639 \begin_inset Quotes eld
36643 \begin_inset Quotes erd
36647 \begin_inset CommandInset citation
36653 that lists some of the ISO rules.
36654 More rules are listed in
36655 \begin_inset CommandInset citation
36669 \begin_layout Itemize
36678 \begin_layout Plain Layout
36679 done with font styles, see
36680 \begin_inset CommandInset ref
36682 reference "sub:Font-Styles"
36691 , no matter if they appear in italic text: 30
36692 \begin_inset space \thinspace{}
36696 \begin_inset Newline newline
36699 Between the value and the unit is the smallest space, see
36700 \begin_inset CommandInset ref
36702 reference "sub:Predefined-Space"
36707 \begin_inset Newline newline
36710 This convention is automatically fulfilled when the command
36717 When it is entered to a formula, two boxes appear.
36718 In the first one the value is inserted, in the second one the unit, and
36720 \begin_inset Formula $\unit[30]{km/h}$
36724 \begin_inset space \thinspace{}
36734 is not a real LaTeX command but the command
36740 , therefore you cannot use it in TeX code.
36743 \begin_layout Itemize
36744 Percent and perthousand signs are set like physical units:
36745 \begin_inset Newline newline
36749 \begin_inset space \thinspace{}
36755 \begin_layout Itemize
36756 The degree sign follows directly on the value: 15°, but not when it is used
36758 \begin_inset space \thinspace{}
36764 \begin_layout Itemize
36765 In numbers with more than four digits the smallest space is inserted before
36766 every third digit to group them:
36776 \begin_inset space \thinspace{}
36780 \begin_inset space \thinspace{}
36786 \begin_layout Itemize
36787 For dimensions like 120×90×40
36788 \begin_inset space \thinspace{}
36791 cm the multiplication sign
36792 \begin_inset Quotes eld
36796 \begin_inset Quotes erd
36800 It is available either via the command
36808 Insert\SpecialChar \menuseparator
36809 Special Character\SpecialChar \menuseparator
36815 \begin_layout Itemize
36816 Functions with names consisting of several letters are set upright to avoid
36818 \begin_inset CommandInset ref
36820 reference "sub:Predefined-Functions"
36827 \begin_layout Itemize
36828 Indices consisting of several letters, are set upright:
36829 \begin_inset Formula $E_{\mathrm{kin}}$
36833 \begin_inset Newline newline
36836 Components of matrices are set italic:
36837 \begin_inset Formula $\hat{H}_{kl}$
36843 \begin_layout Itemize
36844 The differentiation/integration operator 'd', the Euler's number 'e' and
36845 the imaginary unit 'i' should be set upright, to avoid mixing them up with
36849 \begin_layout Itemize
36850 The character that denotes a
36854 transformation is inserted either by the command
36862 \begin_layout Plain Layout
36875 Insert\SpecialChar \menuseparator
36876 Special Character\SpecialChar \menuseparator
36877 Symbols\SpecialChar \menuseparator
36879 \begin_inset space ~
36885 \begin_inset Formula $\mathscr{F}$
36891 \begin_layout Standard
36892 \begin_inset Newpage newpage
36898 \begin_layout Section
36900 \begin_inset Index idx
36903 \begin_layout Plain Layout
36912 \begin_layout Standard
36913 Some characters and symbols can be created with several commands.
36914 Here is a list of the synonym commands:
36917 \begin_layout Standard
36918 \begin_inset VSpace bigskip
36922 \begin_inset space \hfill{}
36926 \begin_inset Tabular
36927 <lyxtabular version="3" rows="12" columns="2">
36928 <features tabularvalignment="middle">
36929 <column alignment="center" valignment="top" width="0pt">
36930 <column alignment="center" valignment="top" width="0pt">
36932 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
36935 \begin_layout Plain Layout
36941 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
36944 \begin_layout Plain Layout
36946 \begin_inset Note Note
36949 \begin_layout Plain Layout
36956 is only used as spacer.
36968 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36971 \begin_layout Plain Layout
36979 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36982 \begin_layout Plain Layout
36986 \begin_layout Plain Layout
36999 \begin_layout Plain Layout
37013 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37016 \begin_layout Plain Layout
37024 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37027 \begin_layout Plain Layout
37037 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37040 \begin_layout Plain Layout
37048 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37051 \begin_layout Plain Layout
37061 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37064 \begin_layout Plain Layout
37072 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37075 \begin_layout Plain Layout
37083 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37086 \begin_layout Plain Layout
37094 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37097 \begin_layout Plain Layout
37105 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37108 \begin_layout Plain Layout
37116 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37119 \begin_layout Plain Layout
37129 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37132 \begin_layout Plain Layout
37140 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37143 \begin_layout Plain Layout
37153 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37156 \begin_layout Plain Layout
37164 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37167 \begin_layout Plain Layout
37177 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37180 \begin_layout Plain Layout
37188 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37191 \begin_layout Plain Layout
37201 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37204 \begin_layout Plain Layout
37212 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37215 \begin_layout Plain Layout
37223 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37226 \begin_layout Plain Layout
37234 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37237 \begin_layout Plain Layout
37249 \begin_inset space \hfill{}
37253 \begin_inset Tabular
37254 <lyxtabular version="3" rows="12" columns="2">
37255 <features tabularvalignment="middle">
37256 <column alignment="center" valignment="top" width="0pt">
37257 <column alignment="center" valignment="top" width="0pt">
37259 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37262 \begin_layout Plain Layout
37268 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37271 \begin_layout Plain Layout
37279 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37282 \begin_layout Plain Layout
37290 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37293 \begin_layout Plain Layout
37305 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37308 \begin_layout Plain Layout
37316 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37319 \begin_layout Plain Layout
37329 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37332 \begin_layout Plain Layout
37340 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37343 \begin_layout Plain Layout
37353 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37356 \begin_layout Plain Layout
37364 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37367 \begin_layout Plain Layout
37375 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37378 \begin_layout Plain Layout
37386 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37389 \begin_layout Plain Layout
37397 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37400 \begin_layout Plain Layout
37408 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37411 \begin_layout Plain Layout
37421 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37424 \begin_layout Plain Layout
37432 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37435 \begin_layout Plain Layout
37445 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37448 \begin_layout Plain Layout
37456 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37459 \begin_layout Plain Layout
37469 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37472 \begin_layout Plain Layout
37480 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37483 \begin_layout Plain Layout
37493 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37496 \begin_layout Plain Layout
37504 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37507 \begin_layout Plain Layout
37517 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37520 \begin_layout Plain Layout
37528 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37531 \begin_layout Plain Layout
37545 \begin_inset space \hfill{}
37551 \begin_layout Standard
37552 \begin_inset Newpage newpage
37558 \begin_layout Bibliography
37559 \labelwidthstring References
37560 \begin_inset CommandInset bibitem
37561 LatexCommand bibitem
37573 The LaTeX Companion
37576 Addison Wesley, 2004
37579 \begin_layout Bibliography
37580 \labelwidthstring References
37581 \begin_inset CommandInset bibitem
37582 LatexCommand bibitem
37588 \begin_inset CommandInset href
37591 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
37595 of LaTeX's math abilities
37598 \begin_layout Bibliography
37599 \labelwidthstring References
37600 \begin_inset CommandInset bibitem
37601 LatexCommand bibitem
37607 \begin_inset CommandInset href
37610 target "ftp://ftp.ams.org/pub/tex/doc/amsmath/amsldoc.pdf"
37618 \begin_layout Plain Layout
37630 \begin_layout Bibliography
37631 \labelwidthstring References
37632 \begin_inset CommandInset bibitem
37633 LatexCommand bibitem
37639 \begin_inset CommandInset href
37642 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
37646 of all symbols available with LaTeX-packages
37649 \begin_layout Bibliography
37650 \labelwidthstring References
37651 \begin_inset CommandInset bibitem
37652 LatexCommand bibitem
37658 \begin_inset CommandInset href
37660 name "Documentation"
37661 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
37665 of the LaTeX-package
37670 \begin_inset Index idx
37673 \begin_layout Plain Layout
37674 Packages ! hyperref
37682 \begin_layout Bibliography
37683 \labelwidthstring References
37684 \begin_inset CommandInset bibitem
37685 LatexCommand bibitem
37691 \begin_inset CommandInset href
37693 name "Documentation"
37694 target "http://www.ctan.org/tex-archive/macros/latex/contrib/mhchem/mhchem.pdf"
37698 of the LaTeX-package
37703 \begin_inset Index idx
37706 \begin_layout Plain Layout
37715 \begin_layout Bibliography
37716 \labelwidthstring References
37717 \begin_inset CommandInset bibitem
37718 LatexCommand bibitem
37724 \begin_inset CommandInset href
37727 target "http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf"
37738 \begin_inset CommandInset ref
37740 reference "sub:Operator-Limits"
37745 \begin_inset Index idx
37748 \begin_layout Plain Layout
37759 \begin_layout Bibliography
37760 \labelwidthstring References
37761 \begin_inset CommandInset bibitem
37762 LatexCommand bibitem
37773 Auflage, Duden 2001
37776 \begin_layout Bibliography
37777 \labelwidthstring References
37778 \begin_inset CommandInset bibitem
37779 LatexCommand bibitem
37785 \begin_inset CommandInset href
37788 target "http://physics.nist.gov/Document/checklist.pdf"
37792 for reviewing manuscripts
37795 \begin_layout Standard
37796 \begin_inset CommandInset index_print
37797 LatexCommand printindex