1 #LyX 2.0 created this file. For more info see http://www.lyx.org/
7 % DO NOT ALTER THIS PREAMBLE!!!
9 % This preamble is designed to ensure that the file prints
10 % out as advertised. If you mess with this preamble,
11 % parts of this document may not print out as expected. If you
12 % have problems LaTeXing this file, please contact
13 % the documentation team
14 % email: lyx-docs@lists.lyx.org
20 % set fonts for nicer pdf view
21 \IfFileExists{lmodern.sty}
22 {\usepackage{lmodern}}{}
24 \fi % end if pdflatex is used
26 % Folgendes Problem lösen:
27 % Besteht die Kapitelnummer aus zu vielen Ziffern, wird die
28 % Kapitelüberschrift im Inhaltsverzeichnis direkt an oder über
29 % die Kapitelnummer geschrieben.
30 % Als Lösung wird mehr Platz zwischen Nummer und
31 % Überschrift eingefügt.
32 \renewcommand{\l@subsection}{\@dottedtocline{2}{1.5em}{2.8em}}
33 \renewcommand{\l@subsubsection}{\@dottedtocline{3}{4.3em}{3.6em}}
35 % To be able to enter the character ° and · directly in LyX,
37 \DeclareInputText{176}{\ifmmode^\circ\else\textdegree\fi}
38 \DeclareInputText{183}{\ifmmode\cdot\else\textperiodcentered\fi}
40 % increase link area for cross-references and autoname them,
41 \AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}}
43 \settowidth{\abc}{\space}
46 \renewcommand{\equationautorefname}{\hspace{-\abc}}
47 \renewcommand{\sectionautorefname}{sec.\negthinspace}
48 \renewcommand{\subsectionautorefname}{sec.\negthinspace}
49 \renewcommand{\subsubsectionautorefname}{sec.\negthinspace}}
52 % don't load packages twice
53 % see first footnote in sec. 9.3
54 \@ifundefined{textcolor}{\usepackage{color}}{}
56 % the pages of the TOC are numbered roman
57 % and a PDF-bookmark for the TOC is added
59 \let\myTOC\tableofcontents
60 \renewcommand{\tableofcontents}{%
62 \pdfbookmark[1]{\contentsname}{}
65 \pagenumbering{arabic}}
67 % insert additional vertical space of 1.5 mm between footnotes,
69 \renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
71 % provides caption formatting
72 \setkomafont{captionlabel}{\bfseries}
75 \usepackage[samesize]{cancel}
77 % enables calculation of values
80 % for multiple columns used in sec. 23.7
86 % for the Fourier transformation symbol
89 % define a color, used in sec.9.3
90 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
92 % declare operators (see sec. 10.4 and sec. 15.2)
93 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
94 \DeclareMathOperator{\sgn}{sgn}
96 \newcommand{\spce}{\textvisiblespace}
98 % example definitions for sec. 20.1
99 \newcommand{\gr}{\Longrightarrow}
100 \newcommand{\us}[1]{\underline{#1}}
101 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
102 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
103 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
105 % example macro from sec. 19.4
106 %\def\tagform@#1{\maketag@@@{|#1|}}
108 % macro from sec. 10.2
109 \def\clap#1{\hbox to 0pt{\hss #1\hss}}
110 \def\mathclap {\mathpalette \mathclapinternal}
111 \def\mathclapinternal #1#2{\clap{$\mathsurround =0pt #1{#2}$}}
114 % ------------------------------------
115 % used to check for needed LaTeX packages
118 % check for package eurosym
119 % used for the Euro symbol
121 \IfFileExists{eurosym.sty}
122 {\usepackage[gennarrow]{eurosym}
123 \setboolean{eurosym}{true}}
124 {\setboolean{eurosym}{false}}
126 % check for package braket
127 % used for physical vectors
129 \IfFileExists{braket.sty}
131 \setboolean{braket}{true}}
132 {\setboolean{braket}{false}}
134 % check for package cancel
136 \IfFileExists{cancel.sty}
138 \setboolean{cancel}{true}}
139 {\setboolean{cancel}{false}}
141 % check for package upgreek
143 \IfFileExists{upgreek.sty}
144 {\usepackage{upgreek}
145 \setboolean{upgreek}{true}}
146 {\setboolean{upgreek}{false}}
148 \options bibliography=totoc,index=totoc,BCOR7.5mm,titlepage,captions=tableheading
149 \use_default_options false
150 \maintain_unincluded_children false
152 \language_package default
157 \font_typewriter default
158 \font_default_family default
159 \use_non_tex_fonts false
166 \default_output_format default
168 \bibtex_command default
169 \index_command default
173 \pdf_title "LyX's Math Manual"
174 \pdf_author "LyX Team, Uwe Stöhr"
175 \pdf_subject "LyX-documentation about math"
176 \pdf_keywords "LyX, Mathed"
178 \pdf_bookmarksnumbered true
179 \pdf_bookmarksopen true
180 \pdf_bookmarksopenlevel 1
181 \pdf_breaklinks false
185 \pdf_pdfusetitle false
186 \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false"
196 \paperorientation portrait
199 \notefontcolor #0000ff
206 \paragraph_separation skip
208 \quotes_language english
211 \paperpagestyle plain
215 \tracking_changes false
216 \output_changes false
219 \html_be_strict false
225 LyX's detailed Math manual
233 \begin_layout Plain Layout
235 If you have comments or error corrections, please send them to the LyX Documenta
239 \begin_inset CommandInset href
241 name "lyx-docs@lists.lyx.org"
242 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
253 \begin_inset Note Note
256 \begin_layout Plain Layout
263 \begin_inset Newline newline
267 \begin_inset Newline newline
275 \begin_layout Standard
276 \begin_inset CommandInset toc
277 LatexCommand tableofcontents
284 \begin_layout Standard
285 \begin_inset Note Note
288 \begin_layout Plain Layout
289 To export this document to PDF, PS or DVI the LaTeX-packages
291 braket, cancel, eurosym, mathdots, mhchem
298 If they are not installed the document can be export anyway but the sections
299 where the packages are required will not appear in the output.
304 ; if it is not installed, this file cannot be exported.
307 \begin_layout Plain Layout
308 The latest PDF-version of this document can be found here:
309 \begin_inset Newline newline
314 http://wiki.lyx.org/LyX/DocumentationDevelopment#Math
322 \begin_layout Standard
323 \begin_inset Newpage newpage
329 \begin_layout Section
333 \begin_layout Standard
334 This document explains LyX's math features and is furthermore a collection
335 of LaTeX-commands used for mathematical characters and constructs.
336 The explanations are designed for the usage of commands.
337 It is therefore required that you have read the section
348 \begin_layout Standard
349 Most of the characters and many constructs explained in this manual are
350 also accessible via the menu
354 \SpecialChar \menuseparator
370 But everybody who has to write lots of formulas will notice that it is
371 much faster to use commands instead of the math toolbar.
372 Therefore this manual is focused on commands but also mentions the correspondin
373 g toolbar buttons when available.
376 \begin_layout Standard
377 If not specially mentioned the commands are only available within formulas.
378 To be able to use all commands explained in this document, the option
382 must be used in the document settings (menu
384 Document\SpecialChar \menuseparator
385 Settings\SpecialChar \menuseparator
396 \begin_layout Plain Layout
399 Use AMS math package automatically
405 \begin_layout Plain Layout
414 -math when math constructs are found that are supported by LyX.
422 \begin_layout Standard
423 This document doesn't list all
427 \begin_layout Plain Layout
440 \begin_layout Plain Layout
445 \begin_layout Plain Layout
454 -math commands is in the file
457 \begin_inset CommandInset href
460 target "ftp://ctan.tug.org/tex-archive/macros/amstex/doc/amsguide.ps"
466 , which is part of every LaTeX standard installation.
471 for lucidity reasons.
474 \begin_layout Section
478 \begin_layout Standard
479 To create an inline formula
480 \begin_inset Index idx
483 \begin_layout Plain Layout
489 that is embedded into a text line, use one of the shortcuts
495 or the toolbar button
496 \begin_inset Graphics
497 filename ../images/math-mode.png
503 \begin_inset Newline newline
506 To create a display style formula
507 \begin_inset Index idx
510 \begin_layout Plain Layout
511 Formula ! display style
516 that will appear bigger and in an own paragraph, use one of these shortcuts:
526 \begin_layout Standard
527 To change a display style formula to an inline formula, set the cursor into
528 the formula and use one of the shortcuts
536 Edit\SpecialChar \menuseparator
537 Math\SpecialChar \menuseparator
541 The same way is used to change an inline formula to a display style formula.
544 \begin_layout Standard
545 To display parts of an inline formula in the size of a display style formula,
553 \begin_inset Index idx
556 \begin_layout Plain Layout
565 Then a new blue box appears in which the desired formula part is inserted.
568 \begin_layout Standard
569 Only inline formulas are allowed inside tables.
572 \begin_layout Standard
577 can be turned on in the menu
579 View\SpecialChar \menuseparator
583 When you click there on
584 \begin_inset Quotes eld
588 \begin_inset Quotes erd
591 the toolbar will be shown permanently at the bottom; this state is visualized
596 menu with a checkmark.
597 When you click in this state again on
598 \begin_inset Quotes eld
602 \begin_inset Quotes erd
613 is only shown when the cursor is within a formula; this state is visualized
614 by the renaming of the menu entry from
615 \begin_inset Quotes eld
619 \begin_inset Quotes erd
623 \begin_inset Quotes eld
631 \begin_inset Quotes erd
637 \begin_layout Standard
639 \begin_inset Index idx
642 \begin_layout Plain Layout
648 is invoked by pressing the toolbar button
649 \begin_inset Graphics
650 filename ../images/ert-insert.png
657 Insert\SpecialChar \menuseparator
662 \begin_layout Plain Layout
678 \begin_inset Note Note
681 \begin_layout Plain Layout
682 In LyX there are three
683 \begin_inset Quotes eld
687 \begin_inset Quotes erd
690 that appear in the output with sub- and superscript letters: TeX, LaTeX
694 \begin_layout Plain Layout
695 To avoid that these names are recognized as proper names, a TeX-brace pair
704 \begin_layout Standard
705 To change the LaTeX-preamble
706 \begin_inset Index idx
709 \begin_layout Plain Layout
717 Document\SpecialChar \menuseparator
718 Settings\SpecialChar \menuseparator
723 \begin_layout Plain Layout
739 \begin_layout Standard
740 To edit matrices, case differentiations and multiline formulas subsequently,
743 Edit\SpecialChar \menuseparator
748 Edit\SpecialChar \menuseparator
750 \begin_inset space \thinspace{}
754 \begin_inset space \thinspace{}
764 When lines and columns are swapped via the menu, the column or line where
765 the cursor is in is exchanged with the column to the right or the line
767 Is the cursor in the last column or row, the exchange is done with the
768 column to the left or the line above.
771 \begin_layout Standard
772 To write text in formulas
776 \begin_layout Plain Layout
777 For multiline formulas the command
784 \begin_inset CommandInset ref
786 reference "sub:Text-in-multiline"
800 \begin_inset Index idx
803 \begin_layout Plain Layout
810 \begin_inset Index idx
813 \begin_layout Plain Layout
820 This mode is invoked with the shortcut
826 or by the insertion of the command
833 \begin_inset Index idx
836 \begin_layout Plain Layout
845 The text appears black in LyX and can therefore be distinguished from the
846 other formula parts that appear blue.
847 In the output mathematical text is set upright, in contrary to other formula
851 \begin_layout Subsection*
855 \begin_layout Standard
856 Most of the LaTeX-commands for math constructs have the following scheme:
859 \begin_layout Standard
875 \begin_layout Standard
876 A command starts always with a backslash
877 \begin_inset Quotes gld
887 \begin_inset Quotes grd
891 To omit optional arguments, also omit the associated brackets.
892 The braces around the required arguments are named in this document as
894 \begin_inset Index idx
897 \begin_layout Plain Layout
904 If you add in a formula a left brace to a command name, LyX creates automatical
906 In all other cases TeX-braces are created in formulas with the command
914 TeX-braces appear red in LyX, in contrary to normal braces that appear
916 In TeX-mode no command is needed to get TeX-braces.
917 TeX-braces don't appear in the output.
920 \begin_layout Standard
921 When commands without arguments, like commands for symbols are entered in
922 TeX-mode, a space character must
926 be behind the command to end it.
927 This space doesn't appear in the output.
928 When the space should appear in the output, the space must be followed
929 by a protected space in normal text.
932 \begin_layout Standard
933 A protected space is inserted with
936 arg "space-insert protected"
942 \begin_layout Subsection*
943 \begin_inset Newpage newpage
949 \begin_layout Itemize
954 \begin_layout Plain Layout
955 This visible space character can be created with the command
962 \begin_inset Index idx
965 \begin_layout Plain Layout
973 , inserted in TeX-mode.
982 \begin_layout Plain Layout
995 denotes a space character to be input.
998 \begin_layout Itemize
1000 \begin_inset Formula $\to$
1003 denotes the usage of the corresponding arrow key on the keyboard.
1006 \begin_layout Subsection*
1010 \begin_layout Standard
1012 \begin_inset Float table
1018 \begin_layout Plain Layout
1020 \begin_inset Caption
1022 \begin_layout Plain Layout
1023 \begin_inset CommandInset label
1025 name "tab:Available-units"
1037 \begin_layout Plain Layout
1039 \begin_inset Tabular
1040 <lyxtabular version="3" rows="13" columns="2">
1041 <features tabularvalignment="middle">
1042 <column alignment="center" valignment="top" width="0">
1043 <column alignment="center" valignment="top" width="0">
1045 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1048 \begin_layout Plain Layout
1054 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1057 \begin_layout Plain Layout
1065 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1068 \begin_layout Plain Layout
1074 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1077 \begin_layout Plain Layout
1085 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1088 \begin_layout Plain Layout
1094 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1097 \begin_layout Plain Layout
1105 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1108 \begin_layout Plain Layout
1114 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1117 \begin_layout Plain Layout
1119 \begin_inset space \thinspace{}
1123 \begin_inset space \thinspace{}
1133 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1136 \begin_layout Plain Layout
1142 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1145 \begin_layout Plain Layout
1147 \begin_inset space \thinspace{}
1151 \begin_inset space \thinspace{}
1161 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1164 \begin_layout Plain Layout
1170 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1173 \begin_layout Plain Layout
1175 \begin_inset space \thinspace{}
1179 \begin_inset space \thinspace{}
1189 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1192 \begin_layout Plain Layout
1198 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1201 \begin_layout Plain Layout
1203 \begin_inset space \thinspace{}
1207 \begin_inset space \thinspace{}
1217 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1220 \begin_layout Plain Layout
1226 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1229 \begin_layout Plain Layout
1231 \begin_inset space \thinspace{}
1235 \begin_inset space \thinspace{}
1245 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1248 \begin_layout Plain Layout
1254 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1257 \begin_layout Plain Layout
1259 \begin_inset space \thinspace{}
1263 \begin_inset Formula $\approx$
1267 \begin_inset space \thinspace{}
1277 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1280 \begin_layout Plain Layout
1286 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1289 \begin_layout Plain Layout
1291 \begin_inset space \thinspace{}
1295 \begin_inset space \thinspace{}
1305 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1308 \begin_layout Plain Layout
1314 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1317 \begin_layout Plain Layout
1321 \begin_inset Quotes eld
1327 \begin_inset Quotes erd
1337 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1340 \begin_layout Plain Layout
1346 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1349 \begin_layout Plain Layout
1351 \begin_inset Quotes eld
1359 \begin_inset Quotes erd
1369 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1372 \begin_layout Plain Layout
1378 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1381 \begin_layout Plain Layout
1383 \begin_inset space \thinspace{}
1387 \begin_inset Formula $\nicefrac{1}{18}$
1391 \begin_inset space \thinspace{}
1412 \begin_layout Standard
1413 \begin_inset Newpage newpage
1419 \begin_layout Section
1423 \begin_layout Subsection
1425 \begin_inset Index idx
1428 \begin_layout Plain Layout
1435 \begin_inset Index idx
1438 \begin_layout Plain Layout
1445 \begin_inset Index idx
1448 \begin_layout Plain Layout
1453 \begin_layout Plain Layout
1464 \begin_layout Plain Layout
1477 \begin_inset Index idx
1480 \begin_layout Plain Layout
1485 \begin_layout Plain Layout
1496 \begin_layout Plain Layout
1511 \begin_layout Standard
1512 Indices are created with an underscore
1513 \begin_inset Quotes eld
1517 \begin_inset Quotes erd
1520 or via the math toolbar button
1521 \begin_inset Graphics
1522 filename ../images/math-subscript.png
1527 , exponents with a caret
1528 \begin_inset Quotes eld
1532 \begin_inset Quotes erd
1535 or via the math toolbar button
1536 \begin_inset Graphics
1537 filename ../images/math-superscript.png
1545 \begin_layout Standard
1547 \begin_inset Tabular
1548 <lyxtabular version="3" rows="4" columns="2">
1549 <features tabularvalignment="middle">
1550 <column alignment="center" valignment="top" width="0pt">
1551 <column alignment="center" valignment="top" width="0pt">
1553 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1556 \begin_layout Plain Layout
1562 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1565 \begin_layout Plain Layout
1567 \begin_inset Note Note
1570 \begin_layout Plain Layout
1577 is only used as spacer.
1589 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1592 \begin_layout Plain Layout
1598 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1601 \begin_layout Plain Layout
1602 \begin_inset Formula $B_{V}$
1612 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1615 \begin_layout Plain Layout
1621 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1624 \begin_layout Plain Layout
1625 \begin_inset Formula $\raisebox{5mm}{}B^{V}$
1635 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1638 \begin_layout Plain Layout
1643 \begin_layout Plain Layout
1657 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1660 \begin_layout Plain Layout
1661 \begin_inset Formula $\raisebox{5mm}{}B^{A}$
1677 \begin_layout Standard
1678 As the caret is in some languages an accent, vowels will be accentuated
1679 in this case and not set as exponents
1683 \begin_layout Plain Layout
1684 Depending on the used keyboard settings this can also happen for other character
1691 To get in this case exponents, press
1695 after the caret as in the last example.
1698 \begin_layout Subsection
1700 \begin_inset CommandInset label
1702 name "sub:Fractions"
1707 \begin_inset Index idx
1710 \begin_layout Plain Layout
1719 \begin_layout Standard
1720 Fractions are generated with the command
1727 \begin_inset Index idx
1730 \begin_layout Plain Layout
1738 or via the math toolbar button
1739 \begin_inset Graphics
1740 filename ../images/math/frac.png
1746 The font size is adjusted automatically, depending on whether the fraction
1747 is in an inline or display style formula.
1748 With the math toolbar button
1749 \begin_inset Graphics
1750 filename ../images/math/frac-square.png
1755 you can select different fraction types.
1758 \begin_layout Standard
1766 \begin_inset Index idx
1769 \begin_layout Plain Layout
1777 a fraction can be created that has in any case the size of a display style
1786 \begin_inset Index idx
1789 \begin_layout Plain Layout
1797 the fraction appears always with the size of an inline formula.
1801 \begin_layout Standard
1802 A line with the fraction
1803 \begin_inset Formula $\frac{1}{2}$
1806 that was created with the command
1815 \begin_layout Standard
1816 A line with the fraction
1817 \begin_inset Formula $\dfrac{1}{2}$
1820 that was created with the command
1829 \begin_layout Standard
1831 \begin_inset Tabular
1832 <lyxtabular version="3" rows="4" columns="2">
1833 <features tabularvalignment="middle">
1834 <column alignment="center" valignment="top" width="0pt">
1835 <column alignment="center" valignment="top" width="0pt">
1837 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1840 \begin_layout Plain Layout
1846 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1849 \begin_layout Plain Layout
1851 \begin_inset Note Note
1854 \begin_layout Plain Layout
1861 is only used as spacer.
1873 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1876 \begin_layout Plain Layout
1883 \begin_layout Plain Layout
1893 \begin_inset Formula $\downarrow$
1901 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1904 \begin_layout Plain Layout
1905 \begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$
1915 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1918 \begin_layout Plain Layout
1925 \begin_layout Plain Layout
1935 \begin_inset Formula $\downarrow$
1943 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1946 \begin_layout Plain Layout
1947 \begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$
1957 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1960 \begin_layout Plain Layout
1967 \begin_layout Plain Layout
1980 \begin_layout Plain Layout
1995 \begin_layout Plain Layout
2005 \begin_inset Formula $\downarrow$
2009 \begin_inset Formula $\downarrow\downarrow$
2017 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2020 \begin_layout Plain Layout
2021 \begin_inset Formula $\raisebox{8mm}{}\dfrac{e^{\frac{1}{2}}}{3}\raisebox{-4mm}{}$
2037 \begin_layout Standard
2038 \begin_inset VSpace bigskip
2042 \begin_inset Newpage newpage
2045 For nested fractions the command
2052 \begin_inset Index idx
2055 \begin_layout Plain Layout
2065 \begin_inset VSpace -3mm
2071 \begin_layout Standard
2072 \begin_inset Formula
2074 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
2075 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}
2083 \begin_layout Standard
2084 The command for the example above is:
2087 \begin_layout Standard
2096 \begin_layout Plain Layout
2106 \begin_inset Formula $\downarrow$
2115 \begin_layout Plain Layout
2130 \begin_layout Plain Layout
2140 \begin_inset Formula $\downarrow$
2144 \begin_inset Formula $\downarrow$
2150 \begin_layout Standard
2151 \begin_inset VSpace medskip
2157 \begin_layout Standard
2164 sets the fraction always in the size of a displayed formula, also when
2165 it is part of another fraction.
2168 \begin_layout Standard
2169 It is possible to specify the alignment of the numerator.
2176 is used to left align it, the command
2189 centers the numerator.
2190 These fractions demonstrate the different alignments:
2193 \begin_layout Standard
2194 \begin_inset Formula $\cfrac[l]{A}{B+C}$
2198 \begin_inset Formula $\cfrac{A}{B+C}$
2202 \begin_inset Formula $\cfrac[r]{A}{B+C}$
2208 \begin_layout Standard
2209 \begin_inset Note Greyedout
2212 \begin_layout Plain Layout
2229 are no real LaTeX commands but represent the command
2233 cfrac[alignment]{numerator}{denominator}
2236 Therefore you cannot use them in TeX code.
2244 \begin_layout Standard
2245 \begin_inset VSpace medskip
2248 It is often advantageous to combine
2261 \begin_inset Formula
2263 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}
2271 \begin_layout Standard
2272 For inline fractions with a sloped fraction stroke you can use the command
2280 \begin_inset Index idx
2283 \begin_layout Plain Layout
2292 \begin_inset Formula $\nicefrac{5}{31}$
2302 \begin_inset Index idx
2305 \begin_layout Plain Layout
2314 \begin_inset Formula $\unitfrac{5}{31}$
2317 There is furthermore the command
2323 that offers to write a fraction in combination with a number:
2324 \begin_inset Formula $\unitfrac[2]{1}{3}$
2330 \begin_layout Standard
2331 \begin_inset Note Greyedout
2334 \begin_layout Plain Layout
2345 is not a real LaTeX command but the command
2346 \begin_inset Newline newline
2353 unitfrac[number]{numerator}{denominator}
2356 Therefore you cannot use it in TeX code.
2364 \begin_layout Standard
2365 How to define own fractions where the fraction stroke can be changed, is
2367 \begin_inset CommandInset ref
2369 reference "sub:Self-defined-Fractions"
2376 \begin_layout Subsection
2378 \begin_inset Index idx
2381 \begin_layout Plain Layout
2390 \begin_layout Standard
2391 Square roots are created with
2398 \begin_inset Index idx
2401 \begin_layout Plain Layout
2409 or the math toolbar button
2410 \begin_inset Graphics
2411 filename ../images/math/sqrt.png
2416 , all other roots with the command
2423 \begin_inset Index idx
2426 \begin_layout Plain Layout
2434 or with the math toolbar button
2435 \begin_inset Graphics
2436 filename ../images/math/root.png
2444 \begin_layout Standard
2446 \begin_inset Tabular
2447 <lyxtabular version="3" rows="3" columns="2">
2448 <features tabularvalignment="middle">
2449 <column alignment="center" valignment="top" width="0pt">
2450 <column alignment="center" valignment="top" width="0pt">
2452 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2455 \begin_layout Plain Layout
2461 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2464 \begin_layout Plain Layout
2466 \begin_inset Note Note
2469 \begin_layout Plain Layout
2476 is only used as spacer.
2488 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2491 \begin_layout Plain Layout
2498 \begin_layout Plain Layout
2512 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2515 \begin_layout Plain Layout
2516 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$
2526 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
2529 \begin_layout Plain Layout
2536 \begin_layout Plain Layout
2546 \begin_inset Formula $\downarrow$
2554 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
2557 \begin_layout Plain Layout
2558 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$
2574 \begin_layout Standard
2575 A square root can also be created with
2581 when the root index field is left empty.
2584 \begin_layout Standard
2585 With certain indices the distance to the root is too small, like in this
2587 \begin_inset Formula $\sqrt[\beta]{B}$
2591 \begin_inset Newline newline
2595 \begin_inset Formula $\beta$
2599 To avoid this, the commands
2606 \begin_inset Index idx
2609 \begin_layout Plain Layout
2624 \begin_inset Index idx
2627 \begin_layout Plain Layout
2635 are used with the following scheme:
2638 \begin_layout Standard
2652 \begin_layout Standard
2653 Distance is the number of Big Points (unit bp;
2654 \begin_inset Formula $\mathrm{72\, bp=1\, inch}$
2657 ), that the index should be moved to the left or top, resp..
2658 The commands are written to the index.
2659 This way the command
2660 \begin_inset Newline newline
2670 \begin_inset Formula $\to$
2676 \begin_inset Formula $\to$
2685 \begin_layout Plain Layout
2695 \begin_inset Formula $\to$
2699 \begin_inset Newline newline
2704 produces a correct typeset formula:
2705 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2711 \begin_layout Subsection
2712 Binomial Coefficients
2713 \begin_inset Index idx
2716 \begin_layout Plain Layout
2717 Binomial coefficients
2725 \begin_layout Standard
2726 Binomial coefficients are inserted with the command
2733 \begin_inset Index idx
2736 \begin_layout Plain Layout
2744 or with the submenu of the math toolbar button
2745 \begin_inset Graphics
2746 filename ../images/math/frac-square.png
2752 Analog to fractions (
2771 \begin_inset Index idx
2774 \begin_layout Plain Layout
2789 \begin_inset Index idx
2792 \begin_layout Plain Layout
2801 For other brackets around binomial coeficients there are the commands
2808 \begin_inset Index idx
2811 \begin_layout Plain Layout
2826 \begin_inset Index idx
2829 \begin_layout Plain Layout
2840 \begin_layout Standard
2842 \begin_inset Tabular
2843 <lyxtabular version="3" rows="6" columns="2">
2844 <features tabularvalignment="middle">
2845 <column alignment="center" valignment="top" width="0pt">
2846 <column alignment="center" valignment="top" width="0pt">
2848 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2851 \begin_layout Plain Layout
2857 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2860 \begin_layout Plain Layout
2862 \begin_inset Note Note
2865 \begin_layout Plain Layout
2872 is only used as spacer.
2884 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2887 \begin_layout Plain Layout
2894 \begin_layout Plain Layout
2904 \begin_inset Formula $\downarrow$
2912 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2915 \begin_layout Plain Layout
2916 \begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$
2926 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2929 \begin_layout Plain Layout
2936 \begin_layout Plain Layout
2946 \begin_inset Formula $\downarrow$
2954 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2957 \begin_layout Plain Layout
2958 \begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$
2968 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2971 \begin_layout Plain Layout
2978 \begin_layout Plain Layout
2988 \begin_inset Formula $\downarrow$
2996 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2999 \begin_layout Plain Layout
3000 \begin_inset Formula $\raisebox{5mm}{}\tbinom{A}{B}\raisebox{-2.5mm}{}$
3010 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3013 \begin_layout Plain Layout
3020 \begin_layout Plain Layout
3030 \begin_inset Formula $\downarrow$
3038 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3041 \begin_layout Plain Layout
3042 \begin_inset Formula $\raisebox{5mm}{}{A \brack B}\raisebox{-2.5mm}{}$
3052 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3055 \begin_layout Plain Layout
3062 \begin_layout Plain Layout
3072 \begin_inset Formula $\downarrow$
3080 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3083 \begin_layout Plain Layout
3084 \begin_inset Formula $\raisebox{5mm}{}{A \brace B}\raisebox{-2.5mm}{}$
3100 \begin_layout Subsection
3101 Case Differentiations
3102 \begin_inset Index idx
3105 \begin_layout Plain Layout
3106 Case differentiations
3114 \begin_layout Standard
3116 \begin_inset Tabular
3117 <lyxtabular version="3" rows="3" columns="2">
3118 <features tabularvalignment="middle">
3119 <column alignment="center" valignment="top" width="0pt">
3120 <column alignment="center" valignment="top" width="0pt">
3122 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3125 \begin_layout Plain Layout
3131 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3134 \begin_layout Plain Layout
3142 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3145 \begin_layout Plain Layout
3152 \begin_layout Plain Layout
3162 \begin_inset Formula $\to$
3166 \begin_inset Index idx
3169 \begin_layout Plain Layout
3182 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3185 \begin_layout Plain Layout
3186 \begin_inset Formula $\begin{cases}
3197 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3200 \begin_layout Plain Layout
3207 \begin_layout Plain Layout
3219 arg "newline-insert newline"
3227 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3230 \begin_layout Plain Layout
3231 \begin_inset Formula $\begin{cases}
3232 A & \textrm{for }x>0\\
3233 B & \textrm{for }x=0
3250 \begin_layout Standard
3257 or the usage of the math toolbar button
3258 \begin_inset Graphics
3259 filename ../images/math/cases.png
3264 you can create new lines with the shortcut
3267 arg "newline-insert newline"
3270 or the table toolbar button
3271 \begin_inset Graphics
3272 filename ../images/tabular-feature_append-row.png
3280 \begin_layout Standard
3287 is also available via the menu
3289 Insert\SpecialChar \menuseparator
3290 Math\SpecialChar \menuseparator
3296 \begin_layout Subsection
3298 \begin_inset Index idx
3301 \begin_layout Plain Layout
3310 \begin_layout Standard
3318 \begin_inset Index idx
3321 \begin_layout Plain Layout
3329 every character can be displayed canceled.
3330 The characters are quasi accentuated by a slash.
3333 \begin_layout Standard
3335 \begin_inset Tabular
3336 <lyxtabular version="3" rows="4" columns="2">
3337 <features tabularvalignment="middle">
3338 <column alignment="center" valignment="top" width="0pt">
3339 <column alignment="center" valignment="top" width="0pt">
3341 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3344 \begin_layout Plain Layout
3350 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3353 \begin_layout Plain Layout
3361 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3364 \begin_layout Plain Layout
3372 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3375 \begin_layout Plain Layout
3376 \begin_inset Formula $\not=$
3386 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3389 \begin_layout Plain Layout
3399 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3402 \begin_layout Plain Layout
3403 \begin_inset Formula $\not\le$
3413 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3416 \begin_layout Plain Layout
3426 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3429 \begin_layout Plain Layout
3430 \begin_inset Formula $\not\parallel$
3446 \begin_layout Standard
3447 The last example shows, that not all negations look good.
3448 Therefore there are for some negations special commands (see
3449 \begin_inset CommandInset ref
3451 reference "sub:Mathematical-Symbols"
3456 \begin_inset CommandInset ref
3458 reference "sec:Relations"
3465 \begin_layout Subsection
3467 \begin_inset CommandInset label
3469 name "sub:Placeholders"
3474 \begin_inset Index idx
3477 \begin_layout Plain Layout
3484 \begin_inset Index idx
3487 \begin_layout Plain Layout
3488 Chemical characters ! Isotopes
3494 \begin_inset Index idx
3497 \begin_layout Plain Layout
3502 \begin_layout Plain Layout
3513 \begin_layout Plain Layout
3528 \begin_layout Standard
3530 \begin_inset space \thinspace{}
3534 \begin_inset space \space{}
3541 \begin_layout Plain Layout
3542 Typesetting isotopes and chemical symbols is described in
3543 \begin_inset CommandInset ref
3545 reference "sub:Chemical-Symbols-and"
3554 the following problem occurs:
3557 \begin_layout Standard
3559 \begin_inset Tabular
3560 <lyxtabular version="3" rows="2" columns="2">
3561 <features tabularvalignment="middle">
3562 <column alignment="center" valignment="top" width="0pt">
3563 <column alignment="center" valignment="top" width="0pt">
3565 <cell alignment="center" valignment="top" usebox="none">
3568 \begin_layout Plain Layout
3569 Indices created with sub- and superscripts:
3574 <cell alignment="center" valignment="top" usebox="none">
3577 \begin_layout Plain Layout
3578 \begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
3588 <cell alignment="center" valignment="top" usebox="none">
3591 \begin_layout Plain Layout
3597 <cell alignment="center" valignment="top" usebox="none">
3600 \begin_layout Plain Layout
3601 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3615 \begin_inset Note Note
3618 \begin_layout Plain Layout
3625 is only used as spacer.
3633 \begin_layout Standard
3634 The shorter index is by default placed below or above the first character
3635 of the longer index.
3636 To avoid this there is the command
3643 \begin_inset Index idx
3646 \begin_layout Plain Layout
3654 or the math toolbar button
3655 \begin_inset space \thinspace{}
3662 \begin_layout Plain Layout
3663 can be found in the submenu of the toolbar button
3664 \begin_inset Graphics
3665 filename ../images/math/space.png
3676 \begin_inset Graphics
3677 filename ../images/math/phantom.png
3682 that creates one or more phantom characters.
3689 a small blue box appears that is superposed with two red arrows.
3690 The arrows indicate that the complete width and height of the box content
3691 will be created as placeholder.
3692 Phantom characters are accordingly placeholders with the size of the characters.
3695 \begin_layout Standard
3697 \begin_inset Tabular
3698 <lyxtabular version="3" rows="4" columns="2">
3699 <features tabularvalignment="middle">
3700 <column alignment="center" valignment="top" width="0">
3701 <column alignment="center" valignment="top" width="0">
3703 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3706 \begin_layout Plain Layout
3712 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3715 \begin_layout Plain Layout
3717 \begin_inset Note Note
3720 \begin_layout Plain Layout
3727 is only used as spacer.
3739 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3742 \begin_layout Plain Layout
3747 \begin_layout Plain Layout
3762 \begin_layout Plain Layout
3772 \begin_inset Formula $\to$
3779 \begin_layout Plain Layout
3793 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3796 \begin_layout Plain Layout
3797 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
3807 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3810 \begin_layout Plain Layout
3815 \begin_layout Plain Layout
3830 \begin_layout Plain Layout
3840 \begin_inset Formula $\to$
3847 \begin_layout Plain Layout
3861 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3864 \begin_layout Plain Layout
3865 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
3875 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3878 \begin_layout Plain Layout
3885 \begin_layout Plain Layout
3900 \begin_layout Plain Layout
3910 \begin_inset Formula $\to$
3917 \begin_layout Plain Layout
3931 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3934 \begin_layout Plain Layout
3935 \begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
3951 \begin_layout Standard
3952 Furthermore there are the commands
3959 \begin_inset Index idx
3962 \begin_layout Plain Layout
3971 \begin_inset space ~
3975 \begin_inset Graphics
3976 filename ../images/math/vphantom.png
3988 \begin_inset Index idx
3991 \begin_layout Plain Layout
4000 \begin_inset space ~
4004 \begin_inset Graphics
4005 filename ../images/math/hphantom.png
4017 creates only space for the maximal height of the characters in the box
4018 but not for its width.
4025 creates only space for the width of the box content.
4026 Therefore the boxes of both commands have only one red arrow.
4029 \begin_layout Standard
4040 \begin_layout Plain Layout
4055 space for the height of the integral sign,
4059 \begin_layout Plain Layout
4066 creates an integral sign, see
4067 \begin_inset CommandInset ref
4069 reference "sub:Big-Operators"
4078 because this is the larger character.
4079 An example application is in
4080 \begin_inset CommandInset ref
4082 reference "sub:Multiline-Brackets"
4089 \begin_layout Standard
4090 Placeholders can also be used for text when it is inserted via the menu
4093 Insert\SpecialChar \menuseparator
4094 Formatting\SpecialChar \menuseparator
4100 \begin_layout Standard
4102 \begin_inset Newline newline
4106 \begin_inset Phantom Phantom
4109 \begin_layout Plain Layout
4118 \begin_layout Subsection
4120 \begin_inset Index idx
4123 \begin_layout Plain Layout
4130 \begin_inset Index idx
4133 \begin_layout Plain Layout
4134 Formula ! underlined
4142 \begin_layout Standard
4144 \begin_inset Tabular
4145 <lyxtabular version="3" rows="4" columns="2">
4146 <features tabularvalignment="middle">
4147 <column alignment="center" valignment="top" width="0pt">
4148 <column alignment="center" valignment="top" width="0pt">
4150 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4153 \begin_layout Plain Layout
4159 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4162 \begin_layout Plain Layout
4164 \begin_inset Note Note
4167 \begin_layout Plain Layout
4174 is only used as spacer.
4186 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4189 \begin_layout Plain Layout
4196 \begin_layout Plain Layout
4206 \begin_inset Index idx
4209 \begin_layout Plain Layout
4222 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4225 \begin_layout Plain Layout
4226 \begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
4236 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
4239 \begin_layout Plain Layout
4246 \begin_layout Plain Layout
4256 \begin_inset Index idx
4259 \begin_layout Plain Layout
4272 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
4275 \begin_layout Plain Layout
4276 \begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
4286 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4289 \begin_layout Plain Layout
4296 \begin_layout Plain Layout
4311 \begin_layout Plain Layout
4325 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4328 \begin_layout Plain Layout
4329 \begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
4345 \begin_layout Standard
4346 In the last example it doesn't matter if first
4361 \begin_layout Standard
4362 To double underline e.
4363 \begin_inset space \thinspace{}
4367 \begin_inset space \space{}
4379 \begin_layout Standard
4380 It is possible to place up to 6 lines above or below characters.
4383 \begin_layout Standard
4384 \begin_inset VSpace bigskip
4387 Custom lines can be created using the command
4394 \begin_inset Index idx
4397 \begin_layout Plain Layout
4405 which has the following scheme:
4408 \begin_layout Standard
4413 rule[vertical offset]{length}{thickness}
4416 \begin_layout Standard
4417 The optional vertical offset shifts the line upwards (or downwards, when
4418 the value is negative).
4420 \begin_inset CommandInset ref
4422 reference "tab:Available-units"
4426 can be used for the values.
4427 Here are two example lines created with the commands
4428 \begin_inset Newline newline
4435 rule[-2ex]{3cm}{2pt}
4446 \begin_layout Standard
4448 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4454 \begin_layout Standard
4461 can also be used for text when a line is inserted via the menu
4463 Insert\SpecialChar \menuseparator
4464 Formatting\SpecialChar \menuseparator
4466 \begin_inset space ~
4474 \begin_layout Standard
4476 \begin_inset CommandInset line
4487 \begin_layout Subsection
4489 \begin_inset CommandInset label
4496 \begin_inset Index idx
4499 \begin_layout Plain Layout
4508 \begin_layout Standard
4509 There are different types of ellipses available.
4513 \begin_layout Plain Layout
4514 In the math toolbar in the submenu of the button
4515 \begin_inset Graphics
4516 filename ../images/math/ldots.png
4526 For listings dots at the baseline are used (
4533 \begin_inset Index idx
4536 \begin_layout Plain Layout
4544 ), while for operations dots are needed that are on the same height as the
4552 \begin_inset Index idx
4555 \begin_layout Plain Layout
4564 When using the command
4571 \begin_inset Index idx
4574 \begin_layout Plain Layout
4582 , LaTeX decides on the basis of the next character what type is used.
4585 \begin_layout Standard
4587 \begin_inset Tabular
4588 <lyxtabular version="3" rows="9" columns="2">
4589 <features tabularvalignment="middle">
4590 <column alignment="center" valignment="top" width="0pt">
4591 <column alignment="center" valignment="top" width="0pt">
4593 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4596 \begin_layout Plain Layout
4602 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4605 \begin_layout Plain Layout
4613 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4616 \begin_layout Plain Layout
4621 \begin_layout Plain Layout
4636 \begin_layout Plain Layout
4650 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4653 \begin_layout Plain Layout
4654 \begin_inset Formula $A_{1},\dots,A_{n}$
4664 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4667 \begin_layout Plain Layout
4672 \begin_layout Plain Layout
4687 \begin_layout Plain Layout
4701 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4704 \begin_layout Plain Layout
4705 \begin_inset Formula $A_{1}+\dots+A_{n}$
4715 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4718 \begin_layout Plain Layout
4723 \begin_layout Plain Layout
4738 \begin_layout Plain Layout
4752 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4755 \begin_layout Plain Layout
4756 \begin_inset Formula $A_{1},\ldots,A_{n}$
4766 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4769 \begin_layout Plain Layout
4774 \begin_layout Plain Layout
4789 \begin_layout Plain Layout
4803 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4806 \begin_layout Plain Layout
4807 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4817 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4820 \begin_layout Plain Layout
4828 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4831 \begin_layout Plain Layout
4832 \begin_inset Formula $\vdots$
4842 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4845 \begin_layout Plain Layout
4853 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4856 \begin_layout Plain Layout
4857 \begin_inset Formula $\ddots$
4867 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4870 \begin_layout Plain Layout
4878 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4881 \begin_layout Plain Layout
4882 \begin_inset Formula $\iddots$
4892 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4895 \begin_layout Plain Layout
4897 \begin_inset space \thinspace{}
4900 matrix with the different dots
4905 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4908 \begin_layout Plain Layout
4909 \begin_inset Formula $\begin{array}{ccc}
4910 A_{11} & \cdots & A_{1m}\\
4911 \vdots & \ddots & \vdots\\
4912 A_{n1} & \cdots & A_{nm}
4929 \begin_layout Standard
4930 The ellipses available in menu
4932 Insert\SpecialChar \menuseparator
4934 \begin_inset space ~
4948 \begin_layout Standard
4949 \begin_inset VSpace medskip
4958 , one of the options
4960 Use mathdots package (automatically)
4962 must be set in the document settings under
4965 \begin_inset space ~
4971 \begin_inset Newline newline
4976 Use mathdots package
4978 will improve the appearance of all dots in the documents if their font
4979 style or size is not the default.
4982 \begin_layout Standard
4983 \begin_inset VSpace medskip
4986 Specially for matrices there are ellipses that span over several columns.
4987 They are created with the command
4994 \begin_inset Index idx
4997 \begin_layout Plain Layout
5005 , that has the following scheme:
5008 \begin_layout Standard
5013 hdotsfor[distance]{number of columns}
5016 \begin_layout Standard
5017 The number of columns specifies how many columns should be spanned.
5018 Distance is a factor for the distance between the dots.
5021 \begin_layout Standard
5022 In the following matrix the command
5028 was inserted in the first box of the second line, to get an ellipsis with
5029 a dot distance twice as long as with the command
5036 \begin_inset Formula
5038 \left(\begin{array}{cccc}
5047 Note that the matrix fields that should be spanned must be empty, otherwise
5048 you get LaTeX-errors.
5051 \begin_layout Standard
5052 \begin_inset VSpace bigskip
5055 Furthermore you can fill with the command
5062 \begin_inset Index idx
5065 \begin_layout Plain Layout
5073 the rest of a line with dots.
5074 The effect of these commands is the same like with
5081 \begin_inset CommandInset ref
5083 reference "sub:Variable-Space"
5090 \begin_layout Standard
5091 For example the command
5099 \begin_layout Plain Layout
5113 \begin_layout Standard
5114 \begin_inset Formula $A\dotfill B$
5120 \begin_layout Standard
5127 there is for a line the command
5134 \begin_inset Index idx
5137 \begin_layout Plain Layout
5148 \begin_layout Standard
5149 \begin_inset Formula $A\hrulefill B$
5155 \begin_layout Standard
5156 To use the commands for text, they have to be inserted in TeX-mode.
5159 \begin_layout Section
5161 \begin_inset CommandInset label
5168 \begin_inset Index idx
5171 \begin_layout Plain Layout
5180 \begin_layout Standard
5181 Matrices can be inserted via the math toolbar button
5182 \begin_inset Graphics
5183 filename ../images/dialog-show_mathmatrix.png
5190 Insert\SpecialChar \menuseparator
5191 Math\SpecialChar \menuseparator
5195 In the matrix dialog you can specify the number of columns and rows, the
5196 alignment and the decoration.
5197 The vertical alignment is hereby only of importance for matrices in inline
5201 \begin_layout Standard
5202 The first matrix is top
5203 \begin_inset Formula $\begin{array}[t]{cccc}
5211 \begin_inset Formula $\begin{array}{cccc}
5218 and the third bottom
5219 \begin_inset Formula $\begin{array}[b]{cccc}
5229 \begin_layout Standard
5230 The horizontal alignment specifies how the column entries should be aligned.
5231 It is set by entering a letter for every column.
5236 denotes left aligned,
5245 To create for example a 4
5250 \begin_inset space ~
5253 matrix where the first column is left aligned, the second and third are
5254 centered and the last one is right aligned, one enters for the horizontal
5260 Normally are in a matrix all columns centered, therefore the default is
5261 for every column is a
5268 \begin_layout Standard
5269 Horizontal alignment:
5272 \begin_layout Standard
5278 \begin_inset Formula $\begin{array}{lll}
5290 \begin_inset Formula $\begin{array}{ccc}
5302 \begin_inset Formula $\begin{array}{rrr}
5312 \begin_layout Standard
5313 To add or delete rows and columns subsequently, the math toolbar buttons
5315 \begin_inset Graphics
5316 filename ../images/tabular-feature_append-row.png
5322 \begin_inset Graphics
5323 filename ../images/tabular-feature_delete-row.png
5329 \begin_inset space \thinspace{}
5334 Edit\SpecialChar \menuseparator
5338 New rows can also be created with
5341 arg "newline-insert newline"
5347 \begin_layout Standard
5348 \begin_inset VSpace bigskip
5355 adds parentheses in the selected style around the matrix.
5356 Alternatively, parentheses can can either be created with the commands
5364 \begin_inset Index idx
5367 \begin_layout Plain Layout
5382 \begin_inset Index idx
5385 \begin_layout Plain Layout
5396 \begin_inset space ~
5402 \begin_inset CommandInset ref
5404 reference "sub:Automatic-Bracket-Size"
5408 , or by using the following commands:
5409 \begin_inset VSpace medskip
5415 \begin_layout Standard
5416 \begin_inset space \hfill{}
5420 \begin_inset Tabular
5421 <lyxtabular version="3" rows="4" columns="2">
5422 <features tabularvalignment="middle">
5423 <column alignment="center" valignment="top" width="0">
5424 <column alignment="center" valignment="top" width="0">
5426 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5429 \begin_layout Plain Layout
5435 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5438 \begin_layout Plain Layout
5440 \begin_inset Note Note
5443 \begin_layout Plain Layout
5450 is only used as spacer.
5462 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5465 \begin_layout Plain Layout
5472 \begin_layout Plain Layout
5486 \begin_inset space \thinspace{}
5494 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5497 \begin_layout Plain Layout
5498 \begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
5499 0 & \textrm{-}\mathrm{i}\\
5501 \end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
5511 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5514 \begin_layout Plain Layout
5521 \begin_layout Plain Layout
5535 \begin_inset space \thinspace{}
5543 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5546 \begin_layout Plain Layout
5547 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
5548 0 & \textrm{-}\mathrm{i}\\
5550 \end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
5560 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5563 \begin_layout Plain Layout
5570 \begin_layout Plain Layout
5584 \begin_inset space \thinspace{}
5592 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5595 \begin_layout Plain Layout
5596 \begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
5597 0 & \textrm{-}\mathrm{i}\\
5599 \end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
5613 \begin_inset space \hfill{}
5617 \begin_inset Tabular
5618 <lyxtabular version="3" rows="4" columns="2">
5619 <features tabularvalignment="middle">
5620 <column alignment="center" valignment="top" width="0">
5621 <column alignment="center" valignment="top" width="0">
5623 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5626 \begin_layout Plain Layout
5632 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5635 \begin_layout Plain Layout
5643 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5646 \begin_layout Plain Layout
5653 \begin_layout Plain Layout
5667 \begin_inset space \thinspace{}
5675 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5678 \begin_layout Plain Layout
5679 \begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
5680 0 & \textrm{-}\mathrm{i}\\
5682 \end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
5692 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5695 \begin_layout Plain Layout
5702 \begin_layout Plain Layout
5716 \begin_inset space \thinspace{}
5724 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5727 \begin_layout Plain Layout
5728 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
5729 0 & \textrm{-}\mathrm{i}\\
5731 \end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
5741 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5744 \begin_layout Plain Layout
5751 \begin_layout Plain Layout
5765 \begin_inset space \thinspace{}
5773 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5776 \begin_layout Plain Layout
5777 \begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
5778 0 & \textrm{-}\mathrm{i}\\
5780 \end{array}\end{matrix}\raisebox{-5.3mm}{}$
5794 \begin_inset space \hfill{}
5800 \begin_layout Standard
5801 \begin_inset VSpace medskip
5805 \begin_inset space \thinspace{}
5809 \begin_inset space \space{}
5818 is inserted, a blue box appears between two vertical lines where the matrix
5820 \begin_inset Newline newline
5823 Note that decorated matrices ignore the vertical alignment.
5826 \begin_layout Standard
5827 \begin_inset Note Greyedout
5830 \begin_layout Plain Layout
5835 LaTeX limits the number of matrix columns with decorations to 10.
5836 If you need more than 10
5837 \begin_inset space ~
5840 columns, you have to add this line to the document preamble:
5843 \begin_layout Plain Layout
5848 setcounter{MaxMatrixCols}{number}
5851 \begin_layout Plain Layout
5856 is the number of columns between 11 and 99.
5864 \begin_layout Standard
5865 \begin_inset VSpace bigskip
5868 As all multiline formulas are matrices, the length
5875 \begin_inset Index idx
5878 \begin_layout Plain Layout
5886 that is described in
5887 \begin_inset CommandInset ref
5889 reference "sub:Column-Separation"
5893 can also be used to change the column separation of matrices.
5896 \begin_layout Standard
5897 To change the row separation, the command
5904 \begin_inset Index idx
5907 \begin_layout Plain Layout
5916 It is used as follows:
5919 \begin_layout Standard
5926 arraystretch}{stretch factor}
5927 \begin_inset Index idx
5930 \begin_layout Plain Layout
5941 \begin_layout Standard
5948 assigns the stretch factor to the predefined command
5956 \begin_inset space \thinspace{}
5960 \begin_inset space \space{}
5963 the row separation, use the factor 2.
5964 This is then used for all following matrices.
5965 To go back to the original separation, assign the factor 1 to
5974 \begin_layout Standard
5975 To set matrices into a text line, the command
5982 \begin_inset Index idx
5985 \begin_layout Plain Layout
5994 When it is inserted a blue box with two dashed lines appears.
5995 In this box the matrix is inserted.
5998 \begin_layout Standard
6000 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
6002 \end{smallmatrix}\right)$
6008 \begin_layout Section
6009 Brackets and Delimiters
6010 \begin_inset Index idx
6013 \begin_layout Plain Layout
6020 \begin_inset Index idx
6023 \begin_layout Plain Layout
6032 \begin_layout Subsection
6033 Vertical Brackets and Delimiters
6034 \begin_inset Index idx
6037 \begin_layout Plain Layout
6046 \begin_layout Standard
6047 \begin_inset space \hfill{}
6051 \begin_inset Tabular
6052 <lyxtabular version="3" rows="9" columns="2">
6053 <features tabularvalignment="middle">
6054 <column alignment="center" valignment="top" width="0pt">
6055 <column alignment="center" valignment="top" width="0pt">
6057 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6060 \begin_layout Plain Layout
6066 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6069 \begin_layout Plain Layout
6077 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6080 \begin_layout Plain Layout
6086 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6089 \begin_layout Plain Layout
6090 \begin_inset Formula $($
6100 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6103 \begin_layout Plain Layout
6109 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6112 \begin_layout Plain Layout
6113 \begin_inset Formula $\{$
6123 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6126 \begin_layout Plain Layout
6132 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6135 \begin_layout Plain Layout
6136 \begin_inset Formula $[$
6146 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6149 \begin_layout Plain Layout
6157 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6160 \begin_layout Plain Layout
6161 \begin_inset Formula $\langle$
6171 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6174 \begin_layout Plain Layout
6182 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6185 \begin_layout Plain Layout
6186 \begin_inset Formula $\lceil$
6196 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6199 \begin_layout Plain Layout
6207 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6210 \begin_layout Plain Layout
6211 \begin_inset Formula $\lfloor$
6221 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6224 \begin_layout Plain Layout
6230 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6233 \begin_layout Plain Layout
6234 \begin_inset Formula $/$
6244 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6247 \begin_layout Plain Layout
6253 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6256 \begin_layout Plain Layout
6257 \begin_inset Formula $|$
6271 \begin_inset space \hfill{}
6275 \begin_inset Tabular
6276 <lyxtabular version="3" rows="9" columns="2">
6277 <features tabularvalignment="middle">
6278 <column alignment="center" valignment="top" width="0pt">
6279 <column alignment="center" valignment="top" width="0pt">
6281 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6284 \begin_layout Plain Layout
6290 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6293 \begin_layout Plain Layout
6301 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6304 \begin_layout Plain Layout
6310 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6313 \begin_layout Plain Layout
6314 \begin_inset Formula $)$
6324 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6327 \begin_layout Plain Layout
6333 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6336 \begin_layout Plain Layout
6337 \begin_inset Formula $\}$
6347 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6350 \begin_layout Plain Layout
6356 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6359 \begin_layout Plain Layout
6360 \begin_inset Formula $]$
6370 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6373 \begin_layout Plain Layout
6381 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6384 \begin_layout Plain Layout
6385 \begin_inset Formula $\rangle$
6395 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6398 \begin_layout Plain Layout
6406 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6409 \begin_layout Plain Layout
6410 \begin_inset Formula $\rceil$
6420 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6423 \begin_layout Plain Layout
6431 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6434 \begin_layout Plain Layout
6435 \begin_inset Formula $\rfloor$
6445 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6448 \begin_layout Plain Layout
6458 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6461 \begin_layout Plain Layout
6462 \begin_inset Formula $\backslash$
6472 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6475 \begin_layout Plain Layout
6483 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6486 \begin_layout Plain Layout
6487 \begin_inset Formula $\|$
6501 \begin_inset space \hfill{}
6507 \begin_layout Standard
6510 \begin_inset Note Greyedout
6513 \begin_layout Plain Layout
6518 In TeX-mode the command
6525 \begin_inset Index idx
6528 \begin_layout Plain Layout
6536 must be used for the backslash, because the command
6544 produces there a line break.
6552 \begin_layout Standard
6553 For all characters listed above the size can be adjusted with the commands
6554 described in the following two subsections.
6555 When using these commands, the characters < and > can directly be used
6556 instead of the commands
6571 \begin_layout Subsubsection
6573 \begin_inset CommandInset label
6575 name "sub:Manual-Bracket-Size"
6580 \begin_inset Index idx
6583 \begin_layout Plain Layout
6584 Bracket size ! manual
6592 \begin_layout Standard
6593 The bracket size can be specified manually by the LaTeX-commands
6600 \begin_inset Index idx
6603 \begin_layout Plain Layout
6636 denotes the smallest and
6642 the largest bracket size.
6645 \begin_layout Standard
6646 These commands are used to emphasize levels of brackets:
6649 \begin_layout Standard
6651 \begin_inset Tabular
6652 <lyxtabular version="3" rows="2" columns="2">
6653 <features tabularvalignment="middle">
6654 <column alignment="center" valignment="top" width="0pt">
6655 <column alignment="center" valignment="top" width="0pt">
6657 <cell alignment="center" valignment="top" usebox="none">
6660 \begin_layout Plain Layout
6661 all brackets in the same size:
6666 <cell alignment="center" valignment="top" usebox="none">
6669 \begin_layout Plain Layout
6670 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
6680 <cell alignment="center" valignment="top" usebox="none">
6683 \begin_layout Plain Layout
6689 <cell alignment="center" valignment="top" usebox="none">
6692 \begin_layout Plain Layout
6693 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6707 \begin_inset Note Note
6710 \begin_layout Plain Layout
6717 is only used as spacer.
6725 \begin_layout Standard
6726 For the second formula the command
6736 \begin_layout Plain Layout
6750 \begin_layout Standard
6751 Here is an overview about all bracket sizes:
6754 \begin_layout Standard
6774 \begin_layout Plain Layout
6791 \begin_layout Plain Layout
6804 \begin_layout Plain Layout
6820 \begin_layout Standard
6822 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6828 \begin_layout Standard
6835 -commands there is the variant
6842 \begin_inset Index idx
6845 \begin_layout Plain Layout
6853 that adds a bit more space between the bracket and its content, and the
6867 \begin_inset Index idx
6870 \begin_layout Plain Layout
6880 , that don't add additional space.
6885 at the end of the command
6891 is for a left bracket; for a right bracket this will be replaced by an
6897 A left or right bracket can each be an opening or closing bracket.
6900 \begin_layout Standard
6901 In the following table is a comparison of the variants:
6904 \begin_layout Standard
6906 \begin_inset Tabular
6907 <lyxtabular version="3" rows="5" columns="2">
6908 <features tabularvalignment="middle">
6909 <column alignment="center" valignment="middle" width="0">
6910 <column alignment="center" valignment="middle" width="0">
6912 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6915 \begin_layout Plain Layout
6921 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6924 \begin_layout Plain Layout
6926 \begin_inset Note Note
6929 \begin_layout Plain Layout
6936 is only used as spacer.
6948 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6951 \begin_layout Plain Layout
6966 \begin_layout Plain Layout
6984 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6987 \begin_layout Plain Layout
6988 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
6998 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7001 \begin_layout Plain Layout
7016 \begin_layout Plain Layout
7034 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7037 \begin_layout Plain Layout
7038 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
7048 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7051 \begin_layout Plain Layout
7066 \begin_layout Plain Layout
7084 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7087 \begin_layout Plain Layout
7088 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
7098 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7101 \begin_layout Plain Layout
7113 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7116 \begin_layout Plain Layout
7117 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
7133 \begin_layout Subsubsection
7134 Automatic Bracket Size
7135 \begin_inset CommandInset label
7137 name "sub:Automatic-Bracket-Size"
7142 \begin_inset Index idx
7145 \begin_layout Plain Layout
7146 Bracket size ! automatic
7154 \begin_layout Standard
7155 Brackets with variable size can be inserted with the commands
7162 \begin_inset Index idx
7165 \begin_layout Plain Layout
7180 \begin_inset Index idx
7183 \begin_layout Plain Layout
7191 or via the math toolbar button
7192 \begin_inset Graphics
7193 filename ../images/dialog-show_mathdelimiter.png
7211 the wanted bracket must be inserted.
7212 The bracket size will then automatically be calculated for the output.
7215 \begin_layout Standard
7217 normal bracket: The command
7227 \begin_layout Plain Layout
7237 \begin_inset Formula $\downarrow$
7244 \begin_layout Plain Layout
7256 \begin_inset Formula
7266 \begin_layout Standard
7268 multiline bracket: The command
7280 \begin_layout Plain Layout
7290 \begin_inset Formula $\downarrow$
7297 \begin_layout Plain Layout
7311 \begin_inset Formula
7313 \ln\left(\frac{A}{C}\right)
7321 \begin_layout Standard
7337 \begin_inset space ~
7343 This has the advantage that you can see in LyX immediately the real bracket
7344 size and that the matching right bracket will be created too.
7345 \begin_inset Newline newline
7348 The command for the last example would then be:
7362 \begin_layout Plain Layout
7372 \begin_inset Formula $\downarrow$
7378 \begin_layout Standard
7379 To omit a left or right bracket, a dot is inserted for the omitted bracket.
7380 For example the command
7390 \begin_layout Plain Layout
7400 \begin_inset Formula $\downarrow$
7407 \begin_layout Plain Layout
7423 \begin_inset Formula
7425 \left.\frac{A}{B}\right\}
7444 will be converted by LyX to brackets in the right size when the document
7445 is reloaded and an omitted bracket will appear as dashed line.
7448 \begin_layout Standard
7449 \begin_inset VSpace bigskip
7452 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
7460 \begin_inset Index idx
7463 \begin_layout Plain Layout
7471 is additionally available for all brackets and limits.
7472 With this command the height of the following character is adapted to the
7473 one of the surrounding brackets, what is e.
7474 \begin_inset space \thinspace{}
7478 \begin_inset space \space{}
7481 needed for physical vectors:
7482 \begin_inset Formula
7484 \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle
7489 For physical vectors there is a special LaTeX-package, described in
7490 \begin_inset CommandInset ref
7492 reference "sub:Physical-Vectors"
7499 \begin_layout Subsection
7501 \begin_inset Index idx
7504 \begin_layout Plain Layout
7505 Brackets ! horizontal
7513 \begin_layout Standard
7515 \begin_inset Tabular
7516 <lyxtabular version="3" rows="4" columns="2">
7517 <features tabularvalignment="middle">
7518 <column alignment="center" valignment="top" width="0pt">
7519 <column alignment="center" valignment="top" width="0pt">
7521 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7524 \begin_layout Plain Layout
7526 \begin_inset Note Note
7529 \begin_layout Plain Layout
7536 is only used as spacer.
7546 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7549 \begin_layout Plain Layout
7557 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7560 \begin_layout Plain Layout
7564 \begin_layout Plain Layout
7579 \begin_layout Plain Layout
7592 \begin_layout Plain Layout
7605 \begin_layout Plain Layout
7618 \begin_layout Plain Layout
7626 \begin_inset Index idx
7629 \begin_layout Plain Layout
7642 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7645 \begin_layout Plain Layout
7646 \begin_inset Formula $\overbrace{A+B}^{3}$
7656 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7659 \begin_layout Plain Layout
7663 \begin_layout Plain Layout
7678 \begin_layout Plain Layout
7691 \begin_layout Plain Layout
7704 \begin_layout Plain Layout
7712 \begin_inset Index idx
7715 \begin_layout Plain Layout
7728 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7731 \begin_layout Plain Layout
7732 \begin_inset Formula $\underbrace{A+B}_{5}$
7742 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7745 \begin_layout Plain Layout
7752 \begin_layout Plain Layout
7767 \begin_layout Plain Layout
7780 \begin_layout Plain Layout
7793 \begin_layout Plain Layout
7806 \begin_layout Plain Layout
7819 \begin_layout Plain Layout
7832 \begin_layout Plain Layout
7846 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7849 \begin_layout Plain Layout
7850 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
7866 \begin_layout Standard
7867 In the last example it doesn't matter if
7879 is inserted at first.
7882 \begin_layout Standard
7883 \begin_inset VSpace bigskip
7886 When brackets are needed that overlap each other, multiline formulas, as
7888 \begin_inset CommandInset ref
7890 reference "sec:Multiline-Formulas"
7895 \begin_inset Formula
7897 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
7898 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
7903 In the first row the formula is inserted together with the first brace.
7904 It is hereby important that the space command
7908 \begin_layout Plain Layout
7909 Space commands are explained in
7910 \begin_inset CommandInset ref
7912 reference "sub:Predefined-Space"
7927 is inserted before the first
7928 \begin_inset Formula $d$
7931 , because the brace that ends behind the
7932 \begin_inset Formula $q$
7935 prevents that the following
7936 \begin_inset Quotes eld
7940 \begin_inset Quotes erd
7943 is surrounded by space.
7947 \begin_layout Plain Layout
7948 because a bracket is not handled as character, see
7949 \begin_inset CommandInset ref
7951 reference "sub:Binary-Operators"
7960 In the second row the second brace is inserted.
7961 As it should begin before the
7962 \begin_inset Formula $b$
7977 \begin_layout Plain Layout
7985 \begin_inset CommandInset ref
7987 reference "sub:Placeholders"
7996 This space is needed because the
7997 \begin_inset Quotes eld
8001 \begin_inset Quotes erd
8004 is also surrounded by space in the formula.
8005 The brace is placed under the command
8014 \begin_layout Standard
8015 It gets more complicated when brackets overlap each other, like in the following
8020 \begin_layout Plain Layout
8032 \begin_inset Formula
8034 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
8035 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd
8044 \begin_layout Plain Layout
8055 The first formula row is the same as the second row of the previous example,
8056 with the difference that the brace is above.
8057 The second row contains the formula together with the second brace.
8058 To avoid that there is space between the upper brace in the first row and
8059 the formula, the row spacing need to be reduced.
8060 This is not easily possible due to a bug in LyX
8064 \begin_layout Plain Layout
8065 \begin_inset CommandInset href
8067 name "LyX-bug #1505"
8068 target "http://www.lyx.org/trac/ticket/1505"
8078 As solution for the problem, the global formula row separation
8085 \begin_inset Index idx
8088 \begin_layout Plain Layout
8096 must be changed to -6
8097 \begin_inset space \thinspace{}
8100 pt before the formula with the command
8115 is set back after the formula to the standard value of 3
8116 \begin_inset space \thinspace{}
8119 pt using the same command.
8120 More about the row separation in formulas is explained in
8121 \begin_inset CommandInset ref
8123 reference "sub:Line-Separation"
8130 \begin_layout Section
8132 \begin_inset Index idx
8135 \begin_layout Plain Layout
8144 \begin_layout Standard
8145 Arrows can be inserted via the math toolbar button
8146 \begin_inset Graphics
8147 filename ../images/math/leftarrow.png
8152 or the commands listed in the following subsections.
8155 \begin_layout Subsection
8157 \begin_inset Index idx
8160 \begin_layout Plain Layout
8169 \begin_layout Standard
8170 \begin_inset space \hfill{}
8174 \begin_inset Tabular
8175 <lyxtabular version="3" rows="8" columns="2">
8176 <features tabularvalignment="middle">
8177 <column alignment="center" valignment="top" width="0pt">
8178 <column alignment="center" valignment="top" width="0pt">
8180 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8183 \begin_layout Plain Layout
8189 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8192 \begin_layout Plain Layout
8200 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8203 \begin_layout Plain Layout
8211 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8214 \begin_layout Plain Layout
8215 \begin_inset Formula $\gets$
8225 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8228 \begin_layout Plain Layout
8236 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8239 \begin_layout Plain Layout
8240 \begin_inset Formula $\Leftarrow$
8250 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8253 \begin_layout Plain Layout
8261 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8264 \begin_layout Plain Layout
8265 \begin_inset Formula $\longleftarrow$
8275 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8278 \begin_layout Plain Layout
8286 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8289 \begin_layout Plain Layout
8290 \begin_inset Formula $\Longleftarrow$
8300 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8303 \begin_layout Plain Layout
8311 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8314 \begin_layout Plain Layout
8315 \begin_inset Formula $\leftharpoonup$
8325 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8328 \begin_layout Plain Layout
8336 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8339 \begin_layout Plain Layout
8340 \begin_inset Formula $\leftharpoondown$
8350 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8353 \begin_layout Plain Layout
8361 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8364 \begin_layout Plain Layout
8365 \begin_inset Formula $\hookleftarrow$
8379 \begin_inset space \hfill{}
8383 \begin_inset Tabular
8384 <lyxtabular version="3" rows="8" columns="2">
8385 <features tabularvalignment="middle">
8386 <column alignment="center" valignment="top" width="0pt">
8387 <column alignment="center" valignment="top" width="0pt">
8389 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8392 \begin_layout Plain Layout
8398 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8401 \begin_layout Plain Layout
8409 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8412 \begin_layout Plain Layout
8420 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8423 \begin_layout Plain Layout
8424 \begin_inset Formula $\to$
8434 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8437 \begin_layout Plain Layout
8445 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8448 \begin_layout Plain Layout
8449 \begin_inset Formula $\Rightarrow$
8459 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8462 \begin_layout Plain Layout
8470 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8473 \begin_layout Plain Layout
8474 \begin_inset Formula $\longrightarrow$
8484 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8487 \begin_layout Plain Layout
8495 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8498 \begin_layout Plain Layout
8499 \begin_inset Formula $\Longrightarrow$
8509 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8512 \begin_layout Plain Layout
8520 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8523 \begin_layout Plain Layout
8524 \begin_inset Formula $\rightharpoonup$
8534 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8537 \begin_layout Plain Layout
8545 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8548 \begin_layout Plain Layout
8549 \begin_inset Formula $\rightharpoondown$
8559 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8562 \begin_layout Plain Layout
8570 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8573 \begin_layout Plain Layout
8574 \begin_inset Formula $\hookrightarrow$
8588 \begin_inset space \hfill{}
8594 \begin_layout Standard
8595 \begin_inset space \hfill{}
8599 \begin_inset Tabular
8600 <lyxtabular version="3" rows="6" columns="2">
8601 <features tabularvalignment="middle">
8602 <column alignment="center" valignment="top" width="0pt">
8603 <column alignment="center" valignment="top" width="0pt">
8605 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8608 \begin_layout Plain Layout
8614 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8617 \begin_layout Plain Layout
8625 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8628 \begin_layout Plain Layout
8636 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8639 \begin_layout Plain Layout
8640 \begin_inset Formula $\leftrightarrow$
8650 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8653 \begin_layout Plain Layout
8661 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8664 \begin_layout Plain Layout
8665 \begin_inset Formula $\Leftrightarrow$
8675 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8678 \begin_layout Plain Layout
8686 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8689 \begin_layout Plain Layout
8690 \begin_inset Formula $\longleftrightarrow$
8700 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8703 \begin_layout Plain Layout
8711 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8714 \begin_layout Plain Layout
8715 \begin_inset Formula $\Longleftrightarrow$
8725 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8728 \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
8740 \begin_inset Formula $\rightleftharpoons$
8754 \begin_inset space \hspace{}
8759 \begin_inset space \hfill{}
8763 \begin_inset Tabular
8764 <lyxtabular version="3" rows="5" columns="2">
8765 <features tabularvalignment="middle">
8766 <column alignment="center" valignment="top" width="0pt">
8767 <column alignment="center" valignment="top" width="0pt">
8769 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8772 \begin_layout Plain Layout
8778 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8781 \begin_layout Plain Layout
8789 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8792 \begin_layout Plain Layout
8800 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8803 \begin_layout Plain Layout
8804 \begin_inset Formula $\mapsto$
8814 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8817 \begin_layout Plain Layout
8825 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8828 \begin_layout Plain Layout
8829 \begin_inset Formula $\longmapsto$
8839 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8842 \begin_layout Plain Layout
8850 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8853 \begin_layout Plain Layout
8854 \begin_inset Formula $\leadsto$
8864 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8867 \begin_layout Plain Layout
8875 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8878 \begin_layout Plain Layout
8879 \begin_inset Formula $\dasharrow$
8893 \begin_inset space \hfill{}
8899 \begin_layout Standard
8900 \begin_inset VSpace medskip
8903 Arrows used as accent like e.
8904 \begin_inset space \thinspace{}
8908 \begin_inset space \space{}
8911 vector arrows are listed in
8912 \begin_inset CommandInset ref
8914 reference "sec:Accents"
8921 \begin_layout Standard
8922 \begin_inset VSpace bigskip
8925 Furthermore there are the labeled arrows
8926 \begin_inset Index idx
8929 \begin_layout Plain Layout
8942 \begin_inset Index idx
8945 \begin_layout Plain Layout
8960 \begin_inset Index idx
8963 \begin_layout Plain Layout
8970 \begin_layout Plain Layout
8985 When inserting one of these commands in a formula, an arrow with two blue
8986 boxes appear where the label can be inserted.
8987 The length of the arrow adapts to the label width.
8990 \begin_layout Standard
8992 \begin_inset Tabular
8993 <lyxtabular version="3" rows="3" columns="2">
8994 <features tabularvalignment="middle">
8995 <column alignment="center" valignment="top" width="0pt">
8996 <column alignment="center" valignment="top" width="0pt">
8998 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9001 \begin_layout Plain Layout
9007 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9010 \begin_layout Plain Layout
9012 \begin_inset Note Note
9015 \begin_layout Plain Layout
9022 is only used as spacer.
9034 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9037 \begin_layout Plain Layout
9044 \begin_layout Plain Layout
9054 \begin_inset Formula $\downarrow$
9058 \begin_inset Formula $\to$
9066 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9069 \begin_layout Plain Layout
9070 \begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
9080 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9083 \begin_layout Plain Layout
9090 \begin_layout Plain Layout
9100 \begin_inset Formula $\downarrow$
9104 \begin_inset Formula $\to$
9112 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9115 \begin_layout Plain Layout
9116 \begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
9132 \begin_layout Subsection
9133 Vertical and diagonal Arrows
9134 \begin_inset Index idx
9137 \begin_layout Plain Layout
9144 \begin_inset Index idx
9147 \begin_layout Plain Layout
9156 \begin_layout Standard
9157 \begin_inset space \hfill{}
9161 \begin_inset Tabular
9162 <lyxtabular version="3" rows="7" columns="2">
9163 <features tabularvalignment="middle">
9164 <column alignment="center" valignment="top" width="0pt">
9165 <column alignment="center" valignment="top" width="0pt">
9167 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9170 \begin_layout Plain Layout
9176 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9179 \begin_layout Plain Layout
9187 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9190 \begin_layout Plain Layout
9198 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9201 \begin_layout Plain Layout
9202 \begin_inset Formula $\uparrow$
9212 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9215 \begin_layout Plain Layout
9223 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9226 \begin_layout Plain Layout
9227 \begin_inset Formula $\Uparrow$
9237 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9240 \begin_layout Plain Layout
9248 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9251 \begin_layout Plain Layout
9252 \begin_inset Formula $\updownarrow$
9262 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9265 \begin_layout Plain Layout
9273 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9276 \begin_layout Plain Layout
9277 \begin_inset Formula $\Updownarrow$
9287 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9290 \begin_layout Plain Layout
9298 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9301 \begin_layout Plain Layout
9302 \begin_inset Formula $\Downarrow$
9312 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9315 \begin_layout Plain Layout
9323 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9326 \begin_layout Plain Layout
9327 \begin_inset Formula $\downarrow$
9341 \begin_inset space \hfill{}
9345 \begin_inset Tabular
9346 <lyxtabular version="3" rows="5" columns="2">
9347 <features tabularvalignment="middle">
9348 <column alignment="center" valignment="top" width="0pt">
9349 <column alignment="center" valignment="top" width="0pt">
9351 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9354 \begin_layout Plain Layout
9360 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9363 \begin_layout Plain Layout
9371 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9374 \begin_layout Plain Layout
9382 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9385 \begin_layout Plain Layout
9386 \begin_inset Formula $\nearrow$
9396 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9399 \begin_layout Plain Layout
9407 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9410 \begin_layout Plain Layout
9411 \begin_inset Formula $\searrow$
9421 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9424 \begin_layout Plain Layout
9432 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9435 \begin_layout Plain Layout
9436 \begin_inset Formula $\swarrow$
9446 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9449 \begin_layout Plain Layout
9457 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9460 \begin_layout Plain Layout
9461 \begin_inset Formula $\nwarrow$
9475 \begin_inset space \hfill{}
9481 \begin_layout Standard
9482 \begin_inset VSpace medskip
9485 Vertical arrows can be used also as delimiter together with the commands
9487 \begin_inset CommandInset ref
9489 reference "sub:Manual-Bracket-Size"
9494 \begin_inset CommandInset ref
9496 reference "sub:Automatic-Bracket-Size"
9503 \begin_layout Section
9505 \begin_inset CommandInset label
9512 \begin_inset Index idx
9515 \begin_layout Plain Layout
9524 \begin_layout Standard
9525 Accents can be inserted via the math toolbar button
9526 \begin_inset Graphics
9527 filename ../images/math/hat.png
9532 or the commands listed in the following subsections.
9535 \begin_layout Subsection
9536 Accents for one Character
9540 \begin_layout Plain Layout
9553 \begin_layout Plain Layout
9555 \begin_inset CommandInset ref
9557 reference "sub:Accents-in-Text"
9570 \begin_layout Plain Layout
9578 \begin_inset Note Note
9581 \begin_layout Plain Layout
9588 is used to avoid that the footnote appears in the PDF-bookmark.
9591 \begin_layout Plain Layout
9599 \begin_inset CommandInset ref
9601 reference "sub:Formulas-in-Section"
9611 \begin_inset CommandInset label
9613 name "sub:Accents-for-one"
9618 \begin_inset Index idx
9621 \begin_layout Plain Layout
9622 Accents ! for one character
9630 \begin_layout Standard
9631 \begin_inset space \hfill{}
9635 \begin_inset Tabular
9636 <lyxtabular version="3" rows="8" columns="2">
9637 <features tabularvalignment="middle">
9638 <column alignment="center" valignment="top" width="0pt">
9639 <column alignment="center" valignment="top" width="0pt">
9641 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9644 \begin_layout Plain Layout
9650 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9653 \begin_layout Plain Layout
9655 \begin_inset Note Note
9658 \begin_layout Plain Layout
9665 is only used as spacer.
9677 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9680 \begin_layout Plain Layout
9687 \begin_layout Plain Layout
9701 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9704 \begin_layout Plain Layout
9705 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
9715 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9718 \begin_layout Plain Layout
9725 \begin_layout Plain Layout
9739 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9742 \begin_layout Plain Layout
9743 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
9753 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9756 \begin_layout Plain Layout
9763 \begin_layout Plain Layout
9777 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9780 \begin_layout Plain Layout
9781 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
9791 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9794 \begin_layout Plain Layout
9801 \begin_layout Plain Layout
9815 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9818 \begin_layout Plain Layout
9819 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
9829 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9832 \begin_layout Plain Layout
9839 \begin_layout Plain Layout
9849 \begin_inset Index idx
9852 \begin_layout Plain Layout
9863 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9866 \begin_layout Plain Layout
9867 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
9877 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9880 \begin_layout Plain Layout
9887 \begin_layout Plain Layout
9901 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9904 \begin_layout Plain Layout
9905 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
9915 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9918 \begin_layout Plain Layout
9925 \begin_layout Plain Layout
9939 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9942 \begin_layout Plain Layout
9943 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
9957 \begin_inset space \hfill{}
9961 \begin_inset Tabular
9962 <lyxtabular version="3" rows="7" columns="2">
9963 <features tabularvalignment="middle">
9964 <column alignment="center" valignment="top" width="0pt">
9965 <column alignment="center" valignment="top" width="0pt">
9967 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9970 \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
9987 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9990 \begin_layout Plain Layout
9997 \begin_layout Plain Layout
10011 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10014 \begin_layout Plain Layout
10015 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
10025 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10028 \begin_layout Plain Layout
10035 \begin_layout Plain Layout
10049 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10052 \begin_layout Plain Layout
10053 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
10063 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10066 \begin_layout Plain Layout
10073 \begin_layout Plain Layout
10087 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10090 \begin_layout Plain Layout
10091 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
10101 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10104 \begin_layout Plain Layout
10111 \begin_layout Plain Layout
10125 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10128 \begin_layout Plain Layout
10129 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
10139 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10142 \begin_layout Plain Layout
10149 \begin_layout Plain Layout
10163 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10166 \begin_layout Plain Layout
10167 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
10177 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10180 \begin_layout Plain Layout
10187 \begin_layout Plain Layout
10201 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10204 \begin_layout Plain Layout
10205 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
10219 \begin_inset space \hfill{}
10225 \begin_layout Standard
10226 \begin_inset VSpace bigskip
10232 \begin_layout Standard
10233 You can directly insert accents like é to formulas.
10234 LyX will transform them to the corresponding accent command.
10236 \begin_inset Index idx
10239 \begin_layout Plain Layout
10245 it is better to insert a quotation mark before the vowel.
10246 These two characters are then treated by LaTeX as
10250 character when the formula part with the umlaut is marked as German.
10258 \begin_inset Quotes eld
10262 \begin_inset Quotes erd
10265 umlauts are created as demonstrated in the following example:
10268 \begin_layout Standard
10269 \begin_inset VSpace -2mm
10275 \begin_layout Standard
10277 \begin_inset Tabular
10278 <lyxtabular version="3" rows="3" columns="2">
10279 <features tabularvalignment="middle">
10280 <column alignment="center" valignment="top" width="0">
10281 <column alignment="center" valignment="top" width="0">
10283 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10286 \begin_layout Plain Layout
10292 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10295 \begin_layout Plain Layout
10297 \begin_inset Note Note
10300 \begin_layout Plain Layout
10308 \begin_inset space \thinspace{}
10311 pt space are only used as spacer.
10323 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10326 \begin_layout Plain Layout
10329 \begin_inset Quotes grd
10337 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10340 \begin_layout Plain Layout
10341 \begin_inset space \hspace{}
10348 \begin_inset Formula $"i$
10358 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10361 \begin_layout Plain Layout
10368 \begin_layout Plain Layout
10382 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10385 \begin_layout Plain Layout
10386 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
10402 \begin_layout Standard
10403 Another advantage to
10409 is that umlauts can directly be converted to mathematical text because
10410 the accent commands above are
10416 in mathematical text
10419 To convert an accented character to mathematical text, only the character
10420 under the accent may be converted.
10421 This applies also for all other conversions, e.
10422 \begin_inset space \thinspace{}
10426 \begin_inset space \space{}
10432 \begin_layout Standard
10433 In mathematical text, umlauts and other accented characters can directly
10437 \begin_layout Subsection
10438 Accents for Operators
10439 \begin_inset Index idx
10442 \begin_layout Plain Layout
10443 Accents ! for operators
10451 \begin_layout Standard
10459 \begin_inset Index idx
10462 \begin_layout Plain Layout
10477 \begin_inset Index idx
10480 \begin_layout Plain Layout
10488 characters can be placed above or below an operator, respectively, to accent
10497 \begin_inset Index idx
10500 \begin_layout Plain Layout
10508 characters can be set before and behind an operator.
10509 The command scheme is:
10512 \begin_layout Standard
10528 \begin_layout Standard
10535 must always be before the operator that should be accented.
10536 You can accent with several characters and even with other operators and
10544 for example only characters behind an operator, write nothing between the
10545 first braces but don't omit the braces.
10548 \begin_layout Standard
10549 For example the command
10554 \begin_inset Formula $\to$
10564 \begin_inset Formula $\to$
10573 \begin_layout Plain Layout
10589 \begin_inset Formula
10591 \sideset{}{'}\sum_{k=1}^{n}
10599 \begin_layout Standard
10608 \begin_layout Plain Layout
10623 \begin_layout Plain Layout
10635 \begin_inset Formula $\uparrow$
10643 \begin_inset Formula
10645 \overset{a}{\maltese}
10650 As seen in the last example, with
10662 also symbols and characters can be accented; with
10668 this is not possible.
10671 \begin_layout Subsection
10672 Accents for several Characters
10673 \begin_inset Index idx
10676 \begin_layout Plain Layout
10677 Accents ! for several characters
10685 \begin_layout Standard
10686 \begin_inset space \hfill{}
10690 \begin_inset Tabular
10691 <lyxtabular version="3" rows="5" columns="2">
10692 <features tabularvalignment="middle">
10693 <column alignment="center" valignment="top" width="0pt">
10694 <column alignment="center" valignment="top" width="0pt">
10696 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10699 \begin_layout Plain Layout
10705 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10708 \begin_layout Plain Layout
10710 \begin_inset Note Note
10713 \begin_layout Plain Layout
10720 is only used as spacer.
10732 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10735 \begin_layout Plain Layout
10742 \begin_layout Plain Layout
10756 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10759 \begin_layout Plain Layout
10760 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
10770 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10773 \begin_layout Plain Layout
10780 \begin_layout Plain Layout
10794 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10797 \begin_layout Plain Layout
10798 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
10808 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10811 \begin_layout Plain Layout
10818 \begin_layout Plain Layout
10832 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10835 \begin_layout Plain Layout
10836 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
10846 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10849 \begin_layout Plain Layout
10852 underleftrightarrow
10856 \begin_layout Plain Layout
10870 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10873 \begin_layout Plain Layout
10874 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
10888 \begin_inset space \hfill{}
10892 \begin_inset Tabular
10893 <lyxtabular version="3" rows="5" columns="2">
10894 <features tabularvalignment="middle">
10895 <column alignment="center" valignment="top" width="0pt">
10896 <column alignment="center" valignment="top" width="0pt">
10898 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10901 \begin_layout Plain Layout
10907 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10910 \begin_layout Plain Layout
10918 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10921 \begin_layout Plain Layout
10928 \begin_layout Plain Layout
10942 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10945 \begin_layout Plain Layout
10946 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
10956 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10959 \begin_layout Plain Layout
10966 \begin_layout Plain Layout
10980 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10983 \begin_layout Plain Layout
10984 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
10994 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10997 \begin_layout Plain Layout
11004 \begin_layout Plain Layout
11018 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11021 \begin_layout Plain Layout
11022 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
11032 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11035 \begin_layout Plain Layout
11042 \begin_layout Plain Layout
11056 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11059 \begin_layout Plain Layout
11060 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
11074 \begin_inset space \hfill{}
11080 \begin_layout Standard
11081 \begin_inset VSpace medskip
11084 With these commands as many characters as you like can be accented.
11097 will only be set in the output with a length of three characters, as shown
11098 in the following example:
11099 \begin_inset Formula
11101 \widetilde{A+B=C-D}
11109 \begin_layout Standard
11117 \begin_inset Index idx
11120 \begin_layout Plain Layout
11135 \begin_inset Index idx
11138 \begin_layout Plain Layout
11146 described in the previous subsection it is also possible to accent several
11156 \begin_layout Plain Layout
11166 \begin_inset Formula $\downarrow$
11172 \begin_inset Formula
11174 \underset{***}{A=B}
11182 \begin_layout Section
11184 \begin_inset CommandInset label
11191 \begin_inset Index idx
11194 \begin_layout Plain Layout
11203 \begin_layout Subsection
11205 \begin_inset CommandInset label
11207 name "sub:Predefined-Space"
11212 \begin_inset Index idx
11215 \begin_layout Plain Layout
11216 Space ! horizontal ! predefined
11224 \begin_layout Standard
11225 Sometimes it is necessary to insert horizontal space to a formula.
11226 This is done by inserting a protected space (shortcut
11229 arg "space-insert protected"
11234 \begin_inset Quotes eld
11243 \begin_layout Plain Layout
11255 \begin_inset Quotes erd
11258 appears and by pressing
11262 several times one can select one of eight different space sizes.
11263 The spaces can also be inserted using the math toolbar button
11264 \begin_inset Graphics
11265 filename ../images/math/space.png
11270 or special commands.
11271 Independent from the inserted command, one can select the size again by
11279 \begin_layout Standard
11282 \begin_inset VSpace -5mm
11286 \begin_inset Tabular
11287 <lyxtabular version="3" rows="3" columns="7">
11288 <features tabularvalignment="middle">
11289 <column alignment="center" valignment="middle" width="6.8cm">
11290 <column alignment="center" valignment="top" width="0">
11291 <column alignment="center" valignment="top" width="0">
11292 <column alignment="center" valignment="top" width="0">
11293 <column alignment="center" valignment="top" width="0">
11294 <column alignment="center" valignment="top" width="0">
11295 <column alignment="center" valignment="top" width="0">
11297 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11300 \begin_layout Plain Layout
11306 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11309 \begin_layout Plain Layout
11317 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11320 \begin_layout Plain Layout
11328 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11331 \begin_layout Plain Layout
11339 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11342 \begin_layout Plain Layout
11350 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11353 \begin_layout Plain Layout
11361 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11364 \begin_layout Plain Layout
11374 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11377 \begin_layout Plain Layout
11382 keystrokes after inserting the protected space
11387 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11390 \begin_layout Plain Layout
11396 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11399 \begin_layout Plain Layout
11405 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11408 \begin_layout Plain Layout
11414 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11417 \begin_layout Plain Layout
11423 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11426 \begin_layout Plain Layout
11432 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11435 \begin_layout Plain Layout
11443 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11446 \begin_layout Plain Layout
11452 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11455 \begin_layout Plain Layout
11456 \begin_inset Formula $A\, B$
11464 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11467 \begin_layout Plain Layout
11468 \begin_inset Formula $A\: B$
11476 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11479 \begin_layout Plain Layout
11480 \begin_inset Formula $A\; B$
11488 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11491 \begin_layout Plain Layout
11492 \begin_inset Formula $A\quad B$
11500 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11503 \begin_layout Plain Layout
11504 \begin_inset Formula $A\qquad B$
11512 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11515 \begin_layout Plain Layout
11516 \begin_inset Formula $A\! B$
11532 \begin_layout Standard
11533 The last size seem to produce no space.
11534 It is displayed red in LyX contrary to the other sizes, because it is a
11536 There are two more negative spaces:
11539 \begin_layout Standard
11541 \begin_inset Tabular
11542 <lyxtabular version="3" rows="3" columns="3">
11543 <features tabularvalignment="middle">
11544 <column alignment="center" valignment="middle" width="6.8cm">
11545 <column alignment="center" valignment="top" width="0pt">
11546 <column alignment="center" valignment="top" width="0pt">
11548 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11551 \begin_layout Plain Layout
11557 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11560 \begin_layout Plain Layout
11568 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11571 \begin_layout Plain Layout
11581 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11584 \begin_layout Plain Layout
11589 keystrokes after inserting the protected space
11594 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11597 \begin_layout Plain Layout
11603 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11606 \begin_layout Plain Layout
11614 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11617 \begin_layout Plain Layout
11623 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11626 \begin_layout Plain Layout
11627 \begin_inset Formula $A\negmedspace B$
11635 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11638 \begin_layout Plain Layout
11639 \begin_inset Formula $A\negthickspace B$
11655 \begin_layout Standard
11656 Negative spaces can lead to characters overlapping each other.
11657 Thus they can be used to enforce ligatures, what is e.
11658 \begin_inset space \thinspace{}
11662 \begin_inset space \space{}
11665 useful for summation operators:
11668 \begin_layout Standard
11670 \begin_inset Tabular
11671 <lyxtabular version="3" rows="3" columns="2">
11672 <features tabularvalignment="middle">
11673 <column alignment="center" valignment="top" width="0">
11674 <column alignment="center" valignment="top" width="0">
11676 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11679 \begin_layout Plain Layout
11685 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11688 \begin_layout Plain Layout
11690 \begin_inset Note Note
11693 \begin_layout Plain Layout
11700 is only used as spacer.
11712 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11715 \begin_layout Plain Layout
11724 \begin_layout Plain Layout
11738 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11741 \begin_layout Plain Layout
11742 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
11752 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11755 \begin_layout Plain Layout
11766 \begin_layout Plain Layout
11780 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11783 \begin_layout Plain Layout
11784 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
11800 \begin_layout Standard
11801 Relations like for example equal signs, are always surrounded by space.
11802 To suppress this, the equal sign is placed into a TeX-brace.
11803 The following example demonstrates this:
11806 \begin_layout Standard
11808 \begin_inset Tabular
11809 <lyxtabular version="3" rows="2" columns="2">
11810 <features tabularvalignment="middle">
11811 <column alignment="center" valignment="top" width="0pt">
11812 <column alignment="center" valignment="top" width="0pt">
11814 <cell alignment="center" valignment="top" usebox="none">
11817 \begin_layout Plain Layout
11823 <cell alignment="center" valignment="top" usebox="none">
11826 \begin_layout Plain Layout
11827 \begin_inset Formula $A=B$
11837 <cell alignment="center" valignment="top" usebox="none">
11840 \begin_layout Plain Layout
11841 \begin_inset Note Note
11844 \begin_layout Plain Layout
11851 is only used as spacer.
11857 \begin_inset Formula $\raisebox{5mm}{}$
11860 equation without space
11865 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11868 \begin_layout Plain Layout
11869 \begin_inset Formula $A{=}B$
11885 \begin_layout Standard
11887 The command for the last formula is:
11892 \begin_inset Formula $\to$
11898 \begin_layout Standard
11899 \begin_inset VSpace bigskip
11902 Spaces are needed for physical units, because the space between the value
11903 and the unit is the smallest one and not a normal space.
11904 For units in text, the smallest space is inserted via the menu
11906 Insert\SpecialChar \menuseparator
11907 Formatting\SpecialChar \menuseparator
11909 \begin_inset space ~
11917 arg "space-insert thin"
11923 \begin_layout Standard
11924 An example to visualize the difference:
11927 \begin_layout Standard
11928 \begin_inset Tabular
11929 <lyxtabular version="3" rows="2" columns="2">
11930 <features tabularvalignment="middle">
11931 <column alignment="left" valignment="top" width="0">
11932 <column alignment="left" valignment="top" width="0">
11934 <cell alignment="center" valignment="top" usebox="none">
11937 \begin_layout Plain Layout
11939 \begin_inset Formula $\cdot$
11947 <cell alignment="center" valignment="top" usebox="none">
11950 \begin_layout Plain Layout
11951 space between value and unit
11958 <cell alignment="center" valignment="top" usebox="none">
11961 \begin_layout Plain Layout
11963 \begin_inset space \thinspace{}
11967 \begin_inset Formula $\cdot$
11975 <cell alignment="center" valignment="top" usebox="none">
11978 \begin_layout Plain Layout
11979 smallest space between value and unit
11992 \begin_layout Subsection
11997 \begin_layout Plain Layout
12010 \begin_layout Plain Layout
12011 for vertical space in formulas see
12012 \begin_inset CommandInset ref
12014 reference "sub:Line-Separation"
12027 \begin_layout Plain Layout
12035 \begin_inset Note Note
12038 \begin_layout Plain Layout
12041 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
12044 \begin_layout Plain Layout
12047 texorpdfstring is in section
12048 \begin_inset CommandInset ref
12050 reference "sub:Formulas-in-Section"
12060 \begin_inset CommandInset label
12062 name "sub:Variable-Space"
12067 \begin_inset Index idx
12070 \begin_layout Plain Layout
12071 Space ! horizontal ! variable
12079 \begin_layout Standard
12080 Space with a defined length can be inserted with the command
12087 \begin_inset Index idx
12090 \begin_layout Plain Layout
12100 \begin_inset Quotes eld
12109 \begin_layout Plain Layout
12121 \begin_inset Quotes erd
12125 The length can be specified by left-clicking on the
12126 \begin_inset Quotes eld
12135 \begin_layout Plain Layout
12147 \begin_inset Quotes erd
12151 The length may also be negative.
12152 To insert so many space that the formula uses all available space, the
12160 \begin_inset Index idx
12163 \begin_layout Plain Layout
12174 \begin_layout Standard
12175 \begin_inset VSpace -1mm
12181 \begin_layout Standard
12183 \begin_inset Tabular
12184 <lyxtabular version="3" rows="4" columns="2">
12185 <features tabularvalignment="middle">
12186 <column alignment="center" valignment="top" width="0">
12187 <column alignment="center" valignment="top" width="0">
12189 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12192 \begin_layout Plain Layout
12200 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12203 \begin_layout Plain Layout
12211 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12214 \begin_layout Plain Layout
12221 \begin_layout Plain Layout
12231 \begin_inset Formula $\to$
12237 \begin_inset space \thinspace{}
12245 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12248 \begin_layout Plain Layout
12249 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
12259 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12262 \begin_layout Plain Layout
12269 \begin_layout Plain Layout
12279 \begin_inset Formula $\to$
12285 \begin_inset space \thinspace{}
12293 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12296 \begin_layout Plain Layout
12297 \begin_inset Formula $A\hspace{-1mm}A\not=A$
12307 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12310 \begin_layout Plain Layout
12317 \begin_layout Plain Layout
12331 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12334 \begin_layout Plain Layout
12335 \begin_inset Formula $A=A\hfill B=B$
12351 \begin_layout Standard
12352 In the last example the available space is given by the longest column entry
12354 In an inline formula the space depends on the length of the line in which
12362 Thus, when the line uses the full width, no space will be created.
12369 only has an effect on displayed formulas when the formula style
12374 (Formula styles are explained in
12375 \begin_inset CommandInset ref
12377 reference "sec:Formula-Styles"
12384 \begin_layout Standard
12391 , there are the commands
12403 that fill the space with a pattern, see
12404 \begin_inset CommandInset ref
12406 reference "sub:Ellipses"
12413 \begin_layout Standard
12414 For text, variable space can be inserted via the menu
12416 Insert\SpecialChar \menuseparator
12417 Formatting\SpecialChar \menuseparator
12419 \begin_inset space ~
12427 \begin_layout Standard
12428 This is a line with
12429 \begin_inset space \hspace{}
12434 \begin_inset space \thinspace{}
12440 \begin_layout Standard
12441 This is a line with
12442 \begin_inset space \hfill{}
12448 \begin_layout Subsection
12449 Space besides inline Formulas
12450 \begin_inset Index idx
12453 \begin_layout Plain Layout
12454 Space ! besides inline formulas
12462 \begin_layout Standard
12463 The space that surrounds inline formulas can be adjusted with the length
12471 \begin_inset Index idx
12474 \begin_layout Plain Layout
12483 The value of a length is set with the command
12490 \begin_inset Index idx
12493 \begin_layout Plain Layout
12501 that has the following scheme:
12504 \begin_layout Standard
12509 setlength{length name}{value}
12512 \begin_layout Standard
12520 \begin_inset space \thinspace{}
12526 \begin_layout Standard
12536 \begin_layout Standard
12537 is inserted in TeX-mode.
12539 \begin_inset space \thinspace{}
12542 mm space will now be set around all inline formulas:
12546 \begin_layout Plain Layout
12560 \begin_layout Standard
12561 This is a line with an inline formula
12562 \begin_inset Formula $A=B$
12566 \begin_inset space \thinspace{}
12569 mm surrounding space.
12573 \begin_layout Plain Layout
12587 \begin_layout Standard
12588 To return to the predefined value,
12594 is set to the value 0
12595 \begin_inset space \thinspace{}
12601 \begin_layout Section
12603 \begin_inset Index idx
12606 \begin_layout Plain Layout
12613 \begin_inset Index idx
12616 \begin_layout Plain Layout
12621 \begin_layout Plain Layout
12632 \begin_layout Plain Layout
12647 \begin_layout Standard
12648 Boxes for text are described in chapter
12655 \begin_inset space ~
12663 \begin_layout Subsection
12665 \begin_inset CommandInset label
12667 name "sub:Boxes-with-Frame"
12672 \begin_inset Index idx
12675 \begin_layout Plain Layout
12684 \begin_layout Standard
12685 It is possible to frame formulas or parts of it with the commands
12692 \begin_inset Index idx
12695 \begin_layout Plain Layout
12710 \begin_inset Index idx
12713 \begin_layout Plain Layout
12724 \begin_layout Standard
12725 When one of these commands is inserted to a formula, a blue box appears
12726 within a frame to enter formula parts.
12733 an additional formula has to be created by
12737 within this box, because the box content will otherwise be treated as mathemati
12745 is used, a new formula is automatically created inside the frame.
12748 \begin_layout Standard
12755 is not suitable to frame displayed formulas because the formula will always
12756 be set in the size of the text.
12763 is in contrary not suitable to frame inline formulas, because the formula
12764 will always be set in the size of a displayed formula.
12767 \begin_layout Standard
12774 there is the command
12781 \begin_inset Index idx
12784 \begin_layout Plain Layout
12792 where additionally the frame width and the alignment can be specified.
12799 is used in the following scheme:
12802 \begin_layout Standard
12807 framebox[frame width][position]{box content}
12810 \begin_layout Standard
12811 The position can either be
12828 right aligns the formula in the box.
12829 When no position is given, the formula will be centered.
12830 \begin_inset Newline newline
12833 Is no width given, also no position can be given.
12834 In this case the frame width is adjusted to the box content like for
12843 \begin_layout Standard
12850 is inserted, a box appears containing three blue boxes.
12851 The first two boxes are surrounded by brackets and denote the two optional
12853 The third box is for formula parts like for
12862 \begin_layout Standard
12864 \begin_inset Tabular
12865 <lyxtabular version="3" rows="5" columns="2">
12866 <features tabularvalignment="middle">
12867 <column alignment="center" valignment="top" width="0">
12868 <column alignment="center" valignment="top" width="0">
12870 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12873 \begin_layout Plain Layout
12879 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12882 \begin_layout Plain Layout
12884 \begin_inset Note Note
12887 \begin_layout Plain Layout
12894 is only used as spacer.
12906 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12909 \begin_layout Plain Layout
12916 \begin_layout Plain Layout
12935 \begin_layout Plain Layout
12949 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12952 \begin_layout Plain Layout
12953 \begin_inset Formula $\raisebox{6mm}{}\fbox{\ensuremath{\int A=B}}\raisebox{-4mm}{}$
12963 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12966 \begin_layout Plain Layout
12973 \begin_layout Plain Layout
12988 \begin_layout Plain Layout
13002 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13005 \begin_layout Plain Layout
13006 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
13016 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13019 \begin_layout Plain Layout
13026 \begin_layout Plain Layout
13040 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13043 \begin_layout Plain Layout
13044 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
13054 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13057 \begin_layout Plain Layout
13064 \begin_layout Plain Layout
13074 \begin_inset Formula $\to$
13078 \begin_inset Formula $\to$
13091 \begin_layout Plain Layout
13101 \begin_inset Formula $\downarrow$
13109 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13112 \begin_layout Plain Layout
13113 \begin_inset Formula $\raisebox{6mm}{}$
13117 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
13121 \begin_inset Formula $\raisebox{-4mm}{}$
13137 \begin_layout Standard
13138 The frame thickness can also be adjusted.
13139 To do this the following commands have to be inserted in TeX-mode before
13143 \begin_layout Standard
13153 \begin_inset Quotes eld
13157 \begin_inset Quotes erd
13171 \begin_inset Quotes eld
13175 \begin_inset Quotes erd
13181 \begin_layout Standard
13182 \begin_inset Quotes eld
13186 \begin_inset Quotes erd
13189 specifies the minimal distance between the frame and the first character
13191 An example for this is the following framed formula:
13195 \begin_layout Plain Layout
13207 \begin_inset Formula
13214 Before this formula the commands
13217 \begin_layout Standard
13239 \begin_layout Standard
13240 were inserted in TeX-mode.
13241 The given values are used for all following boxes.
13244 \begin_layout Standard
13245 To return to the standard frame size, the command
13248 \begin_layout Standard
13273 \begin_layout Plain Layout
13287 \begin_layout Standard
13288 is inserted in TeX-mode before the next formula.
13291 \begin_layout Subsection
13292 Boxes without Frame
13293 \begin_inset CommandInset label
13295 name "sub:Boxes-without-Frame"
13300 \begin_inset Index idx
13303 \begin_layout Plain Layout
13304 Boxes ! without frame
13312 \begin_layout Standard
13313 For boxes without a frame there are the following box commands:
13320 \begin_inset Index idx
13323 \begin_layout Plain Layout
13338 \begin_inset Index idx
13341 \begin_layout Plain Layout
13356 \begin_inset Index idx
13359 \begin_layout Plain Layout
13370 \begin_layout Standard
13377 a box can be super- or subscripted.
13378 But in contrary to normal super- and subscripting, the characters in the
13379 box keep their font size.
13386 is used in the following scheme:
13389 \begin_layout Standard
13394 raisebox{height}{box content}
13397 \begin_layout Standard
13398 When the box should contain a formula, an extra formula is needed like for
13409 \begin_inset Note Greyedout
13412 \begin_layout Plain Layout
13423 this extra formula is created by pressing
13427 twice instead of once because LyX doesn't yet support
13441 \begin_layout Standard
13443 \begin_inset Tabular
13444 <lyxtabular version="3" rows="4" columns="2">
13445 <features tabularvalignment="middle">
13446 <column alignment="center" valignment="top" width="0">
13447 <column alignment="center" valignment="top" width="0">
13449 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13452 \begin_layout Plain Layout
13458 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13461 \begin_layout Plain Layout
13469 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13472 \begin_layout Plain Layout
13476 \begin_inset Formula $\to$
13482 \begin_inset Formula $\to$
13490 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13493 \begin_layout Plain Layout
13494 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13504 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13507 \begin_layout Plain Layout
13511 \begin_inset Formula $\to$
13517 \begin_inset Formula $\to$
13525 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13528 \begin_layout Plain Layout
13529 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13539 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13542 \begin_layout Plain Layout
13546 \begin_inset Formula $\to$
13565 \begin_layout Plain Layout
13579 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13582 \begin_layout Plain Layout
13583 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
13599 \begin_layout Standard
13624 , with the difference that there is no frame.
13627 \begin_layout Subsection
13629 \begin_inset CommandInset label
13631 name "sub:Colored-Boxes"
13636 \begin_inset Index idx
13639 \begin_layout Plain Layout
13648 \begin_layout Standard
13649 To be able to use all commands explained in this section, the LaTeX-package
13658 \begin_layout Plain Layout
13663 is part of every LaTeX standard installation.
13669 \begin_inset Index idx
13672 \begin_layout Plain Layout
13678 has to be loaded in the LaTeX-preamble with the line
13682 \begin_layout Plain Layout
13683 When text is colored somewhere in the document with a predefined color,
13684 LyX loads the LaTeX-package
13689 Thus it is possible that the package is loaded twice, but this doesn't
13696 \begin_inset Note Note
13699 \begin_layout Plain Layout
13700 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
13709 \begin_layout Standard
13717 \begin_layout Standard
13718 \begin_inset VSpace medskip
13721 To color boxes, the command
13728 \begin_inset Index idx
13731 \begin_layout Plain Layout
13739 is used in the following scheme:
13742 \begin_layout Standard
13747 colorbox{color}{box content}
13750 \begin_layout Standard
13751 The box content can also be a box and a
13757 can also be part of another box (see the 2nd and 3rd example).
13758 When the box should contain a formula, an extra formula has to be created,
13759 the same way as for
13769 \begin_layout Plain Layout
13770 This also applies for the command
13784 \begin_layout Standard
13785 One of the following predefined colors can be chosen:
13788 \begin_layout Standard
13822 \begin_layout Standard
13824 \begin_inset Tabular
13825 <lyxtabular version="3" rows="4" columns="2">
13826 <features tabularvalignment="middle">
13827 <column alignment="center" valignment="top" width="0">
13828 <column alignment="center" valignment="top" width="0">
13830 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13833 \begin_layout Plain Layout
13839 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13842 \begin_layout Plain Layout
13844 \begin_inset Note Note
13847 \begin_layout Plain Layout
13854 is only used as spacer.
13866 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13869 \begin_layout Plain Layout
13873 \begin_inset Formula $\to$
13883 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13886 \begin_layout Plain Layout
13887 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
13897 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13900 \begin_layout Plain Layout
13904 \begin_inset Formula $\to$
13915 \begin_layout Plain Layout
13929 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13932 \begin_layout Plain Layout
13933 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
13943 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13946 \begin_layout Plain Layout
13953 \begin_layout Plain Layout
13965 \begin_inset Formula $\to$
13984 \begin_layout Plain Layout
13998 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14001 \begin_layout Plain Layout
14002 \begin_inset Formula $\raisebox{7mm}{}\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}\raisebox{-5mm}{}$
14018 \begin_layout Standard
14025 only colors the box but not the characters in the box.
14026 To color all characters, the whole formula is highlighted and the wanted
14027 color is chosen in the
14030 \begin_inset space ~
14036 The dialog can be called with the toolbar button
14037 \begin_inset Graphics
14038 filename ../images/dialog-show_character.png
14045 Edit\SpecialChar \menuseparator
14047 \begin_inset space ~
14050 Style\SpecialChar \menuseparator
14054 The formula number has then the same color as the formula.
14055 When the formula number should get another color than the formula characters,
14056 the color must be changed within the formula.
14059 \begin_layout Standard
14063 \begin_layout Standard
14066 \begin_inset Formula
14068 \int A=B\label{eq:red}
14076 \begin_inset Formula
14078 \textcolor{red}{\int A=B}\label{eq:redgreen}
14086 \begin_layout Standard
14088 \begin_inset CommandInset ref
14094 is completely colored red.
14095 \begin_inset Newline newline
14099 \begin_inset CommandInset ref
14101 reference "eq:redgreen"
14105 was first completely colored green to set the color for the formula number.
14106 Subsequently the formula characters were colored red.
14109 \begin_layout Standard
14110 \begin_inset VSpace bigskip
14113 To color the frame different than the rest of the box, the command
14120 \begin_inset Index idx
14123 \begin_layout Plain Layout
14131 is used in the following scheme:
14134 \begin_layout Standard
14139 fcolorbox{frame color}{color}{box content}
14142 \begin_layout Standard
14149 is an extension of the command
14156 The frame width is set, like for
14179 \begin_layout Plain Layout
14191 \begin_inset Formula
14193 \fcolorbox{cyan}{magenta}{A=B}
14202 \begin_layout Plain Layout
14216 \begin_layout Standard
14217 This formula was created with the command
14218 \begin_inset Newline newline
14226 \begin_inset Formula $\to$
14232 \begin_inset Formula $\to$
14242 \begin_layout Standard
14243 \begin_inset VSpace bigskip
14246 To use other colors than the predefined ones, they have to be defined first.
14249 \begin_layout Standard
14250 One can for example define the color
14251 \begin_inset Quotes eld
14259 \begin_inset Quotes erd
14262 with the LaTeX-preamble line:
14265 \begin_layout Standard
14270 definecolor{darkgreen}{cmyk}{0.5,
14285 \begin_inset Index idx
14288 \begin_layout Plain Layout
14299 \begin_layout Standard
14304 is the color space that denotes the colors
14321 The four comma separated numbers are the portion factor for the corresponding
14322 colors of the color space.
14323 The factors can be in the range of 0
14324 \begin_inset space \thinspace{}
14328 \begin_inset space \thinspace{}
14336 also the color space
14340 can be used for definitions.
14357 , so that there are in this case three portion factors for the corresponding
14359 Furthermore there is the color space
14363 with one portion factor for the gray value.
14366 \begin_layout Standard
14367 As example a framed box with the new defined color
14371 where the characters have been colored
14376 \begin_inset Formula
14378 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}
14386 \begin_layout Standard
14387 Self-defined colors can also be used for text with the help of the command
14395 \begin_inset Index idx
14398 \begin_layout Plain Layout
14407 \begin_layout Standard
14411 \begin_layout Plain Layout
14415 textcolor{darkgreen}{
14421 \begin_inset Quotes eld
14425 \begin_inset Quotes erd
14432 \begin_layout Plain Layout
14442 \begin_layout Standard
14450 \begin_inset Index idx
14453 \begin_layout Plain Layout
14461 is used in the scheme
14465 textcolor{color}{characters to color}
14470 \begin_layout Subsection
14472 \begin_inset CommandInset label
14474 name "sub:Paragraph-Boxes"
14479 \begin_inset Index idx
14482 \begin_layout Plain Layout
14483 Boxes ! as paragraph
14491 \begin_layout Standard
14492 A box that can contain several lines and paragraphs, a so called paragraph
14493 box (parbox), can be created with the menu
14495 Insert\SpecialChar \menuseparator
14498 or the toolbar button
14499 \begin_inset Graphics
14500 filename ../images/box-insert.png
14508 \begin_layout Standard
14509 The following example shows a framed parbox in a line:
14512 \begin_layout Standard
14513 \begin_inset VSpace medskip
14517 \begin_inset Box Boxed
14527 height_special "totalheight"
14530 \begin_layout Plain Layout
14531 This is a paragraph box.
14533 \begin_inset space \thinspace{}
14536 cm long and can also contain formulas:
14537 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14548 \begin_layout Standard
14549 \begin_inset VSpace medskip
14555 \begin_layout Standard
14556 Such a box is created by right-clicking on the gray box inset.
14557 A dialog pops up showing the box properties.
14571 \begin_inset space \thinspace{}
14576 Vertical Box Alignment
14581 \begin_layout Standard
14582 \begin_inset VSpace medskip
14585 In LaTeX a parbox is created with the command
14592 \begin_inset Index idx
14595 \begin_layout Plain Layout
14603 that has the following scheme:
14606 \begin_layout Standard
14611 parbox[position]{width}{box content}
14614 \begin_layout Standard
14628 for bottom means that the box is aligned within the surrounding text with
14634 for top this is done with the first line.
14635 When no position is given, the box will be vertically centered, see section
14643 \begin_inset space ~
14648 manual for examples.
14651 \begin_layout Standard
14652 \begin_inset VSpace bigskip
14655 To frame formulas completely, including the formula number, the formula
14656 must be set into a parbox.
14657 To do this, the command
14671 is inserted in TeX-mode before the formula.
14679 \begin_inset Index idx
14682 \begin_layout Plain Layout
14690 is hereby the line width set for the document.
14691 Because the frame is outside the parbox, 2
14692 \begin_inset space \thinspace{}
14695 times the frame separation and the frame thickness must be subtracted from
14697 As this is not automatically done by LyX due to a bug
14701 \begin_layout Plain Layout
14702 \begin_inset CommandInset href
14704 name "LyX-bug #4483"
14705 target "http://www.lyx.org/trac/ticket/4483"
14714 , TeX-mode has to be used.
14715 To be able to multiply and subtract in arguments, the LaTeX-package
14723 \begin_layout Plain Layout
14728 is part of every LaTeX standard installation.
14734 \begin_inset Index idx
14737 \begin_layout Plain Layout
14743 must be loaded in the LaTeX-preamble with the line
14746 \begin_layout Standard
14754 \begin_layout Standard
14755 Behind the formula both boxes are closed by entering
14760 Here is an example:
14764 \begin_layout Plain Layout
14778 \begin_layout Standard
14782 \begin_layout Plain Layout
14800 \begin_inset Formula
14802 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}
14811 \begin_layout Plain Layout
14822 \begin_layout Plain Layout
14836 \begin_layout Standard
14837 \begin_inset VSpace medskip
14840 As a parbox is used as argument of
14846 , there is in this case no difference between
14861 \begin_layout Standard
14862 \begin_inset VSpace bigskip
14865 Paragraph boxes are very useful to comment formulas directly.
14872 is used in combination with the command
14886 \begin_inset CommandInset ref
14888 reference "sub:User-defined-Numbering"
14895 \begin_layout Standard
14896 An example of a formula commented with
14905 \begin_layout Standard
14909 \begin_layout Plain Layout
14922 This is a description.
14923 It is distinctly separated from the formula and multiline.
14927 \begin_layout Plain Layout
14939 \begin_layout Standard
14940 Such a formula must be inserted completely in TeX-mode because LyX does
14941 not yet support the command
14948 The formula is created with the following command sequence:
14951 \begin_layout Standard
14964 is inserted in TeX-mode.
14968 \begin_layout Plain Layout
14969 When the formula style
14981 can also be replaced by
14988 (formula styles see
14989 \begin_inset CommandInset ref
14991 reference "sec:Formula-Styles"
15000 Then the description follows as normal text and finally
15006 is inserted in TeX-mode.
15019 hereby create a displayed formula.
15022 \begin_layout Standard
15029 can be seen in this example that was
15030 \begin_inset Quotes eld
15034 \begin_inset Quotes erd
15037 using the mathematical textmode:
15038 \begin_inset Formula
15040 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}
15048 \begin_layout Section
15050 \begin_inset Index idx
15053 \begin_layout Plain Layout
15062 \begin_layout Subsection
15064 \begin_inset CommandInset label
15066 name "sub:Big-Operators"
15071 \begin_inset Index idx
15074 \begin_layout Plain Layout
15081 \begin_inset Index idx
15084 \begin_layout Plain Layout
15091 \begin_inset Index idx
15094 \begin_layout Plain Layout
15103 \begin_layout Standard
15104 To be able to use all integral operators listed here, the option
15106 Use esint package automatically
15108 must be set in the document settings under
15111 \begin_inset space ~
15119 \begin_layout Standard
15120 \begin_inset space \hfill{}
15124 \begin_inset Tabular
15125 <lyxtabular version="3" rows="11" columns="2">
15126 <features tabularvalignment="middle">
15127 <column alignment="center" valignment="top" width="0pt">
15128 <column alignment="center" valignment="top" width="0pt">
15130 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15133 \begin_layout Plain Layout
15139 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15142 \begin_layout Plain Layout
15150 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15153 \begin_layout Plain Layout
15157 \begin_inset Index idx
15160 \begin_layout Plain Layout
15173 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15176 \begin_layout Plain Layout
15177 \begin_inset Formula $\int$
15187 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15190 \begin_layout Plain Layout
15198 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15201 \begin_layout Plain Layout
15202 \begin_inset Formula $\oint$
15212 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15215 \begin_layout Plain Layout
15223 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15226 \begin_layout Plain Layout
15227 \begin_inset Formula $\ointctrclockwise$
15237 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15240 \begin_layout Plain Layout
15248 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15251 \begin_layout Plain Layout
15252 \begin_inset Formula $\ointclockwise$
15262 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15265 \begin_layout Plain Layout
15273 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15276 \begin_layout Plain Layout
15277 \begin_inset Formula $\sqint$
15287 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15290 \begin_layout Plain Layout
15298 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15301 \begin_layout Plain Layout
15303 \begin_inset Formula $\fint$
15313 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15316 \begin_layout Plain Layout
15324 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15327 \begin_layout Plain Layout
15329 \begin_inset Formula $\landupint$
15339 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15342 \begin_layout Plain Layout
15350 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15353 \begin_layout Plain Layout
15355 \begin_inset Formula $\landdownint$
15365 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15368 \begin_layout Plain Layout
15376 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15379 \begin_layout Plain Layout
15380 \begin_inset Formula $\bigcap$
15390 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15393 \begin_layout Plain Layout
15401 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15404 \begin_layout Plain Layout
15405 \begin_inset Formula $\bigcup$
15419 \begin_inset space \hfill{}
15423 \begin_inset Tabular
15424 <lyxtabular version="3" rows="11" columns="2">
15425 <features tabularvalignment="middle">
15426 <column alignment="center" valignment="top" width="0pt">
15427 <column alignment="center" valignment="top" width="0pt">
15429 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15432 \begin_layout Plain Layout
15438 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15441 \begin_layout Plain Layout
15449 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15452 \begin_layout Plain Layout
15456 \begin_inset Index idx
15459 \begin_layout Plain Layout
15472 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15475 \begin_layout Plain Layout
15476 \begin_inset Formula $\sum$
15486 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15489 \begin_layout Plain Layout
15493 \begin_inset Index idx
15496 \begin_layout Plain Layout
15509 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15512 \begin_layout Plain Layout
15513 \begin_inset Formula $\prod$
15523 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15526 \begin_layout Plain Layout
15534 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15537 \begin_layout Plain Layout
15538 \begin_inset Formula $\coprod$
15548 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15551 \begin_layout Plain Layout
15559 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15562 \begin_layout Plain Layout
15563 \begin_inset Formula $\bigodot$
15573 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15576 \begin_layout Plain Layout
15584 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15587 \begin_layout Plain Layout
15588 \begin_inset Formula $\bigotimes$
15598 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15601 \begin_layout Plain Layout
15609 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15612 \begin_layout Plain Layout
15613 \begin_inset Formula $\bigoplus$
15623 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15626 \begin_layout Plain Layout
15634 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15637 \begin_layout Plain Layout
15638 \begin_inset Formula $\bigwedge$
15648 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15651 \begin_layout Plain Layout
15659 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15662 \begin_layout Plain Layout
15663 \begin_inset Formula $\bigvee$
15673 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15676 \begin_layout Plain Layout
15684 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15687 \begin_layout Plain Layout
15688 \begin_inset Formula $\bigsqcup$
15698 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15701 \begin_layout Plain Layout
15709 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15712 \begin_layout Plain Layout
15713 \begin_inset Formula $\biguplus$
15727 \begin_inset space \hfill{}
15733 \begin_layout Standard
15734 All big operators can also be inserted via the math toolbar button
15735 \begin_inset Graphics
15736 filename ../images/math/intop.png
15744 \begin_layout Standard
15745 The operators are called big because they are bigger than the sometimes
15746 equal looking binary operators.
15747 All big operators can have limits as described in the next subsection.
15750 \begin_layout Standard
15751 For all integral operators there is a second version available, ending on
15769 These operators are different from
15776 \begin_inset space \space{}
15779 in the style the operator limits are displayed, see
15780 \begin_inset CommandInset ref
15782 reference "sub:Operator-Limits"
15790 \begin_layout Subsubsection*
15791 Advice for Integrals
15794 \begin_layout Standard
15799 in an integral is an operator, that therefore has to be set upright.
15800 This is done by highlighting the
15804 and using the keyboard shortcut
15814 \begin_layout Plain Layout
15820 \begin_inset CommandInset ref
15822 reference "sub:Font-Styles"
15832 Finally the smallest space is inserted before the
15836 , as this is usual for operators.
15840 \begin_layout Standard
15842 \begin_inset Formula $\int A(x)dx$
15846 \begin_inset Newline newline
15850 \begin_inset Phantom HPhantom
15853 \begin_layout Plain Layout
15860 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15866 \begin_layout Standard
15867 For multiple integrals there are the following commands:
15868 \begin_inset VSpace medskip
15874 \begin_layout Standard
15875 \begin_inset space \hfill{}
15879 \begin_inset Tabular
15880 <lyxtabular version="3" rows="4" columns="2">
15881 <features tabularvalignment="middle">
15882 <column alignment="center" valignment="top" width="0">
15883 <column alignment="center" valignment="top" width="0">
15885 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15888 \begin_layout Plain Layout
15894 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15897 \begin_layout Plain Layout
15899 \begin_inset Note Note
15902 \begin_layout Plain Layout
15909 is only used as spacer.
15921 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15924 \begin_layout Plain Layout
15932 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15935 \begin_layout Plain Layout
15936 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
15946 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15949 \begin_layout Plain Layout
15957 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15960 \begin_layout Plain Layout
15961 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
15971 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15974 \begin_layout Plain Layout
15982 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15985 \begin_layout Plain Layout
15986 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
16000 \begin_inset space \hfill{}
16004 \begin_inset Tabular
16005 <lyxtabular version="3" rows="4" columns="2">
16006 <features tabularvalignment="middle">
16007 <column alignment="center" valignment="top" width="0">
16008 <column alignment="center" valignment="top" width="0">
16010 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16013 \begin_layout Plain Layout
16019 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16022 \begin_layout Plain Layout
16030 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16033 \begin_layout Plain Layout
16041 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16044 \begin_layout Plain Layout
16045 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
16055 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16058 \begin_layout Plain Layout
16066 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16069 \begin_layout Plain Layout
16070 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
16080 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16083 \begin_layout Plain Layout
16091 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16094 \begin_layout Plain Layout
16095 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
16109 \begin_inset space \hfill{}
16115 \begin_layout Subsection
16117 \begin_inset CommandInset label
16119 name "sub:Operator-Limits"
16124 \begin_inset Index idx
16127 \begin_layout Plain Layout
16136 \begin_layout Standard
16137 Limits are created by super- and subscripts:
16140 \begin_layout Standard
16142 \begin_inset Tabular
16143 <lyxtabular version="3" rows="2" columns="2">
16144 <features tabularvalignment="middle">
16145 <column alignment="center" valignment="top" width="0pt">
16146 <column alignment="center" valignment="top" width="0pt">
16148 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16151 \begin_layout Plain Layout
16157 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16160 \begin_layout Plain Layout
16162 \begin_inset Note Note
16165 \begin_layout Plain Layout
16172 is only used as spacer.
16184 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16187 \begin_layout Plain Layout
16196 \begin_layout Plain Layout
16206 \begin_inset Formula $\to$
16210 \begin_inset Formula $\to$
16218 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16221 \begin_layout Plain Layout
16222 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
16238 \begin_layout Standard
16239 Limits of inline formulas are set right beside the operator.
16240 Limits in displayed formulas are set above or below the operator, except
16241 for integral limits.
16244 \begin_layout Standard
16245 To force that the limits are set beside the operator, the cursor is set
16246 directly behind the operator and the limits type is changed with the menu
16249 Edit\SpecialChar \menuseparator
16250 Math\SpecialChar \menuseparator
16269 \begin_layout Standard
16270 The default limits type is this:
16271 \begin_inset Formula
16273 \sum_{x=0}^{\infty}\frac{1}{x^{2}}
16278 This is how it looks when the limits type was changed to
16285 \begin_inset Formula
16287 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}
16292 For integrals, except those ending with
16308 etc., the limits are by default set beside the operator.
16309 But for multiple integrals the limits are often set below the operator.
16310 In the following example the limits type was therefore set to
16314 and so set below the integrals:
16315 \begin_inset Formula
16317 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}
16325 \begin_layout Standard
16326 \begin_inset VSpace medskip
16329 To specify conditions for limits, the commands
16336 \begin_inset Index idx
16339 \begin_layout Plain Layout
16354 \begin_inset Index idx
16357 \begin_layout Plain Layout
16366 To create for example this expression
16367 \begin_inset Formula
16369 \sum_{\begin{subarray}{c}
16373 \end{subarray}}^{n}k^{-2}\label{eq:substack}
16381 \begin_layout Standard
16382 the following has to be done:
16383 \begin_inset Newline newline
16398 \begin_layout Plain Layout
16410 One is now in a blue box under the summation operator and insert there
16419 \begin_layout Plain Layout
16431 The blue box is now within a purple box and now several lines can be written
16433 A new line is created by inserting a line break (
16436 arg "newline-insert newline"
16441 \begin_inset Newline newline
16446 0<k<1000 Ctrl+Return
16447 \begin_inset Newline newline
16452 is typed in, a new box appears below for the new line.
16455 \begin_layout Standard
16456 The alignment of the lines can be changed to left aligned with the
16466 Edit\SpecialChar \menuseparator
16470 To get right alignment,
16478 \begin_layout Plain Layout
16489 is inserted at the beginning of the line.
16492 \begin_layout Standard
16505 with the difference that the lines are always centered.
16508 \begin_layout Standard
16509 \begin_inset VSpace bigskip
16513 \begin_inset CommandInset ref
16515 reference "eq:substack"
16519 there can be too much space beside an operator, because the characters
16520 following the operator are set beside the limits.
16523 \begin_layout Standard
16524 To avoid this, the following macro can be used in the LaTeX-preamble:
16527 \begin_layout Standard
16541 \begin_inset Newline newline
16553 \begin_inset Newline newline
16560 mathclapinternal #1#2{
16564 mathsurround =0pt #1{#2}$}}
16567 \begin_layout Standard
16568 This defines the command
16575 \begin_inset Index idx
16578 \begin_layout Plain Layout
16586 that sets the width of the limit to 0
16587 \begin_inset space \thinspace{}
16591 The command scheme is
16594 \begin_layout Standard
16602 \begin_layout Standard
16603 where the limit can consist of several conditions.
16606 \begin_layout Standard
16608 \begin_inset CommandInset ref
16610 reference "eq:substack"
16614 , one uses the command
16617 \begin_layout Standard
16630 \begin_layout Plain Layout
16639 0<k<1000 Ctrl+Return
16642 \begin_layout Standard
16643 to create the lower limit.
16644 The summand is now directly behind the summation operator:
16645 \begin_inset Formula
16647 \sum_{\mathclap{\substack{0<k<1000\\
16659 \begin_layout Standard
16660 \begin_inset VSpace bigskip
16663 How to use one limit for several operators is described in
16664 \begin_inset CommandInset ref
16666 reference "sub:Self-defined-Operators"
16673 \begin_layout Standard
16674 \begin_inset Newpage newpage
16680 \begin_layout Subsection
16682 \begin_inset CommandInset label
16684 name "sub:Binary-Operators"
16689 \begin_inset Index idx
16692 \begin_layout Plain Layout
16701 \begin_layout Standard
16702 Binary operators are surrounded by space when there is a character before
16704 \begin_inset VSpace medskip
16710 \begin_layout Standard
16711 \begin_inset space \hfill{}
16715 \begin_inset Tabular
16716 <lyxtabular version="3" rows="13" columns="2">
16717 <features tabularvalignment="middle">
16718 <column alignment="center" valignment="top" width="0pt">
16719 <column alignment="center" valignment="top" width="0pt">
16721 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16724 \begin_layout Plain Layout
16726 \begin_inset Note Note
16729 \begin_layout Plain Layout
16736 is only used as spacer.
16746 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16749 \begin_layout Plain Layout
16757 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16760 \begin_layout Plain Layout
16766 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16769 \begin_layout Plain Layout
16770 \begin_inset Formula $+$
16780 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16783 \begin_layout Plain Layout
16789 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16792 \begin_layout Plain Layout
16793 \begin_inset Formula $-$
16803 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16806 \begin_layout Plain Layout
16814 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16817 \begin_layout Plain Layout
16818 \begin_inset Formula $\pm$
16828 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16831 \begin_layout Plain Layout
16839 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16842 \begin_layout Plain Layout
16843 \begin_inset Formula $\mp$
16853 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16856 \begin_layout Plain Layout
16864 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16867 \begin_layout Plain Layout
16868 \begin_inset Formula $\cdot$
16878 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16881 \begin_layout Plain Layout
16889 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16892 \begin_layout Plain Layout
16893 \begin_inset Formula $\times$
16903 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16906 \begin_layout Plain Layout
16914 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16917 \begin_layout Plain Layout
16918 \begin_inset Formula $\div$
16928 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16931 \begin_layout Plain Layout
16935 \begin_layout Plain Layout
16948 \begin_layout Plain Layout
16960 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16963 \begin_layout Plain Layout
16964 \begin_inset Formula $*$
16974 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16977 \begin_layout Plain Layout
16985 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16988 \begin_layout Plain Layout
16989 \begin_inset Formula $\star$
16999 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17002 \begin_layout Plain Layout
17010 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17013 \begin_layout Plain Layout
17014 \begin_inset Formula $\circ$
17024 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17027 \begin_layout Plain Layout
17035 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17038 \begin_layout Plain Layout
17039 \begin_inset Formula $\diamond$
17049 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17052 \begin_layout Plain Layout
17060 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17063 \begin_layout Plain Layout
17064 \begin_inset Formula $\bullet$
17078 \begin_inset space \hfill{}
17082 \begin_inset Tabular
17083 <lyxtabular version="3" rows="13" columns="2">
17084 <features tabularvalignment="middle">
17085 <column alignment="center" valignment="top" width="0pt">
17086 <column alignment="center" valignment="top" width="0pt">
17088 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17091 \begin_layout Plain Layout
17097 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17100 \begin_layout Plain Layout
17108 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17111 \begin_layout Plain Layout
17119 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17122 \begin_layout Plain Layout
17123 \begin_inset Formula $\nabla$
17133 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17136 \begin_layout Plain Layout
17144 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17147 \begin_layout Plain Layout
17148 \begin_inset Formula $\bigtriangledown$
17158 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17161 \begin_layout Plain Layout
17169 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17172 \begin_layout Plain Layout
17173 \begin_inset Formula $\bigtriangleup$
17183 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17186 \begin_layout Plain Layout
17194 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17197 \begin_layout Plain Layout
17198 \begin_inset Formula $\Box$
17208 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17211 \begin_layout Plain Layout
17219 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17222 \begin_layout Plain Layout
17223 \begin_inset Formula $\cap$
17233 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17236 \begin_layout Plain Layout
17244 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17247 \begin_layout Plain Layout
17248 \begin_inset Formula $\cup$
17258 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17261 \begin_layout Plain Layout
17269 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17272 \begin_layout Plain Layout
17273 \begin_inset Formula $\dagger$
17283 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17286 \begin_layout Plain Layout
17294 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17297 \begin_layout Plain Layout
17298 \begin_inset Formula $\ddagger$
17308 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17311 \begin_layout Plain Layout
17319 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17322 \begin_layout Plain Layout
17323 \begin_inset Formula $\wr$
17333 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17336 \begin_layout Plain Layout
17344 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17347 \begin_layout Plain Layout
17348 \begin_inset Formula $\bigcirc$
17358 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17361 \begin_layout Plain Layout
17369 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17372 \begin_layout Plain Layout
17373 \begin_inset Formula $\wedge$
17383 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17386 \begin_layout Plain Layout
17394 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17397 \begin_layout Plain Layout
17398 \begin_inset Formula $\vee$
17412 \begin_inset space \hfill{}
17416 \begin_inset Tabular
17417 <lyxtabular version="3" rows="13" columns="2">
17418 <features tabularvalignment="middle">
17419 <column alignment="center" valignment="top" width="0pt">
17420 <column alignment="center" valignment="top" width="0pt">
17422 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17425 \begin_layout Plain Layout
17431 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17434 \begin_layout Plain Layout
17442 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17445 \begin_layout Plain Layout
17453 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17456 \begin_layout Plain Layout
17457 \begin_inset Formula $\oplus$
17467 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17470 \begin_layout Plain Layout
17478 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17481 \begin_layout Plain Layout
17482 \begin_inset Formula $\ominus$
17492 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17495 \begin_layout Plain Layout
17503 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17506 \begin_layout Plain Layout
17507 \begin_inset Formula $\otimes$
17517 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17520 \begin_layout Plain Layout
17528 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17531 \begin_layout Plain Layout
17532 \begin_inset Formula $\oslash$
17542 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17545 \begin_layout Plain Layout
17553 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17556 \begin_layout Plain Layout
17557 \begin_inset Formula $\odot$
17567 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17570 \begin_layout Plain Layout
17578 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17581 \begin_layout Plain Layout
17582 \begin_inset Formula $\amalg$
17592 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17595 \begin_layout Plain Layout
17603 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17606 \begin_layout Plain Layout
17607 \begin_inset Formula $\uplus$
17617 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17620 \begin_layout Plain Layout
17628 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17631 \begin_layout Plain Layout
17632 \begin_inset Formula $\setminus$
17642 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17645 \begin_layout Plain Layout
17653 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17656 \begin_layout Plain Layout
17657 \begin_inset Formula $\sqcap$
17667 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17670 \begin_layout Plain Layout
17678 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17681 \begin_layout Plain Layout
17682 \begin_inset Formula $\sqcup$
17692 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17695 \begin_layout Plain Layout
17703 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17706 \begin_layout Plain Layout
17707 \begin_inset Formula $\triangleleft$
17717 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17720 \begin_layout Plain Layout
17728 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17731 \begin_layout Plain Layout
17732 \begin_inset Formula $\triangleright$
17746 \begin_inset space \hfill{}
17752 \begin_layout Standard
17753 All binary operators can also be inserted via the math toolbar button
17754 \begin_inset Graphics
17755 filename ../images/math/pm.png
17763 \begin_layout Standard
17764 To typeset the Laplace operator also
17781 \begin_inset Formula $\nabla^{2}$
17784 ) can be used instead of
17793 \begin_layout Standard
17800 Insert\SpecialChar \menuseparator
17812 \begin_layout Subsection
17813 Self-defined Operators
17814 \begin_inset CommandInset label
17816 name "sub:Self-defined-Operators"
17821 \begin_inset Index idx
17824 \begin_layout Plain Layout
17825 Operators ! self-defined
17833 \begin_layout Standard
17834 With the help of the command
17838 DeclareMathOperator
17841 \begin_inset Index idx
17844 \begin_layout Plain Layout
17849 DeclareMathOperator
17854 custom operators can be defined in the LaTeX-preamble.
17855 Its command scheme is:
17858 \begin_layout Standard
17863 DeclareMathOperator{new command}{display}
17866 \begin_layout Standard
17867 Display can be characters or symbols that define how the operator looks
17869 To define a big operator a * is set behind the command.
17870 All self-defined big operators can have limits as described in
17871 \begin_inset CommandInset ref
17873 reference "sub:Operator-Limits"
17880 \begin_layout Standard
17881 For example the LaTeX-preamble line
17884 \begin_layout Standard
17889 DeclareMathOperator*{
17896 \begin_layout Standard
17897 defines the command
17903 , that inserts a big operator consisting of the lozenge symbol from
17904 \begin_inset CommandInset ref
17906 reference "sub:Miscellaneous-Symbols"
17911 \begin_inset Formula
17913 \Lozenge_{n=1}^{\infty}
17918 The command for this formula is:
17929 \begin_inset Formula $\to$
17935 \begin_layout Standard
17936 \begin_inset VSpace bigskip
17939 When self-defined operators are not used several times in the document,
17940 they can also be defined with the commands
17947 \begin_inset Index idx
17950 \begin_layout Plain Layout
17965 \begin_inset Index idx
17968 \begin_layout Plain Layout
17976 , which have the following scheme:
17979 \begin_layout Standard
17993 \begin_layout Standard
18000 defines big operators,
18009 \begin_layout Standard
18017 \begin_inset space \thinspace{}
18021 \begin_inset space \space{}
18024 be used to use one limit for several operators:
18027 \begin_layout Standard
18028 \begin_inset Formula
18030 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
18038 \begin_layout Standard
18039 The command for the formula above is:
18040 \begin_inset Newline newline
18059 \begin_layout Plain Layout
18071 \begin_inset Formula $\to$
18080 \begin_layout Plain Layout
18094 \begin_layout Section
18096 \begin_inset Index idx
18099 \begin_layout Plain Layout
18108 \begin_layout Subsection
18110 \begin_inset CommandInset label
18112 name "sub:Font-Styles"
18117 \begin_inset Index idx
18120 \begin_layout Plain Layout
18129 \begin_layout Standard
18130 Latin letters in formulas can be set in one of the following font styles:
18131 \begin_inset VSpace -2mm
18137 \begin_layout Standard
18139 \begin_inset Tabular
18140 <lyxtabular version="3" rows="7" columns="3">
18141 <features tabularvalignment="middle">
18142 <column alignment="center" valignment="top" width="0">
18143 <column alignment="center" valignment="top" width="0">
18144 <column alignment="center" valignment="top" width="0">
18146 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18149 \begin_layout Plain Layout
18155 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18158 \begin_layout Plain Layout
18164 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18167 \begin_layout Plain Layout
18175 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18178 \begin_layout Plain Layout
18187 \begin_layout Plain Layout
18203 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18206 \begin_layout Plain Layout
18207 \begin_inset Formula $\mathbb{ABC}$
18215 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18218 \begin_layout Plain Layout
18231 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18234 \begin_layout Plain Layout
18243 \begin_layout Plain Layout
18259 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18262 \begin_layout Plain Layout
18263 \begin_inset Formula $\mathbf{AbC}$
18271 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18274 \begin_layout Plain Layout
18287 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18290 \begin_layout Plain Layout
18299 \begin_layout Plain Layout
18315 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18318 \begin_layout Plain Layout
18319 \begin_inset Formula $\boldsymbol{AbC}$
18327 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18330 \begin_layout Plain Layout
18333 arg "font-boldsymbol"
18343 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18346 \begin_layout Plain Layout
18355 \begin_layout Plain Layout
18371 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18374 \begin_layout Plain Layout
18375 \begin_inset Formula $\mathcal{ABC}$
18383 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18386 \begin_layout Plain Layout
18399 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18402 \begin_layout Plain Layout
18411 \begin_layout Plain Layout
18427 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18430 \begin_layout Plain Layout
18431 \begin_inset Formula $\mathfrak{AbC}$
18439 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18442 \begin_layout Plain Layout
18450 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18453 \begin_layout Plain Layout
18462 \begin_layout Plain Layout
18478 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18481 \begin_layout Plain Layout
18482 \begin_inset Formula $\mathscr{AbC}$
18490 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18493 \begin_layout Plain Layout
18507 \begin_layout Standard
18509 \begin_inset Tabular
18510 <lyxtabular version="3" rows="5" columns="3">
18511 <features tabularvalignment="middle">
18512 <column alignment="center" valignment="top" width="0">
18513 <column alignment="center" valignment="top" width="0">
18514 <column alignment="center" valignment="top" width="0">
18516 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18519 \begin_layout Plain Layout
18525 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18528 \begin_layout Plain Layout
18534 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18537 \begin_layout Plain Layout
18545 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18548 \begin_layout Plain Layout
18557 \begin_layout Plain Layout
18573 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18576 \begin_layout Plain Layout
18577 \begin_inset Formula $\mathit{AbC}$
18585 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18588 \begin_layout Plain Layout
18596 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18599 \begin_layout Plain Layout
18608 \begin_layout Plain Layout
18624 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18627 \begin_layout Plain Layout
18628 \begin_inset Formula $\mathrm{AbC}$
18636 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18639 \begin_layout Plain Layout
18652 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18655 \begin_layout Plain Layout
18664 \begin_layout Plain Layout
18680 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18683 \begin_layout Plain Layout
18684 \begin_inset Formula $\mathsf{AbC}$
18692 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18695 \begin_layout Plain Layout
18708 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18711 \begin_layout Plain Layout
18720 \begin_layout Plain Layout
18736 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18739 \begin_layout Plain Layout
18740 \begin_inset Formula $\mathtt{AbC}$
18748 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18751 \begin_layout Plain Layout
18754 arg "font-typewriter"
18770 \begin_layout Standard
18771 \begin_inset Note Greyedout
18774 \begin_layout Plain Layout
18791 can only be used for big letters.
18799 \begin_layout Standard
18800 Predefined is the style
18809 \begin_layout Standard
18810 The style commands work also for letters in mathematical constructs:
18811 \begin_inset Formula
18813 \mathfrak{A=\frac{b}{C}}
18821 \begin_layout Standard
18822 Characters in mathematical text don't appear in a math font style but in
18823 the text font style
18830 That their style can't be set correctly via the text style dialog is a
18835 \begin_layout Plain Layout
18836 \begin_inset CommandInset href
18838 name "LyX-bug #4629"
18839 target "http://www.lyx.org/trac/ticket/4629"
18851 \begin_layout Standard
18852 Instead of the style commands the dialog
18854 Edit\SpecialChar \menuseparator
18855 Math\SpecialChar \menuseparator
18858 or the toolbar button
18859 \begin_inset Graphics
18860 filename ../images/math/font.png
18868 \begin_layout Subsection
18870 \begin_inset CommandInset label
18872 name "sub:Bold-Formulas"
18877 \begin_inset Index idx
18880 \begin_layout Plain Layout
18889 \begin_layout Standard
18890 To make a complete formula bold, the command
18896 from the previous subsection cannot be used, because it doesn't work for
18897 small Greek letters.
18898 Furthermore it prints Latin letters always upright, like in the following
18902 \begin_layout Standard
18903 \begin_inset Formula
18905 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
18913 \begin_layout Standard
18914 To display the formula correctly, the command
18921 \begin_inset Formula
18923 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
18928 It is also possible to set the formula in a
18930 boldmath environment
18933 This environment is created by inserting the command
18940 \begin_inset Index idx
18943 \begin_layout Plain Layout
18952 To end the environment, the command
18959 \begin_inset Index idx
18962 \begin_layout Plain Layout
18970 is inserted in TeX-mode.
18974 \begin_layout Plain Layout
18984 \begin_inset Formula
18986 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
18995 \begin_layout Plain Layout
19007 \begin_layout Subsection
19009 \begin_inset Index idx
19012 \begin_layout Plain Layout
19021 \begin_layout Standard
19022 Formulas can be colored like normal text: Highlight a formula or a formula
19028 Here is a formula in magenta:
19029 \begin_inset Formula
19031 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
19039 \begin_layout Standard
19040 You can also define your own colors as described in
19041 \begin_inset CommandInset ref
19043 reference "sub:Colored-Boxes"
19048 They can be used with the TeX code command
19055 \begin_inset Index idx
19058 \begin_layout Plain Layout
19069 \begin_layout Standard
19074 textcolor{color}{characters or formula}
19077 \begin_layout Standard
19078 The following example was colored completely dark green and partly red:
19081 \begin_layout Standard
19085 \begin_layout Plain Layout
19089 textcolor{darkgreen}{
19095 \begin_inset Formula
19097 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
19106 \begin_layout Plain Layout
19116 \begin_layout Standard
19117 Due to a bug in LyX only complete formulas can be colored with self-defined
19122 \begin_layout Plain Layout
19123 \begin_inset CommandInset href
19125 name "LyX-bug #5269"
19126 target "http://www.lyx.org/trac/ticket/5269"
19138 \begin_layout Subsection
19140 \begin_inset CommandInset label
19142 name "sub:Font-Sizes"
19147 \begin_inset Index idx
19150 \begin_layout Plain Layout
19159 \begin_layout Standard
19160 For characters in formulas there are, analog to characters in text, the
19161 following size commands:
19164 \begin_layout Standard
19208 \begin_inset Newline newline
19230 \begin_layout Standard
19231 The size produced by the commands depends on the document font size, that
19232 corresponds with the command
19239 The other commands produce smaller or larger sizes than
19246 The font size can however not exceed a certain value.
19247 Is for example the document font size 12
19248 \begin_inset space \thinspace{}
19257 switches to the same size as
19267 \begin_layout Standard
19268 A size command is inserted in TeX-mode before the formula and sets the size
19269 for all following formula and text characters.
19270 To switch back to the initial size, the command
19276 is inserted behind the formula in TeX-mode.
19279 \begin_layout Standard
19280 Within a formula the size can be changed using the following size commands:
19283 \begin_layout Standard
19286 \begin_inset Tabular
19287 <lyxtabular version="3" rows="5" columns="2">
19288 <features tabularvalignment="middle">
19289 <column alignment="center" valignment="top" width="0">
19290 <column alignment="center" valignment="top" width="0">
19292 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19295 \begin_layout Plain Layout
19301 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19304 \begin_layout Plain Layout
19306 \begin_inset Note Note
19309 \begin_layout Plain Layout
19316 is only used as spacer.
19328 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19331 \begin_layout Plain Layout
19335 \begin_inset Index idx
19338 \begin_layout Plain Layout
19351 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19354 \begin_layout Plain Layout
19355 \begin_inset Formula $\raisebox{6.5mm}{}{\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-5.5mm}{}$
19365 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19368 \begin_layout Plain Layout
19376 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19379 \begin_layout Plain Layout
19380 \begin_inset Formula $\raisebox{4.5mm}{}{\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-4mm}{}$
19390 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19393 \begin_layout Plain Layout
19401 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19404 \begin_layout Plain Layout
19405 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
19415 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19418 \begin_layout Plain Layout
19426 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19429 \begin_layout Plain Layout
19430 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
19446 \begin_layout Standard
19447 After entering these commands, a blue box appears in which the formula parts
19451 \begin_layout Standard
19452 There is a further method to change the font size, that though only works
19453 for symbols or letters in mathematical text.
19454 To use it, one of the above text size commands is inserted in mathematical
19456 All following characters until the end of the mathematical text or until
19457 another size command will have the selected size.
19459 \begin_inset VSpace -2mm
19465 \begin_layout Standard
19469 \begin_layout Plain Layout
19479 \begin_inset Formula
19481 A=\frac{B}{c}\cdot\maltese
19487 \begin_inset Formula
19489 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
19498 \begin_layout Plain Layout
19510 \begin_layout Standard
19511 \begin_inset VSpace medskip
19514 Before both formulas the command
19521 The command for the second formula is:
19522 \begin_inset Newline newline
19533 \begin_layout Plain Layout
19548 \begin_layout Plain Layout
19563 \begin_layout Plain Layout
19578 \begin_layout Plain Layout
19588 \begin_inset Formula $\to$
19592 \begin_inset Formula $\to$
19596 \begin_inset Newline newline
19600 \begin_inset space \hspace*{}
19614 \begin_layout Plain Layout
19629 \begin_layout Plain Layout
19644 \begin_layout Plain Layout
19656 \begin_layout Standard
19657 If a symbol cannot be displayed in different sizes, it will always be displayed
19658 in the default size.
19661 \begin_layout Section
19663 \begin_inset Index idx
19666 \begin_layout Plain Layout
19675 \begin_layout Standard
19676 Greek letters can also be inserted via the toolbar button
19677 \begin_inset Graphics
19678 filename ../images/math/alpha.png
19684 All international typesetting norms purport that Greek letters in math
19685 have to be typeset italic/slanted.
19686 In some languages, like French or Russian, they are nevertheless sometimes
19690 \begin_layout Subsection
19692 \begin_inset Index idx
19695 \begin_layout Plain Layout
19696 Greek letters ! small
19704 \begin_layout Standard
19705 \begin_inset space \hfill{}
19709 \begin_inset Tabular
19710 <lyxtabular version="3" rows="11" columns="2">
19711 <features tabularvalignment="middle">
19712 <column alignment="center" valignment="top" width="0pt">
19713 <column alignment="center" valignment="top" width="0pt">
19715 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19718 \begin_layout Plain Layout
19724 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19727 \begin_layout Plain Layout
19735 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19738 \begin_layout Plain Layout
19746 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19749 \begin_layout Plain Layout
19750 \begin_inset Formula $\alpha$
19760 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19763 \begin_layout Plain Layout
19771 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19774 \begin_layout Plain Layout
19775 \begin_inset Formula $\beta$
19785 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19788 \begin_layout Plain Layout
19796 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19799 \begin_layout Plain Layout
19800 \begin_inset Formula $\gamma$
19810 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19813 \begin_layout Plain Layout
19821 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19824 \begin_layout Plain Layout
19825 \begin_inset Formula $\delta$
19835 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19838 \begin_layout Plain Layout
19846 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19849 \begin_layout Plain Layout
19850 \begin_inset Formula $\epsilon$
19860 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19863 \begin_layout Plain Layout
19871 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19874 \begin_layout Plain Layout
19875 \begin_inset Formula $\varepsilon$
19885 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19888 \begin_layout Plain Layout
19896 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19899 \begin_layout Plain Layout
19900 \begin_inset Formula $\zeta$
19910 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19913 \begin_layout Plain Layout
19921 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19924 \begin_layout Plain Layout
19925 \begin_inset Formula $\eta$
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 $\theta$
19960 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19963 \begin_layout Plain Layout
19971 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19974 \begin_layout Plain Layout
19975 \begin_inset Formula $\vartheta$
19989 \begin_inset space \hfill{}
19993 \begin_inset Tabular
19994 <lyxtabular version="3" rows="12" columns="2">
19995 <features tabularvalignment="middle">
19996 <column alignment="center" valignment="top" width="0pt">
19997 <column alignment="center" valignment="top" width="0pt">
19999 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20002 \begin_layout Plain Layout
20008 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20011 \begin_layout Plain Layout
20019 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20022 \begin_layout Plain Layout
20030 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20033 \begin_layout Plain Layout
20034 \begin_inset Formula $\iota$
20044 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20047 \begin_layout Plain Layout
20055 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20058 \begin_layout Plain Layout
20059 \begin_inset Formula $\kappa$
20069 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20072 \begin_layout Plain Layout
20080 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20083 \begin_layout Plain Layout
20084 \begin_inset Formula $\varkappa$
20094 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20097 \begin_layout Plain Layout
20105 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20108 \begin_layout Plain Layout
20109 \begin_inset Formula $\lambda$
20119 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20122 \begin_layout Plain Layout
20130 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20133 \begin_layout Plain Layout
20134 \begin_inset Formula $\mu$
20144 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20147 \begin_layout Plain Layout
20155 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20158 \begin_layout Plain Layout
20159 \begin_inset Formula $\nu$
20169 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20172 \begin_layout Plain Layout
20180 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20183 \begin_layout Plain Layout
20184 \begin_inset Formula $\xi$
20194 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20197 \begin_layout Plain Layout
20203 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20206 \begin_layout Plain Layout
20207 \begin_inset Formula $o$
20217 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20220 \begin_layout Plain Layout
20228 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20231 \begin_layout Plain Layout
20232 \begin_inset Formula $\pi$
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 $\varpi$
20267 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20270 \begin_layout Plain Layout
20278 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20281 \begin_layout Plain Layout
20282 \begin_inset Formula $\rho$
20296 \begin_inset space \hfill{}
20300 \begin_inset Tabular
20301 <lyxtabular version="3" rows="11" columns="2">
20302 <features tabularvalignment="middle">
20303 <column alignment="center" valignment="top" width="0pt">
20304 <column alignment="center" valignment="top" width="0pt">
20306 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20309 \begin_layout Plain Layout
20315 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20318 \begin_layout Plain Layout
20326 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20329 \begin_layout Plain Layout
20337 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20340 \begin_layout Plain Layout
20341 \begin_inset Formula $\varrho$
20351 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20354 \begin_layout Plain Layout
20362 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20365 \begin_layout Plain Layout
20366 \begin_inset Formula $\sigma$
20376 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20379 \begin_layout Plain Layout
20387 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20390 \begin_layout Plain Layout
20391 \begin_inset Formula $\varsigma$
20401 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20404 \begin_layout Plain Layout
20412 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20415 \begin_layout Plain Layout
20416 \begin_inset Formula $\tau$
20426 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20429 \begin_layout Plain Layout
20437 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20440 \begin_layout Plain Layout
20441 \begin_inset Formula $\upsilon$
20451 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20454 \begin_layout Plain Layout
20462 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20465 \begin_layout Plain Layout
20466 \begin_inset Formula $\phi$
20476 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20479 \begin_layout Plain Layout
20487 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20490 \begin_layout Plain Layout
20491 \begin_inset Formula $\varphi$
20501 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20504 \begin_layout Plain Layout
20512 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20515 \begin_layout Plain Layout
20516 \begin_inset Formula $\chi$
20526 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20529 \begin_layout Plain Layout
20537 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20540 \begin_layout Plain Layout
20541 \begin_inset Formula $\psi$
20551 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20554 \begin_layout Plain Layout
20562 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20565 \begin_layout Plain Layout
20566 \begin_inset Formula $\omega$
20580 \begin_inset space \hfill{}
20586 \begin_layout Standard
20587 \begin_inset VSpace medskip
20593 \begin_layout Standard
20594 How to create special upright Greek letters is explained in
20595 \begin_inset CommandInset ref
20597 reference "sub:Upright-small-Greek"
20604 \begin_layout Subsection
20606 \begin_inset Index idx
20609 \begin_layout Plain Layout
20610 Greek letters ! big
20618 \begin_layout Standard
20619 \begin_inset space \hfill{}
20623 \begin_inset Tabular
20624 <lyxtabular version="3" rows="7" columns="2">
20625 <features tabularvalignment="middle">
20626 <column alignment="center" valignment="top" width="0pt">
20627 <column alignment="center" valignment="top" width="0pt">
20629 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20632 \begin_layout Plain Layout
20638 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20641 \begin_layout Plain Layout
20649 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20652 \begin_layout Plain Layout
20660 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20663 \begin_layout Plain Layout
20664 \begin_inset Formula $\Gamma$
20674 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20677 \begin_layout Plain Layout
20685 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20688 \begin_layout Plain Layout
20689 \begin_inset Formula $\Delta$
20699 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20702 \begin_layout Plain Layout
20710 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20713 \begin_layout Plain Layout
20714 \begin_inset Formula $\Theta$
20724 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20727 \begin_layout Plain Layout
20735 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20738 \begin_layout Plain Layout
20739 \begin_inset Formula $\Lambda$
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 $\Xi$
20774 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20777 \begin_layout Plain Layout
20785 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20788 \begin_layout Plain Layout
20789 \begin_inset Formula $\Pi$
20803 \begin_inset space \hfill{}
20807 \begin_inset Tabular
20808 <lyxtabular version="3" rows="6" columns="2">
20809 <features tabularvalignment="middle">
20810 <column alignment="center" valignment="top" width="0pt">
20811 <column alignment="center" valignment="top" width="0pt">
20813 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20816 \begin_layout Plain Layout
20822 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20825 \begin_layout Plain Layout
20833 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20836 \begin_layout Plain Layout
20844 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20847 \begin_layout Plain Layout
20848 \begin_inset Formula $\Sigma$
20858 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20861 \begin_layout Plain Layout
20869 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20872 \begin_layout Plain Layout
20873 \begin_inset Formula $\Upsilon$
20883 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20886 \begin_layout Plain Layout
20894 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20897 \begin_layout Plain Layout
20898 \begin_inset Formula $\Phi$
20908 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20911 \begin_layout Plain Layout
20919 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20922 \begin_layout Plain Layout
20923 \begin_inset Formula $\Psi$
20933 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20936 \begin_layout Plain Layout
20944 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20947 \begin_layout Plain Layout
20948 \begin_inset Formula $\Omega$
20962 \begin_inset space \hfill{}
20968 \begin_layout Standard
20969 \begin_inset VSpace medskip
20972 That the big Greek letters appear upright is caused by a design bug when
20974 To get correct italic big letters, begin every command with
20979 For example the command
20986 \begin_inset Formula $\varGamma$
20990 Another way is to load the package
20998 \begin_layout Plain Layout
21003 is part of the LaTeX-package
21008 \begin_inset Index idx
21011 \begin_layout Plain Layout
21016 \begin_layout Plain Layout
21036 \begin_inset Index idx
21039 \begin_layout Plain Layout
21045 with the LaTeX-preamble line
21048 \begin_layout Standard
21053 usepackage{fixmath}
21056 \begin_layout Standard
21057 Then all big Greek letters in a document will automatically be typeset italic.
21060 \begin_layout Subsection
21062 \begin_inset Index idx
21065 \begin_layout Plain Layout
21066 Greek letters ! bold
21074 \begin_layout Standard
21075 Greek letters cannot be set with different font styles like Latin letters.
21076 They can only be made bold with the command
21083 \begin_inset Index idx
21086 \begin_layout Plain Layout
21097 \begin_layout Standard
21099 \begin_inset Tabular
21100 <lyxtabular version="3" rows="3" columns="2">
21101 <features tabularvalignment="middle">
21102 <column alignment="center" valignment="top" width="0">
21103 <column alignment="center" valignment="top" width="0">
21105 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21108 \begin_layout Plain Layout
21114 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21117 \begin_layout Plain Layout
21125 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21128 \begin_layout Plain Layout
21140 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21143 \begin_layout Plain Layout
21144 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
21154 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21157 \begin_layout Plain Layout
21169 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21172 \begin_layout Plain Layout
21173 \begin_inset Formula $\theta\boldsymbol{\theta}$
21189 \begin_layout Standard
21190 \begin_inset Newpage newpage
21196 \begin_layout Section
21201 \begin_layout Plain Layout
21214 \begin_layout Plain Layout
21215 A list with all symbols of most of the LaTeX-packages can be found in
21216 \begin_inset CommandInset citation
21231 \begin_layout Plain Layout
21239 \begin_inset Note Note
21242 \begin_layout Plain Layout
21245 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
21248 \begin_layout Plain Layout
21251 texorpdfstring is in section
21252 \begin_inset CommandInset ref
21254 reference "sub:Formulas-in-Section"
21264 \begin_inset Index idx
21267 \begin_layout Plain Layout
21276 \begin_layout Standard
21277 Many of the symbols listed in this section can also be inserted via the
21279 \begin_inset Graphics
21280 filename ../images/math/nabla.png
21286 \begin_inset Graphics
21287 filename ../images/math/digamma.png
21295 \begin_layout Subsection
21296 Mathematical Symbols
21297 \begin_inset CommandInset label
21299 name "sub:Mathematical-Symbols"
21304 \begin_inset Index idx
21307 \begin_layout Plain Layout
21308 Symbols ! mathematical
21316 \begin_layout Standard
21317 \begin_inset space \hfill{}
21321 \begin_inset Tabular
21322 <lyxtabular version="3" rows="10" columns="2">
21323 <features tabularvalignment="middle">
21324 <column alignment="center" valignment="top" width="0pt">
21325 <column alignment="center" valignment="top" width="0pt">
21327 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21330 \begin_layout Plain Layout
21336 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21339 \begin_layout Plain Layout
21347 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21350 \begin_layout Plain Layout
21358 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21361 \begin_layout Plain Layout
21362 \begin_inset Formula $\neg$
21372 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21375 \begin_layout Plain Layout
21383 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21386 \begin_layout Plain Layout
21387 \begin_inset Formula $\Im$
21397 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21400 \begin_layout Plain Layout
21408 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21411 \begin_layout Plain Layout
21412 \begin_inset Formula $\Re$
21422 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21425 \begin_layout Plain Layout
21433 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21436 \begin_layout Plain Layout
21437 \begin_inset Formula $\aleph$
21447 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21450 \begin_layout Plain Layout
21458 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21461 \begin_layout Plain Layout
21462 \begin_inset Formula $\partial$
21472 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21475 \begin_layout Plain Layout
21483 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21486 \begin_layout Plain Layout
21487 \begin_inset Formula $\infty$
21497 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21500 \begin_layout Plain Layout
21508 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21511 \begin_layout Plain Layout
21512 \begin_inset Formula $\wp$
21522 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21525 \begin_layout Plain Layout
21533 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21536 \begin_layout Plain Layout
21537 \begin_inset Formula $\imath$
21547 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21550 \begin_layout Plain Layout
21558 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21561 \begin_layout Plain Layout
21562 \begin_inset Formula $\jmath$
21576 \begin_inset space \hfill{}
21580 \begin_inset Tabular
21581 <lyxtabular version="3" rows="10" columns="2">
21582 <features tabularvalignment="middle">
21583 <column alignment="center" valignment="top" width="0pt">
21584 <column alignment="center" valignment="top" width="0pt">
21586 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21589 \begin_layout Plain Layout
21595 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21598 \begin_layout Plain Layout
21600 \begin_inset Note Note
21603 \begin_layout Plain Layout
21610 is only used as spacer.
21622 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21625 \begin_layout Plain Layout
21633 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21636 \begin_layout Plain Layout
21637 \begin_inset Formula $\forall$
21647 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21650 \begin_layout Plain Layout
21658 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21661 \begin_layout Plain Layout
21662 \begin_inset Formula $\exists$
21672 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21675 \begin_layout Plain Layout
21683 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21686 \begin_layout Plain Layout
21687 \begin_inset Formula $\nexists$
21697 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21700 \begin_layout Plain Layout
21708 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21711 \begin_layout Plain Layout
21712 \begin_inset Formula $\emptyset$
21722 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21725 \begin_layout Plain Layout
21733 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21736 \begin_layout Plain Layout
21737 \begin_inset Formula $\varnothing$
21747 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21750 \begin_layout Plain Layout
21758 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21761 \begin_layout Plain Layout
21762 \begin_inset Formula $\dag$
21772 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21775 \begin_layout Plain Layout
21783 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21786 \begin_layout Plain Layout
21787 \begin_inset Formula $\ddag$
21797 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21800 \begin_layout Plain Layout
21808 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21811 \begin_layout Plain Layout
21815 \begin_layout Plain Layout
21825 \begin_inset Formula $\complement$
21832 \begin_layout Plain Layout
21846 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21849 \begin_layout Plain Layout
21857 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21860 \begin_layout Plain Layout
21861 \begin_inset Formula $\Bbbk$
21875 \begin_inset space \hfill{}
21879 \begin_inset Tabular
21880 <lyxtabular version="3" rows="10" columns="2">
21881 <features tabularvalignment="middle">
21882 <column alignment="center" valignment="top" width="0pt">
21883 <column alignment="center" valignment="top" width="0pt">
21885 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21888 \begin_layout Plain Layout
21894 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21897 \begin_layout Plain Layout
21905 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21908 \begin_layout Plain Layout
21916 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21919 \begin_layout Plain Layout
21920 \begin_inset Formula $\prime$
21930 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21933 \begin_layout Plain Layout
21941 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21944 \begin_layout Plain Layout
21945 \begin_inset Formula $\backprime$
21955 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21958 \begin_layout Plain Layout
21966 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21969 \begin_layout Plain Layout
21970 \begin_inset Formula $\mho$
21980 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21983 \begin_layout Plain Layout
21991 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21994 \begin_layout Plain Layout
21995 \begin_inset Formula $\triangle$
22005 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22008 \begin_layout Plain Layout
22016 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22019 \begin_layout Plain Layout
22020 \begin_inset Formula $\angle$
22030 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22033 \begin_layout Plain Layout
22041 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22044 \begin_layout Plain Layout
22045 \begin_inset Formula $\measuredangle$
22055 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22058 \begin_layout Plain Layout
22066 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22069 \begin_layout Plain Layout
22070 \begin_inset Formula $\sphericalangle$
22080 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22083 \begin_layout Plain Layout
22091 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22094 \begin_layout Plain Layout
22095 \begin_inset Formula $\top$
22105 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22108 \begin_layout Plain Layout
22116 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22119 \begin_layout Plain Layout
22120 \begin_inset Formula $\bot$
22134 \begin_inset space \hfill{}
22140 \begin_layout Subsection
22141 Miscellaneous Symbols
22142 \begin_inset CommandInset label
22144 name "sub:Miscellaneous-Symbols"
22149 \begin_inset Index idx
22152 \begin_layout Plain Layout
22153 Symbols ! miscellaneous
22161 \begin_layout Standard
22164 \begin_inset Tabular
22165 <lyxtabular version="3" rows="10" columns="2">
22166 <features tabularvalignment="middle">
22167 <column alignment="center" valignment="top" width="0pt">
22168 <column alignment="center" valignment="top" width="0pt">
22170 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22173 \begin_layout Plain Layout
22179 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22182 \begin_layout Plain Layout
22190 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22193 \begin_layout Plain Layout
22201 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22204 \begin_layout Plain Layout
22205 \begin_inset Formula $\flat$
22215 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22218 \begin_layout Plain Layout
22226 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22229 \begin_layout Plain Layout
22230 \begin_inset Formula $\natural$
22240 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22243 \begin_layout Plain Layout
22251 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22254 \begin_layout Plain Layout
22255 \begin_inset Formula $\sharp$
22265 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22268 \begin_layout Plain Layout
22276 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22279 \begin_layout Plain Layout
22280 \begin_inset Formula $\surd$
22290 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22293 \begin_layout Plain Layout
22301 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22304 \begin_layout Plain Layout
22305 \begin_inset Formula $\checkmark$
22315 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22318 \begin_layout Plain Layout
22326 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22329 \begin_layout Plain Layout
22330 \begin_inset Formula $\yen$
22340 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22343 \begin_layout Plain Layout
22351 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22354 \begin_layout Plain Layout
22355 \begin_inset Formula $\pounds$
22365 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22368 \begin_layout Plain Layout
22374 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22377 \begin_layout Plain Layout
22378 \begin_inset Formula $\$$
22388 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22391 \begin_layout Plain Layout
22397 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22400 \begin_layout Plain Layout
22401 \begin_inset Formula $§$
22415 \begin_inset Tabular
22416 <lyxtabular version="3" rows="10" columns="2">
22417 <features tabularvalignment="middle">
22418 <column alignment="center" valignment="top" width="0">
22419 <column alignment="center" valignment="top" width="0">
22421 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22424 \begin_layout Plain Layout
22430 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22433 \begin_layout Plain Layout
22441 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22444 \begin_layout Plain Layout
22452 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22455 \begin_layout Plain Layout
22456 \begin_inset Formula $\hbar$
22466 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22469 \begin_layout Plain Layout
22477 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22480 \begin_layout Plain Layout
22481 \begin_inset Formula $\hslash$
22491 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22494 \begin_layout Plain Layout
22502 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22505 \begin_layout Plain Layout
22506 \begin_inset Formula $\clubsuit$
22516 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22519 \begin_layout Plain Layout
22527 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22530 \begin_layout Plain Layout
22531 \begin_inset Formula $\spadesuit$
22541 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22544 \begin_layout Plain Layout
22552 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22555 \begin_layout Plain Layout
22556 \begin_inset Formula $\bigstar$
22566 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22569 \begin_layout Plain Layout
22577 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22580 \begin_layout Plain Layout
22581 \begin_inset Formula $\blacklozenge$
22591 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22594 \begin_layout Plain Layout
22602 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22605 \begin_layout Plain Layout
22606 \begin_inset Formula $\blacktriangle$
22616 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22619 \begin_layout Plain Layout
22627 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22630 \begin_layout Plain Layout
22631 \begin_inset Formula $\blacktriangledown$
22641 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22644 \begin_layout Plain Layout
22652 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22655 \begin_layout Plain Layout
22656 \begin_inset Formula $\bullet$
22670 \begin_inset Tabular
22671 <lyxtabular version="3" rows="10" columns="2">
22672 <features tabularvalignment="middle">
22673 <column alignment="center" valignment="top" width="0pt">
22674 <column alignment="center" valignment="top" width="0pt">
22676 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22679 \begin_layout Plain Layout
22685 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22688 \begin_layout Plain Layout
22696 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22699 \begin_layout Plain Layout
22707 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22710 \begin_layout Plain Layout
22711 \begin_inset Formula $\diamondsuit$
22721 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22724 \begin_layout Plain Layout
22732 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22735 \begin_layout Plain Layout
22736 \begin_inset Formula $\Diamond$
22746 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22749 \begin_layout Plain Layout
22757 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22760 \begin_layout Plain Layout
22761 \begin_inset Formula $\heartsuit$
22771 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22774 \begin_layout Plain Layout
22782 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22785 \begin_layout Plain Layout
22786 \begin_inset Formula $\P$
22796 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22799 \begin_layout Plain Layout
22807 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22810 \begin_layout Plain Layout
22811 \begin_inset Formula $\copyright$
22821 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22824 \begin_layout Plain Layout
22832 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22835 \begin_layout Plain Layout
22836 \begin_inset Formula $\circledR$
22846 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22849 \begin_layout Plain Layout
22857 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22860 \begin_layout Plain Layout
22861 \begin_inset Formula $\maltese$
22871 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22874 \begin_layout Plain Layout
22882 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22885 \begin_layout Plain Layout
22886 \begin_inset Formula $\diagup$
22896 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22899 \begin_layout Plain Layout
22907 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22910 \begin_layout Plain Layout
22911 \begin_inset Formula $\diagdown$
22927 \begin_layout Standard
22928 \begin_inset VSpace medskip
22931 More symbols are listed in
22932 \begin_inset CommandInset ref
22934 reference "sub:Miscellaneous-special-Characters"
22941 \begin_layout Standard
22942 Some symbols can be displayed in different sizes, see
22943 \begin_inset CommandInset ref
22945 reference "sub:Font-Sizes"
22952 \begin_layout Subsection
22954 \begin_inset Index idx
22957 \begin_layout Plain Layout
22958 Symbols ! Euro-symbol
22964 \begin_inset Index idx
22967 \begin_layout Plain Layout
22974 \begin_layout Plain Layout
22991 \begin_layout Standard
22992 To use the Euro symbol in formulas, the LaTeX-package
22997 \begin_inset Index idx
23000 \begin_layout Plain Layout
23006 must be installed and loaded with the LaTeX-preamble line
23009 \begin_layout Standard
23014 usepackage[gennarrow]{eurosym}
23017 \begin_layout Standard
23018 The Euro symbol can now be inserted with the command
23025 \begin_inset Index idx
23028 \begin_layout Plain Layout
23039 \begin_layout Standard
23040 The Euro symbol can directly be inserted with the € key in mathematical
23041 text, without having
23056 can also be inserted in TeX-mode.
23057 The official currency symbol can then be inserted with the command
23064 \begin_inset Index idx
23067 \begin_layout Plain Layout
23075 , that is only available in TeX-mode.
23078 \begin_layout Standard
23082 \begin_layout Plain Layout
23092 \begin_inset Note Note
23095 \begin_layout Plain Layout
23096 The following table will only be displayed when the LaTeX-package
23108 \begin_layout Standard
23109 An overview about the different Euro symbols:
23112 \begin_layout Standard
23114 \begin_inset Tabular
23115 <lyxtabular version="3" rows="4" columns="3">
23116 <features tabularvalignment="middle">
23117 <column alignment="center" valignment="top" width="0pt">
23118 <column alignment="center" valignment="top" width="0pt">
23119 <column alignment="center" valignment="top" width="0pt">
23121 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
23124 \begin_layout Plain Layout
23130 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23133 \begin_layout Plain Layout
23139 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23142 \begin_layout Plain Layout
23150 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23153 \begin_layout Plain Layout
23159 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23162 \begin_layout Plain Layout
23170 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23173 \begin_layout Plain Layout
23174 \begin_inset Formula $\euro$
23184 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23187 \begin_layout Plain Layout
23193 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23196 \begin_layout Plain Layout
23202 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23205 \begin_layout Plain Layout
23206 \begin_inset Formula $\mbox{€}$
23216 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23219 \begin_layout Plain Layout
23225 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23228 \begin_layout Plain Layout
23236 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23239 \begin_layout Plain Layout
23243 \begin_layout Plain Layout
23265 \begin_layout Standard
23269 \begin_layout Plain Layout
23279 \begin_inset Note Note
23282 \begin_layout Plain Layout
23283 The following will be displayed when the LaTeX-package
23295 \begin_layout Standard
23296 You need to install the LaTeX-package
23300 to see the rest of this subsection in the output.
23303 \begin_layout Standard
23307 \begin_layout Plain Layout
23319 \begin_layout Section
23321 \begin_inset CommandInset label
23323 name "sec:Relations"
23328 \begin_inset Index idx
23331 \begin_layout Plain Layout
23338 \begin_inset Index idx
23341 \begin_layout Plain Layout
23346 \begin_layout Plain Layout
23357 \begin_layout Plain Layout
23372 \begin_layout Standard
23373 All relations can also be inserted via the toolbar button
23374 \begin_inset Graphics
23375 filename ../images/math/leq.png
23383 \begin_layout Standard
23384 \begin_inset space \hfill{}
23388 \begin_inset Tabular
23389 <lyxtabular version="3" rows="17" columns="2">
23390 <features tabularvalignment="middle">
23391 <column alignment="center" valignment="top" width="0pt">
23392 <column alignment="center" valignment="top" width="0pt">
23394 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23397 \begin_layout Plain Layout
23403 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23406 \begin_layout Plain Layout
23414 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23417 \begin_layout Plain Layout
23423 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23426 \begin_layout Plain Layout
23427 \begin_inset Formula $<$
23437 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23440 \begin_layout Plain Layout
23448 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23451 \begin_layout Plain Layout
23452 \begin_inset Formula $\le$
23462 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23465 \begin_layout Plain Layout
23473 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23476 \begin_layout Plain Layout
23477 \begin_inset Formula $\ll$
23487 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23490 \begin_layout Plain Layout
23498 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23501 \begin_layout Plain Layout
23502 \begin_inset Formula $\prec$
23512 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23515 \begin_layout Plain Layout
23523 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23526 \begin_layout Plain Layout
23527 \begin_inset Formula $\preceq$
23537 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23540 \begin_layout Plain Layout
23548 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23551 \begin_layout Plain Layout
23552 \begin_inset Formula $\subset$
23562 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23565 \begin_layout Plain Layout
23573 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23576 \begin_layout Plain Layout
23577 \begin_inset Formula $\subseteq$
23587 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23590 \begin_layout Plain Layout
23598 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23601 \begin_layout Plain Layout
23602 \begin_inset Formula $\sqsubseteq$
23612 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23615 \begin_layout Plain Layout
23623 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23626 \begin_layout Plain Layout
23627 \begin_inset Formula $\in$
23637 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23640 \begin_layout Plain Layout
23648 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23651 \begin_layout Plain Layout
23652 \begin_inset Formula $\vdash$
23662 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23665 \begin_layout Plain Layout
23673 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23676 \begin_layout Plain Layout
23677 \begin_inset Formula $\smile$
23687 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23690 \begin_layout Plain Layout
23698 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23701 \begin_layout Plain Layout
23702 \begin_inset Formula $\lhd$
23712 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23715 \begin_layout Plain Layout
23723 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23726 \begin_layout Plain Layout
23727 \begin_inset Formula $\unlhd$
23737 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23740 \begin_layout Plain Layout
23748 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23751 \begin_layout Plain Layout
23752 \begin_inset Formula $\gtrless$
23762 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23765 \begin_layout Plain Layout
23773 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23776 \begin_layout Plain Layout
23777 \begin_inset Formula $\mid$
23787 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23790 \begin_layout Plain Layout
23798 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23801 \begin_layout Plain Layout
23802 \begin_inset Formula $\nmid$
23816 \begin_inset space \hfill{}
23820 \begin_inset Tabular
23821 <lyxtabular version="3" rows="17" columns="2">
23822 <features tabularvalignment="middle">
23823 <column alignment="center" valignment="top" width="0pt">
23824 <column alignment="center" valignment="top" width="0pt">
23826 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23829 \begin_layout Plain Layout
23835 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23838 \begin_layout Plain Layout
23846 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23849 \begin_layout Plain Layout
23855 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23858 \begin_layout Plain Layout
23859 \begin_inset Formula $=$
23869 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23872 \begin_layout Plain Layout
23880 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23883 \begin_layout Plain Layout
23884 \begin_inset Formula $\not=$
23894 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23897 \begin_layout Plain Layout
23905 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23908 \begin_layout Plain Layout
23909 \begin_inset Formula $\equiv$
23919 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23922 \begin_layout Plain Layout
23930 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23933 \begin_layout Plain Layout
23934 \begin_inset Formula $\sim$
23944 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23947 \begin_layout Plain Layout
23955 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23958 \begin_layout Plain Layout
23959 \begin_inset Formula $\simeq$
23969 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23972 \begin_layout Plain Layout
23980 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23983 \begin_layout Plain Layout
23984 \begin_inset Formula $\approx$
23994 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23997 \begin_layout Plain Layout
24005 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24008 \begin_layout Plain Layout
24009 \begin_inset Formula $\cong$
24019 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24022 \begin_layout Plain Layout
24030 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24033 \begin_layout Plain Layout
24034 \begin_inset Formula $\bowtie$
24044 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24047 \begin_layout Plain Layout
24055 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24058 \begin_layout Plain Layout
24059 \begin_inset Formula $\notin$
24069 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24072 \begin_layout Plain Layout
24080 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24083 \begin_layout Plain Layout
24084 \begin_inset Formula $\perp$
24094 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24097 \begin_layout Plain Layout
24105 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24108 \begin_layout Plain Layout
24109 \begin_inset Formula $\propto$
24119 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24122 \begin_layout Plain Layout
24130 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24133 \begin_layout Plain Layout
24134 \begin_inset Formula $\asymp$
24144 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24147 \begin_layout Plain Layout
24155 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24158 \begin_layout Plain Layout
24159 \begin_inset Formula $\doteq$
24169 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24172 \begin_layout Plain Layout
24180 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24183 \begin_layout Plain Layout
24184 \begin_inset Formula $\circeq$
24194 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24197 \begin_layout Plain Layout
24205 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24208 \begin_layout Plain Layout
24209 \begin_inset Formula $\models$
24219 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24222 \begin_layout Plain Layout
24230 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24233 \begin_layout Plain Layout
24234 \begin_inset Formula $\widehat{=}$
24248 \begin_inset space \hfill{}
24252 \begin_inset Tabular
24253 <lyxtabular version="3" rows="17" columns="2">
24254 <features tabularvalignment="middle">
24255 <column alignment="center" valignment="top" width="0pt">
24256 <column alignment="center" valignment="top" width="0pt">
24258 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24261 \begin_layout Plain Layout
24267 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24270 \begin_layout Plain Layout
24278 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24281 \begin_layout Plain Layout
24287 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24290 \begin_layout Plain Layout
24291 \begin_inset Formula $>$
24301 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24304 \begin_layout Plain Layout
24312 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24315 \begin_layout Plain Layout
24316 \begin_inset Formula $\ge$
24326 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24329 \begin_layout Plain Layout
24337 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24340 \begin_layout Plain Layout
24341 \begin_inset Formula $\gg$
24351 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24354 \begin_layout Plain Layout
24362 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24365 \begin_layout Plain Layout
24366 \begin_inset Formula $\succ$
24376 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24379 \begin_layout Plain Layout
24387 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24390 \begin_layout Plain Layout
24391 \begin_inset Formula $\succeq$
24401 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24404 \begin_layout Plain Layout
24412 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24415 \begin_layout Plain Layout
24416 \begin_inset Formula $\supset$
24426 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24429 \begin_layout Plain Layout
24437 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24440 \begin_layout Plain Layout
24441 \begin_inset Formula $\supseteq$
24451 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24454 \begin_layout Plain Layout
24462 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24465 \begin_layout Plain Layout
24466 \begin_inset Formula $\sqsupseteq$
24476 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24479 \begin_layout Plain Layout
24487 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24490 \begin_layout Plain Layout
24491 \begin_inset Formula $\ni$
24501 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24504 \begin_layout Plain Layout
24512 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24515 \begin_layout Plain Layout
24516 \begin_inset Formula $\dashv$
24526 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24529 \begin_layout Plain Layout
24537 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24540 \begin_layout Plain Layout
24541 \begin_inset Formula $\frown$
24551 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24554 \begin_layout Plain Layout
24562 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24565 \begin_layout Plain Layout
24566 \begin_inset Formula $\rhd$
24576 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24579 \begin_layout Plain Layout
24587 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24590 \begin_layout Plain Layout
24591 \begin_inset Formula $\unrhd$
24601 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24604 \begin_layout Plain Layout
24612 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24615 \begin_layout Plain Layout
24616 \begin_inset Formula $\lessgtr$
24626 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24629 \begin_layout Plain Layout
24637 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24640 \begin_layout Plain Layout
24641 \begin_inset Formula $\parallel$
24651 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24654 \begin_layout Plain Layout
24662 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24665 \begin_layout Plain Layout
24666 \begin_inset Formula $\nparallel$
24680 \begin_inset space \hfill{}
24686 \begin_layout Standard
24687 \begin_inset VSpace medskip
24702 are bigger than the equal looking operators
24717 \begin_layout Standard
24718 Relations are, in contrary to symbols, always surrounded by space.
24721 \begin_layout Standard
24722 Relations with labels can be created with the command
24729 \begin_inset Index idx
24732 \begin_layout Plain Layout
24743 \begin_layout Standard
24745 \begin_inset Tabular
24746 <lyxtabular version="3" rows="2" columns="2">
24747 <features tabularvalignment="middle">
24748 <column alignment="center" valignment="top" width="0">
24749 <column alignment="center" valignment="top" width="0">
24751 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24754 \begin_layout Plain Layout
24760 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24763 \begin_layout Plain Layout
24765 \begin_inset Note Note
24768 \begin_layout Plain Layout
24775 is only used as spacer.
24787 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24790 \begin_layout Plain Layout
24797 \begin_layout Plain Layout
24814 \begin_layout Plain Layout
24824 \begin_inset Formula $\downarrow$
24833 \begin_layout Plain Layout
24846 \begin_layout Plain Layout
24860 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24863 \begin_layout Plain Layout
24864 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
24880 \begin_layout Section
24884 \begin_layout Subsection
24885 Predefined Functions
24886 \begin_inset CommandInset label
24888 name "sub:Predefined-Functions"
24893 \begin_inset Index idx
24896 \begin_layout Plain Layout
24897 Functions ! predefined
24905 \begin_layout Standard
24906 In general, variables are set
24910 in mathematical expressions, but not function names, because
24911 \begin_inset Formula $sin$
24914 could be misunderstood as
24915 \begin_inset Formula $s\cdot i\cdot n$
24919 Therefore there are predefined functions, that are additionally a bit separated
24921 They are inserted as commands starting with a backslash before their name.
24924 \begin_layout Standard
24926 \begin_inset Tabular
24927 <lyxtabular version="3" rows="2" columns="4">
24928 <features tabularvalignment="middle">
24929 <column alignment="center" valignment="top" width="0pt">
24930 <column alignment="center" valignment="top" width="0pt">
24931 <column alignment="center" valignment="top" width="0pt">
24932 <column alignment="center" valignment="top" width="0pt">
24934 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24937 \begin_layout Plain Layout
24943 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24946 \begin_layout Plain Layout
24952 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24955 \begin_layout Plain Layout
24961 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24964 \begin_layout Plain Layout
24972 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24975 \begin_layout Plain Layout
24981 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24984 \begin_layout Plain Layout
24985 \begin_inset Formula $Asin(x)+B$
24993 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24996 \begin_layout Plain Layout
25004 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25007 \begin_layout Plain Layout
25008 \begin_inset Formula $A\sin(x)+B$
25024 \begin_layout Standard
25025 The following functions are predefined:
25028 \begin_layout Standard
25029 \begin_inset VSpace -2mm
25035 \begin_layout Standard
25037 \begin_inset Tabular
25038 <lyxtabular version="3" rows="9" columns="4">
25039 <features tabularvalignment="middle">
25040 <column alignment="center" valignment="top" width="0pt">
25041 <column alignment="center" valignment="top" width="0pt">
25042 <column alignment="center" valignment="top" width="0pt">
25043 <column alignment="center" valignment="top" width="0pt">
25045 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25048 \begin_layout Plain Layout
25054 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25057 \begin_layout Plain Layout
25063 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25066 \begin_layout Plain Layout
25072 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25075 \begin_layout Plain Layout
25083 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25086 \begin_layout Plain Layout
25094 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25097 \begin_layout Plain Layout
25105 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25108 \begin_layout Plain Layout
25116 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25119 \begin_layout Plain Layout
25129 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25132 \begin_layout Plain Layout
25140 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25143 \begin_layout Plain Layout
25151 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25154 \begin_layout Plain Layout
25162 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25165 \begin_layout Plain Layout
25175 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25178 \begin_layout Plain Layout
25186 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25189 \begin_layout Plain Layout
25197 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25200 \begin_layout Plain Layout
25208 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25211 \begin_layout Plain Layout
25221 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25224 \begin_layout Plain Layout
25232 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25235 \begin_layout Plain Layout
25243 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25246 \begin_layout Plain Layout
25254 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25257 \begin_layout Plain Layout
25267 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25270 \begin_layout Plain Layout
25278 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25281 \begin_layout Plain Layout
25289 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25292 \begin_layout Plain Layout
25300 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25303 \begin_layout Plain Layout
25313 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25316 \begin_layout Plain Layout
25324 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25327 \begin_layout Plain Layout
25335 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25338 \begin_layout Plain Layout
25346 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25349 \begin_layout Plain Layout
25359 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25362 \begin_layout Plain Layout
25370 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25373 \begin_layout Plain Layout
25381 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25384 \begin_layout Plain Layout
25392 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25395 \begin_layout Plain Layout
25405 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25408 \begin_layout Plain Layout
25416 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25419 \begin_layout Plain Layout
25427 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25430 \begin_layout Plain Layout
25438 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25441 \begin_layout Plain Layout
25457 \begin_layout Standard
25458 They can also be inserted with the math toolbar button
25459 \begin_inset Graphics
25460 filename ../images/math/functions.png
25468 \begin_layout Subsection
25469 Self-defined Functions
25470 \begin_inset Index idx
25473 \begin_layout Plain Layout
25474 Functions ! self-defined
25482 \begin_layout Standard
25483 To use a function that is not predefined, like for example the sign function
25484 sgn(x), there are two possibilities:
25487 \begin_layout Itemize
25488 Define the function by inserting the following line to the LaTeX-preamble
25492 \begin_layout Plain Layout
25497 DeclareMathOperator
25500 \begin_inset CommandInset ref
25502 reference "sub:Self-defined-Operators"
25512 \begin_inset Newline newline
25516 \begin_inset VSpace -3mm
25520 \begin_inset Newline newline
25527 DeclareMathOperator{
25532 \begin_inset Index idx
25535 \begin_layout Plain Layout
25540 DeclareMathOperator
25546 \begin_inset Newline newline
25550 \begin_inset VSpace -2mm
25554 \begin_inset Newline newline
25557 Now the new defined function can be called with the command
25566 \begin_layout Itemize
25567 Write the formula as usual, mark the formula name, in our example the letters
25572 , and change it to mathematical text.
25573 At last a space is inserted between prefactor and function.
25576 \begin_layout Standard
25577 The result is the same with both methods as with a predefined function
25581 \begin_layout Plain Layout
25582 In LyX self-defined functions are displayed red, predefined ones black.
25590 \begin_layout Standard
25592 \begin_inset Tabular
25593 <lyxtabular version="3" rows="3" columns="2">
25594 <features tabularvalignment="middle">
25595 <column alignment="center" valignment="top" width="0pt">
25596 <column alignment="center" valignment="top" width="0pt">
25598 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25601 \begin_layout Plain Layout
25607 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25610 \begin_layout Plain Layout
25618 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25621 \begin_layout Plain Layout
25629 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25632 \begin_layout Plain Layout
25633 \begin_inset Formula $A\sgn(x)+B$
25643 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25646 \begin_layout Plain Layout
25650 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
25658 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25661 \begin_layout Plain Layout
25662 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
25678 \begin_layout Standard
25679 The first method is more suitable when the self-defined function should
25680 be used several times.
25683 \begin_layout Subsection
25685 \begin_inset Index idx
25688 \begin_layout Plain Layout
25697 \begin_layout Standard
25698 For limits there are defined besides
25705 \begin_inset Index idx
25708 \begin_layout Plain Layout
25728 furthermore the following functions:
25731 \begin_layout Standard
25733 \begin_inset Tabular
25734 <lyxtabular version="3" rows="5" columns="2">
25735 <features tabularvalignment="middle">
25736 <column alignment="center" valignment="top" width="0">
25737 <column alignment="center" valignment="top" width="0">
25739 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25742 \begin_layout Plain Layout
25748 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25751 \begin_layout Plain Layout
25753 \begin_inset Note Note
25756 \begin_layout Plain Layout
25763 is only used as spacer.
25775 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25778 \begin_layout Plain Layout
25786 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25789 \begin_layout Plain Layout
25790 \begin_inset Formula $\varliminf$
25800 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25803 \begin_layout Plain Layout
25811 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25814 \begin_layout Plain Layout
25815 \begin_inset Formula $\varlimsup$
25825 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25828 \begin_layout Plain Layout
25836 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25839 \begin_layout Plain Layout
25840 \begin_inset Formula $\varprojlim$
25850 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25853 \begin_layout Plain Layout
25861 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25864 \begin_layout Plain Layout
25865 \begin_inset Formula $\varinjlim$
25869 \begin_inset Formula $\raisebox{-2.5mm}{}$
25885 \begin_layout Standard
25886 \begin_inset VSpace medskip
25889 The limit is created by inserting a subscript.
25890 It is set right beside the function in an inline formula:
25893 \begin_layout Standard
25895 \begin_inset Tabular
25896 <lyxtabular version="3" rows="2" columns="2">
25897 <features tabularvalignment="middle">
25898 <column alignment="center" valignment="top" width="0pt">
25899 <column alignment="center" valignment="top" width="0pt">
25901 <cell alignment="center" valignment="top" usebox="none">
25904 \begin_layout Plain Layout
25910 <cell alignment="center" valignment="top" usebox="none">
25913 \begin_layout Plain Layout
25914 \begin_inset space \hspace{}
25919 \begin_inset Note Note
25922 \begin_layout Plain Layout
25929 are used here as spacer.
25941 <cell alignment="center" valignment="top" usebox="none">
25944 \begin_layout Plain Layout
25953 \begin_layout Plain Layout
25966 \begin_layout Plain Layout
25980 <cell alignment="center" valignment="top" usebox="none">
25983 \begin_layout Plain Layout
25984 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
26000 \begin_layout Standard
26001 In a displayed formula the limit is set below the formula, as usual:
26002 \begin_inset Formula
26012 \begin_layout Subsection
26014 \begin_inset Index idx
26017 \begin_layout Plain Layout
26018 Functions ! modulo-
26026 \begin_layout Standard
26027 The modulo-function is special, because it exists in four variants.
26030 \begin_layout Standard
26031 The variants in a displayed formula:
26032 \begin_inset Formula
26034 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
26035 \mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
26036 \mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
26037 \mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
26038 \mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b
26046 \begin_layout Standard
26047 In an inline formula less space is set before the function names for all
26051 \begin_layout Section
26053 \begin_inset Index idx
26056 \begin_layout Plain Layout
26065 \begin_layout Subsection
26066 Special Characters in Mathematical Text
26069 \begin_layout Standard
26070 The following commands can only be used in mathematical text or in TeX-mode:
26073 \begin_layout Standard
26074 \begin_inset space \hfill{}
26078 \begin_inset Tabular
26079 <lyxtabular version="3" rows="8" columns="2">
26080 <features tabularvalignment="middle">
26081 <column alignment="block" valignment="top" width="0">
26082 <column alignment="block" valignment="top" width="0">
26084 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26087 \begin_layout Plain Layout
26093 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26096 \begin_layout Plain Layout
26104 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26107 \begin_layout Plain Layout
26115 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26118 \begin_layout Plain Layout
26119 \begin_inset Formula $\textrm{œ}$
26129 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26132 \begin_layout Plain Layout
26140 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26143 \begin_layout Plain Layout
26144 \begin_inset Formula $\textrm{Œ}$
26154 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26157 \begin_layout Plain Layout
26165 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26168 \begin_layout Plain Layout
26169 \begin_inset Formula $\textrm{æ}$
26179 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26182 \begin_layout Plain Layout
26190 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26193 \begin_layout Plain Layout
26194 \begin_inset Formula $\textrm{Æ}$
26204 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26207 \begin_layout Plain Layout
26215 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26218 \begin_layout Plain Layout
26219 \begin_inset Formula $\textrm{\aa}$
26229 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26232 \begin_layout Plain Layout
26236 \begin_inset Index idx
26239 \begin_layout Plain Layout
26246 \begin_layout Plain Layout
26267 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26270 \begin_layout Plain Layout
26271 \begin_inset Formula $\textrm{Å}$
26281 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26284 \begin_layout Plain Layout
26292 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26295 \begin_layout Plain Layout
26296 \begin_inset Formula $\textrm{ı}$
26310 \begin_inset space \hfill{}
26314 \begin_inset Tabular
26315 <lyxtabular version="3" rows="8" columns="2">
26316 <features tabularvalignment="middle">
26317 <column alignment="block" valignment="top" width="0">
26318 <column alignment="center" valignment="top" width="0">
26320 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26323 \begin_layout Plain Layout
26325 \begin_inset Note Note
26328 \begin_layout Plain Layout
26330 \begin_inset space \thinspace{}
26333 mm is used for separation, because otherwise the output will be ¡ and ¿
26344 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26347 \begin_layout Plain Layout
26355 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26358 \begin_layout Plain Layout
26366 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26369 \begin_layout Plain Layout
26370 \begin_inset Formula $\textrm{ø}$
26380 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26383 \begin_layout Plain Layout
26391 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26394 \begin_layout Plain Layout
26395 \begin_inset Formula $\textrm{Ø}$
26405 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26408 \begin_layout Plain Layout
26416 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26419 \begin_layout Plain Layout
26420 \begin_inset Formula $\textrm{ł}$
26430 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26433 \begin_layout Plain Layout
26441 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26444 \begin_layout Plain Layout
26445 \begin_inset Formula $\textrm{Ł}$
26455 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26458 \begin_layout Plain Layout
26460 \begin_inset space \hspace{}
26468 \begin_layout Plain Layout
26482 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26485 \begin_layout Plain Layout
26486 \begin_inset Formula $\textrm{!`}$
26496 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26499 \begin_layout Plain Layout
26501 \begin_inset space \hspace{}
26509 \begin_layout Plain Layout
26523 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26526 \begin_layout Plain Layout
26527 \begin_inset Formula $\textrm{?`}$
26537 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26540 \begin_layout Plain Layout
26548 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26551 \begin_layout Plain Layout
26552 \begin_inset Formula $\textrm{ȷ}$
26566 \begin_inset space \hfill{}
26572 \begin_layout Standard
26574 \begin_inset Formula $\textrm{\textrm{Å}}$
26578 \begin_inset Formula $\textrm{\textrm{Ø}}$
26581 can also be inserted via the math toolbar button
26582 \begin_inset Graphics
26583 filename ../images/math/digamma.png
26591 \begin_layout Standard
26592 An exception are the commands
26595 \begin_inset space \hspace{}
26604 \begin_inset space \hspace{}
26610 , because they can be inserted in LyX directly to text.
26613 \begin_layout Subsection
26615 \begin_inset CommandInset label
26617 name "sub:Accents-in-Text"
26622 \begin_inset Index idx
26625 \begin_layout Plain Layout
26634 \begin_layout Standard
26635 With the following commands all letters can be accented.
26636 The commands must be inserted in TeX-mode.
26639 \begin_layout Standard
26640 \begin_inset space \hfill{}
26644 \begin_inset Tabular
26645 <lyxtabular version="3" rows="8" columns="2">
26646 <features tabularvalignment="middle">
26647 <column alignment="block" valignment="top" width="0">
26648 <column alignment="block" valignment="top" width="0">
26650 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26653 \begin_layout Plain Layout
26659 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26662 \begin_layout Plain Layout
26670 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26673 \begin_layout Plain Layout
26677 \begin_inset Quotes grd
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" leftline="true" usebox="none">
26711 \begin_layout Plain Layout
26719 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26722 \begin_layout Plain Layout
26726 \begin_layout Plain Layout
26742 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26745 \begin_layout Plain Layout
26752 \begin_layout Plain Layout
26766 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26769 \begin_layout Plain Layout
26773 \begin_layout Plain Layout
26789 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26792 \begin_layout Plain Layout
26800 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26803 \begin_layout Plain Layout
26807 \begin_layout Plain Layout
26823 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26826 \begin_layout Plain Layout
26833 \begin_layout Plain Layout
26847 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26850 \begin_layout Plain Layout
26854 \begin_layout Plain Layout
26870 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26873 \begin_layout Plain Layout
26880 \begin_layout Plain Layout
26894 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26897 \begin_layout Plain Layout
26901 \begin_layout Plain Layout
26917 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26920 \begin_layout Plain Layout
26927 \begin_layout Plain Layout
26941 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26944 \begin_layout Plain Layout
26948 \begin_layout Plain Layout
26968 \begin_inset space \hfill{}
26972 \begin_inset Tabular
26973 <lyxtabular version="3" rows="8" columns="2">
26974 <features tabularvalignment="middle">
26975 <column alignment="block" valignment="top" width="0">
26976 <column alignment="center" valignment="top" width="0">
26978 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26981 \begin_layout Plain Layout
26987 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26990 \begin_layout Plain Layout
26998 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27001 \begin_layout Plain Layout
27008 \begin_layout Plain Layout
27022 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27025 \begin_layout Plain Layout
27029 \begin_layout Plain Layout
27045 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27048 \begin_layout Plain Layout
27056 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27059 \begin_layout Plain Layout
27063 \begin_layout Plain Layout
27079 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27082 \begin_layout Plain Layout
27086 \begin_inset Index idx
27089 \begin_layout Plain Layout
27100 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27103 \begin_layout Plain Layout
27107 \begin_layout Plain Layout
27123 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27126 \begin_layout Plain Layout
27134 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27137 \begin_layout Plain Layout
27141 \begin_layout Plain Layout
27157 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27160 \begin_layout Plain Layout
27167 \begin_layout Plain Layout
27181 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27184 \begin_layout Plain Layout
27188 \begin_layout Plain Layout
27204 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27207 \begin_layout Plain Layout
27214 \begin_layout Plain Layout
27228 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27231 \begin_layout Plain Layout
27235 \begin_layout Plain Layout
27251 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27254 \begin_layout Plain Layout
27261 \begin_layout Plain Layout
27275 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27278 \begin_layout Plain Layout
27282 \begin_layout Plain Layout
27302 \begin_inset space \hfill{}
27308 \begin_layout Standard
27309 \begin_inset VSpace medskip
27318 also two different characters can be accented.
27327 \begin_layout Plain Layout
27342 \begin_layout Plain Layout
27354 \begin_layout Standard
27367 can in combination with vowels directly be inserted with the keyboard without
27369 The same applies for the tilde
27373 \begin_layout Plain Layout
27374 This only applies for keyboards where the tilde is defined as accent.
27383 in combination with
27398 \begin_layout Standard
27441 and accents that are inserted directly with the keyboard are also available
27442 in mathematical text.
27443 For the other accents there are special math commands to be used in formulas,
27445 \begin_inset CommandInset ref
27447 reference "sub:Accents-for-one"
27454 \begin_layout Standard
27455 \begin_inset VSpace bigskip
27458 Furthermore, with the command
27465 \begin_inset Index idx
27468 \begin_layout Plain Layout
27476 all numbers and letters can be set into a circle, quasi accented with a
27477 circle, similar to the copyright symbol.
27480 \begin_layout Standard
27482 \begin_inset Tabular
27483 <lyxtabular version="3" rows="3" columns="2">
27484 <features tabularvalignment="middle">
27485 <column alignment="center" valignment="top" width="0">
27486 <column alignment="center" valignment="top" width="0">
27488 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27491 \begin_layout Plain Layout
27497 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27500 \begin_layout Plain Layout
27502 \begin_inset Note Note
27505 \begin_layout Plain Layout
27512 is only used as spacer.
27524 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27527 \begin_layout Plain Layout
27535 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27538 \begin_layout Plain Layout
27542 \begin_layout Plain Layout
27558 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27561 \begin_layout Plain Layout
27572 raisebox{-1.5pt}{W}}
27577 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27580 \begin_layout Plain Layout
27581 \begin_inset Formula $\raisebox{4.5mm}{}$
27588 \begin_layout Plain Layout
27606 \begin_inset Formula $\raisebox{-2mm}{}$
27622 \begin_layout Standard
27623 One has to take care that the character fits in the circle.
27634 \begin_layout Plain Layout
27636 \begin_inset CommandInset ref
27638 reference "sub:Font-Sizes"
27647 specifies thereby the size of the circle.
27658 \begin_layout Plain Layout
27660 \begin_inset CommandInset ref
27662 reference "sub:Boxes-without-Frame"
27671 the character can be centered.
27674 \begin_layout Subsection
27676 \begin_inset Index idx
27679 \begin_layout Plain Layout
27688 \begin_layout Standard
27689 Old-style figures (also known as old-style numerals) are created with the
27697 \begin_inset Index idx
27700 \begin_layout Plain Layout
27709 The command can be used in formulas and in TeX-mode.
27710 The command scheme is:
27713 \begin_layout Standard
27718 oldstylenums{number}
27721 \begin_layout Standard
27726 oldstylenums{0123456789
27729 \begin_inset Formula $\oldstylenums{0123456789}$
27735 \begin_layout Subsection
27736 Miscellaneous special Characters
27737 \begin_inset CommandInset label
27739 name "sub:Miscellaneous-special-Characters"
27744 \begin_inset Index idx
27747 \begin_layout Plain Layout
27748 Special characters ! miscellaneous
27756 \begin_layout Standard
27757 The following characters can only be inserted to formulas by using commands:
27760 \begin_layout Standard
27762 \begin_inset Tabular
27763 <lyxtabular version="3" rows="4" columns="2">
27764 <features tabularvalignment="middle">
27765 <column alignment="center" valignment="top" width="0">
27766 <column alignment="center" valignment="top" width="0">
27768 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27771 \begin_layout Plain Layout
27777 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27780 \begin_layout Plain Layout
27788 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27791 \begin_layout Plain Layout
27798 \begin_layout Plain Layout
27812 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27815 \begin_layout Plain Layout
27816 \begin_inset Formula $\mathcircumflex$
27826 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27829 \begin_layout Plain Layout
27837 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27840 \begin_layout Plain Layout
27841 \begin_inset Formula $\_$
27851 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27854 \begin_layout Plain Layout
27859 \begin_layout Plain Layout
27871 \begin_inset Index idx
27874 \begin_layout Plain Layout
27887 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27890 \begin_layout Plain Layout
27891 \begin_inset Formula $^{\circ}$
27907 \begin_layout Standard
27908 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
27909 contains the following line
27913 \begin_layout Plain Layout
27914 More about this is described in
27915 \begin_inset CommandInset ref
27917 reference "sub:Text-Characters-in"
27929 \begin_layout Standard
27934 DeclareInputtext{176}{
27947 \begin_layout Standard
27948 \begin_inset Newpage newpage
27954 \begin_layout Section
27956 \begin_inset CommandInset label
27958 name "sec:Formula-Styles"
27963 \begin_inset Index idx
27966 \begin_layout Plain Layout
27975 \begin_layout Itemize
27976 There are two different alignment styles:
27980 \begin_layout Description
27981 Centered is the predefined standard
27984 \begin_layout Description
27985 Indented for this the option
27989 must be inserted in the menu
27991 Document\SpecialChar \menuseparator
27997 \begin_inset space ~
28003 \begin_layout Standard
28008 is used, the indentation can be adjusted with the length
28015 \begin_inset Index idx
28018 \begin_layout Plain Layout
28027 Should the distance be 15
28028 \begin_inset space \thinspace{}
28031 mm, the following command line is inserted in the LaTeX-preamble
28034 \begin_layout Standard
28044 \begin_layout Standard
28045 When no length is specified, the predefined value of 30
28046 \begin_inset space \thinspace{}
28053 \begin_layout Itemize
28054 And two different numbering styles:
28058 \begin_layout Description
28059 Right is the predefined standard
28062 \begin_layout Description
28063 Left for this the option
28067 must be inserted in the menu
28069 Document\SpecialChar \menuseparator
28075 \begin_inset space ~
28082 \begin_layout Standard
28091 can also be used together.
28092 In this case both options are inserted, separated by a comma.
28095 \begin_layout Standard
28096 The chosen styles are used for all displayed formulas of the document.
28097 When both, centered and indented formulas should be created in a document,
28103 The indented formulas are then set in a flalign environment, see
28104 \begin_inset CommandInset ref
28106 reference "sub:Flalign-Environment"
28113 \begin_layout Section
28115 \begin_inset CommandInset label
28117 name "sec:Multiline-Formulas"
28122 \begin_inset Index idx
28125 \begin_layout Plain Layout
28126 Formula ! multiline
28134 \begin_layout Subsection
28138 \begin_layout Standard
28139 In LyX multiline formulas are created by pressing
28144 arg "newline-insert newline"
28150 This creates either an
28152 eqnarray environment
28154 that is described in
28155 \begin_inset CommandInset ref
28157 reference "sub:Eqnarray-Environment"
28161 or, when the option
28163 Use AMS math package
28165 in the document settings is selected, an
28169 that is described in
28170 \begin_inset CommandInset ref
28172 reference "sub:Standard-align-Environment"
28179 \begin_layout Standard
28180 There are other multiline formula environments that can be created via the
28183 Insert\SpecialChar \menuseparator
28187 These environments are described in the following sections.
28190 \begin_layout Standard
28191 In all multiline formula environments a new line is created by pressing
28195 arg "newline-insert newline"
28199 To add or delete lines, the math toolbar buttons
28200 \begin_inset Graphics
28201 filename ../images/tabular-feature_append-row.png
28207 \begin_inset Graphics
28208 filename ../images/tabular-feature_delete-row.png
28213 , respectively, or the menu
28215 Edit\SpecialChar \menuseparator
28221 \begin_layout Subsubsection
28223 \begin_inset CommandInset label
28225 name "sub:Line-Separation"
28230 \begin_inset Index idx
28233 \begin_layout Plain Layout
28234 Formula ! multiline ! Line separation
28242 \begin_layout Standard
28243 There is sometimes not enough space in multiline formulas between the lines:
28244 \begin_inset Formula
28246 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}\\
28247 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
28255 \begin_layout Standard
28256 In LaTeX additional line space is specified as optional argument of the
28258 This is not yet possible in LyX
28262 \begin_layout Plain Layout
28264 \begin_inset CommandInset href
28266 name "LyX-bug #1505"
28267 target "http://www.lyx.org/trac/ticket/1505"
28276 , therefore the whole formula must be inserted in TeX-mode.
28277 To add in our example space, the command
28285 is inserted at the end of the first line.
28290 \begin_layout Plain Layout
28297 \begin_layout Plain Layout
28299 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
28302 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
28309 \begin_layout Plain Layout
28313 left(B^{2}+x_{0}^{2}
28321 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
28326 \begin_layout Plain Layout
28338 \begin_layout Standard
28339 \begin_inset VSpace bigskip
28342 To set the line separation for all lines in a formula, the length
28349 \begin_inset Index idx
28352 \begin_layout Plain Layout
28362 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
28373 \begin_inset space \thinspace{}
28378 \begin_inset space \thinspace{}
28381 mm additional line separation as in the previous example, the command
28384 \begin_layout Standard
28394 \begin_layout Standard
28395 is inserted in TeX-mode before the formula.
28396 This requires that the LaTeX-package
28404 \begin_layout Plain Layout
28409 is part of every LaTeX standard installation.
28415 \begin_inset Index idx
28418 \begin_layout Plain Layout
28424 was loaded in LaTeX-preamble with the line
28427 \begin_layout Standard
28435 \begin_layout Standard
28440 \begin_layout Plain Layout
28452 \begin_inset Formula
28454 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}\\
28455 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
28463 \begin_layout Standard
28467 \begin_layout Plain Layout
28478 To get back to the predefined distance,
28484 is set to the value 3
28485 \begin_inset space \thinspace{}
28491 \begin_layout Subsubsection
28493 \begin_inset CommandInset label
28495 name "sub:Column-Separation"
28500 \begin_inset Index idx
28503 \begin_layout Plain Layout
28504 Formula ! multiline ! Column separation
28512 \begin_layout Standard
28513 Multiline formulas form a matrix.
28514 A formula in the eqnarray environment is for example a matrix with three
28516 By changing the column separation in this environment, the space beside
28517 the relation sign can be changed.
28520 \begin_layout Standard
28521 The column separation is specified with the length
28528 \begin_inset Index idx
28531 \begin_layout Plain Layout
28540 \begin_inset Newline newline
28543 column separation = 2
28544 \begin_inset space \thinspace{}
28554 \begin_inset Newline newline
28560 \begin_layout Standard
28570 \begin_layout Standard
28571 inserted in TeX-mode, sets for all following formulas a column separation
28573 \begin_inset space \thinspace{}
28577 To get back to the predefined distance,
28584 \begin_inset space \thinspace{}
28590 \begin_layout Standard
28592 \begin_inset space \thinspace{}
28595 cm column separation:
28599 \begin_layout Plain Layout
28611 \begin_inset Formula
28619 A formula with the predefined column separation for matrices of 10
28620 \begin_inset space \thinspace{}
28627 \begin_layout Plain Layout
28639 \begin_inset Formula
28650 \begin_layout Subsubsection
28652 \begin_inset Index idx
28655 \begin_layout Plain Layout
28664 \begin_layout Standard
28665 Long formulas can be typeset using these methods:
28668 \begin_layout Itemize
28669 When one side of the equation is much shorther than the line width, this
28670 one is chosen for the left side and the right side is typeset over two
28672 \begin_inset Formula
28674 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 \\
28675 & & -\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}
28680 The minus sign at the beginning of the second line does normally not appear
28681 as operator because it is the first character of the line.
28682 Thus it would not be surrounded by space and could not be distinguished
28683 from the fraction bar.
28685 \begin_inset space \thinspace{}
28688 pt space was inserted behind the minus sign with the command
28698 \begin_layout Plain Layout
28706 \begin_inset CommandInset ref
28708 reference "sub:Variable-Space"
28718 \begin_inset Index idx
28721 \begin_layout Plain Layout
28732 \begin_layout Itemize
28733 When both sides of the equation are too long, the command
28740 \begin_inset Index idx
28743 \begin_layout Plain Layout
28752 It is inserted to the first column of the first line and effects that all
28753 further insertions overwrite the following columns:
28754 \begin_inset Formula
28756 \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 \\
28757 & & -\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 \\
28758 & & =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}
28763 After the insertion of
28769 , the cursor is in a purple box that is a bit shifted to the left from the
28771 In this the formula is inserted.
28772 \begin_inset Newline newline
28775 The content of the further lines is inserted to the second or another formula
28777 The greater the column number where it was inserted, the larger the indentation.
28778 \begin_inset VSpace medskip
28782 \begin_inset Newline newline
28786 \begin_inset Note Greyedout
28789 \begin_layout Plain Layout
28790 Note the following when using
28799 \begin_layout Itemize
28800 The formula doesn't use the full page width.
28802 \begin_inset space \thinspace{}
28806 \begin_inset space \space{}
28810 \begin_inset Formula $-B^{2}$
28813 is added to the first line in the above example, it would have been outside
28815 To better use the width, negative space can be inserted at the beginning
28819 \begin_layout Itemize
28820 Due to a bug in LyX the cursor cannot be set with the mouse into the first
28825 \begin_layout Plain Layout
28826 \begin_inset CommandInset href
28828 name "LyX-bug #1429"
28829 target "http://www.lyx.org/trac/ticket/1429"
28838 One can only set the cursor at the beginning of the line and move it with
28847 \begin_layout Itemize
28848 Other methods to set long formulas are offered by the environments described
28850 \begin_inset CommandInset ref
28852 reference "sub:Multline-Environment"
28857 \begin_inset CommandInset ref
28859 reference "sub:Multiline-Formula-Parts"
28866 \begin_layout Subsubsection
28868 \begin_inset CommandInset label
28870 name "sub:Multiline-Brackets"
28875 \begin_inset Index idx
28878 \begin_layout Plain Layout
28879 Brackets ! for multiline expressions
28887 \begin_layout Standard
28888 For brackets spanning multiple lines the following problem occurs:
28889 \begin_inset Formula
28891 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28892 & & \left.\cdots+B-D\right]
28900 \begin_layout Standard
28901 The closing bracket is smaller than the opening bracket because brackets
28902 with variable size may not span multiple lines.
28905 \begin_layout Standard
28906 To set the bracket size for the second line correctly, the first line is
28914 \begin_inset Index idx
28917 \begin_layout Plain Layout
28925 and the second line with
28933 \begin_layout Plain Layout
28947 \begin_inset CommandInset ref
28949 reference "sub:Automatic-Bracket-Size"
28961 \begin_inset Index idx
28964 \begin_layout Plain Layout
28990 \begin_layout Plain Layout
29009 \begin_layout Plain Layout
29028 \begin_layout Plain Layout
29040 \begin_inset Formula $\downarrow$
29046 \begin_inset Index idx
29049 \begin_layout Plain Layout
29057 is inserted, because the multiplication operator with its limits is the
29058 largest symbol in the first line and this should be the size for the bracket
29059 in the second line.
29062 \begin_layout Standard
29063 The result is this:
29064 \begin_inset Formula
29066 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
29067 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
29075 \begin_layout Subsection
29079 \begin_layout Standard
29080 Align environments can be used for every kind of multiline formulas.
29081 They are specially useful to set several formulas side by side.
29084 \begin_layout Standard
29085 Align environments consist of columns.
29086 The odd columns are right aligned, the even ones left aligned.
29087 Every line in an Align environment can be numbered.
29090 \begin_layout Standard
29091 Align environments are created via the menu
29093 Insert\SpecialChar \menuseparator
29099 Edit\SpecialChar \menuseparator
29100 Math\SpecialChar \menuseparator
29101 Change Formula Type
29103 already existing formulas can be converted to Align environments.
29106 \begin_layout Standard
29107 To add or delete columns, the math toolbar buttons
29108 \begin_inset Graphics
29109 filename ../images/tabular-feature_append-column.png
29115 \begin_inset Graphics
29116 filename ../images/tabular-feature_delete-column.png
29121 , respectively, or the menu
29123 Edit\SpecialChar \menuseparator
29129 \begin_layout Subsubsection
29130 Standard align Environment
29131 \begin_inset CommandInset label
29133 name "sub:Standard-align-Environment"
29138 \begin_inset Index idx
29141 \begin_layout Plain Layout
29142 Formula ! multiline ! align environment
29150 \begin_layout Standard
29151 This Align environment is created by presssing
29154 arg "newline-insert newline"
29157 in a formula or by the menu
29159 Insert\SpecialChar \menuseparator
29160 Math\SpecialChar \menuseparator
29161 AMS align Environment
29166 \begin_layout Standard
29167 An example for two formulas set side by side, that are created with a four
29168 column align environment:
29169 \begin_inset Formula
29171 A & =\sin(B) & C & =D\\
29172 C & \ne A & B & \ne D
29177 As it can be seen, the formulas in this environment are placed so as if
29186 \begin_layout Plain Layout
29194 \begin_inset CommandInset ref
29196 reference "sub:Variable-Space"
29207 before the first and after every even column.
29208 When the formula style
29214 \begin_layout Plain Layout
29216 \begin_inset CommandInset ref
29218 reference "sec:Formula-Styles"
29229 is used, the formula is set without the
29235 before the first column.
29238 \begin_layout Subsubsection
29239 Alignat Environment
29240 \begin_inset Index idx
29243 \begin_layout Plain Layout
29244 Formula ! multiline ! alignat environment
29252 \begin_layout Standard
29253 The alignat environment has no predefined column separation.
29254 It can be inserted manually with the spaces that are described
29255 \begin_inset CommandInset ref
29257 reference "sub:Space"
29264 \begin_layout Standard
29265 The above example in the alignat environment where 1
29266 \begin_inset space \thinspace{}
29269 cm space was inserted at the beginning of the second formula:
29270 \begin_inset Formula
29271 \begin{alignat*}{2}
29272 A & =\sin(B) & \hspace{1cm}C & =D\\
29273 C & \ne A & B & \ne D
29278 Because the column separation can be set separately for every column, this
29279 environment is especially suitable to set three and more formulas side
29283 \begin_layout Subsubsection
29284 Flalign Environment
29285 \begin_inset CommandInset label
29287 name "sub:Flalign-Environment"
29292 \begin_inset Index idx
29295 \begin_layout Plain Layout
29296 Formula ! multiline ! flalign environment
29304 \begin_layout Standard
29305 In this environment the first two columns are always set as much as possible
29306 to the left and the last two ones to the right.
29308 \begin_inset Formula
29310 A & =1 & B & =2 & C & =3\\
29311 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
29319 \begin_layout Standard
29320 By creating a flalign environment with an odd number of columns where an
29321 empty TeX-brace is inserted to the last column, several formulas in a document
29322 can be set to the left, although the formula style
29327 As example the indented formula
29328 \begin_inset CommandInset ref
29330 reference "eq:VolInt"
29335 \begin_inset Formula
29337 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}
29342 The first two columns contain the formula.
29343 To indent it as with the formula style
29348 \begin_inset space \thinspace{}
29351 pt space was inserted at the beginning of the first column.
29354 \begin_layout Subsection
29355 Eqnarray Environment
29356 \begin_inset CommandInset label
29358 name "sub:Eqnarray-Environment"
29363 \begin_inset Index idx
29366 \begin_layout Plain Layout
29367 Formula ! multiline ! eqnarray environment
29375 \begin_layout Standard
29376 When this environment has been created, three blue boxes appear.
29377 The content of the first box is right aligned, the content of the last
29379 The content of the middle box appears centered and a bit smaller, because
29380 it is designed to insert there only relation characters.
29381 \begin_inset Formula
29383 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
29393 \begin_layout Subsection
29395 \begin_inset Index idx
29398 \begin_layout Plain Layout
29399 Formula ! multiline ! gather environment
29407 \begin_layout Standard
29408 This environment consists of only one centered column.
29409 Every line can be numbered.
29410 \begin_inset Formula
29421 \begin_layout Subsection
29422 Multline Environment
29423 \begin_inset CommandInset label
29425 name "sub:Multline-Environment"
29430 \begin_inset Index idx
29433 \begin_layout Plain Layout
29434 Formula ! multiline ! multline environment
29442 \begin_layout Standard
29443 The multline environment consists, like the gather environment, of only
29445 But the first line is left aligned, the last one right aligned.
29446 All other lines are centered.
29447 Therefore this environment is suitable for long formulas.
29449 \begin_inset CommandInset ref
29451 reference "eq:lefteqn"
29455 in the multline environment:
29456 \begin_inset Formula
29458 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}\\
29459 -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}\\
29460 =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}}
29468 \begin_layout Standard
29469 In the output only the last (first) line of a multline environment appears
29470 numbered when the document numbering is right (left).
29474 \begin_layout Plain Layout
29475 numbering styles see
29476 \begin_inset CommandInset ref
29478 reference "sec:Formula-Styles"
29490 \begin_layout Standard
29498 \begin_inset Index idx
29501 \begin_layout Plain Layout
29516 \begin_inset Index idx
29519 \begin_layout Plain Layout
29527 a centered line can be right or left aligned, respectively.
29528 The commands are used as follows:
29531 \begin_layout Standard
29536 shoveright{line content}
29542 shoveleft{line content}
29545 \begin_layout Standard
29546 \begin_inset VSpace medskip
29556 \begin_inset Index idx
29559 \begin_layout Plain Layout
29567 specifies the distance of the first line from the left page margin.
29568 Predefined is the length 0
29569 \begin_inset space \thinspace{}
29575 \begin_layout Standard
29576 As example the above formula where the command
29579 \begin_layout Standard
29589 \begin_layout Standard
29590 was inserted in TeX-mode before:
29594 \begin_layout Plain Layout
29606 \begin_inset Formula
29608 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}\\
29609 \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}}\\
29610 =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}}
29619 \begin_layout Plain Layout
29630 The second line was left aligned using
29639 \begin_layout Subsection
29640 Multiline Formula Parts
29641 \begin_inset CommandInset label
29643 name "sub:Multiline-Formula-Parts"
29648 \begin_inset Index idx
29651 \begin_layout Plain Layout
29652 Formula ! multiline ! formula parts
29660 \begin_layout Standard
29661 To display only parts of a formula with multiple lines, one of the following
29662 environments are used:
29679 They can be inserted via the menu
29681 Insert\SpecialChar \menuseparator
29684 or by using the commands described in this section.
29687 \begin_layout Standard
29688 The first three have the same properties as the corresponding multiline
29689 formula environments, but it is possible to set further formula parts beside
29692 \begin_inset Formula
29694 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29695 \Delta E\Delta t & \ge\frac{\hbar}{2}
29697 \right\} \textrm{Uncertainty relations}
29705 \begin_layout Standard
29706 To get this formula, a displayed formula is created where the command
29713 \begin_inset Index idx
29716 \begin_layout Plain Layout
29725 A purple box appears around the blue formula box where now columns and
29726 lines can be added.
29727 Outside the multiline environment other formula parts can be set, like
29731 \begin_layout Standard
29732 The aligned environment is also suitable for long formulas whose lines are
29733 horizontally aligned.
29734 Using aligned in a displayed formula has the advantage that the formula
29735 number is vertically centered behind the lines.
29737 \begin_inset CommandInset ref
29739 reference "eq:shortlong"
29743 in the aligned environment:
29744 \begin_inset Formula
29746 \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}|}\\
29747 & -\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}|}
29756 \begin_layout Standard
29757 To use the environments
29776 \begin_inset Index idx
29779 \begin_layout Plain Layout
29794 \begin_inset Index idx
29797 \begin_layout Plain Layout
29812 \begin_inset Index idx
29815 \begin_layout Plain Layout
29823 are inserted, respectively.
29824 The split environment has the same properties as the aligned environment
29825 but it can only have two columns.
29828 \begin_layout Subsection
29829 Text in multiline Formulas
29830 \begin_inset CommandInset label
29832 name "sub:Text-in-multiline"
29837 \begin_inset Index idx
29840 \begin_layout Plain Layout
29847 \begin_inset Index idx
29850 \begin_layout Plain Layout
29851 Formula ! multiline ! text
29859 \begin_layout Standard
29860 In the Align environments, and the multline and gather environment, text
29861 can be inserted that will appear in a separate line and doesn't affect
29862 the column alignment.
29863 To do this, the command
29870 \begin_inset Index idx
29873 \begin_layout Plain Layout
29881 is used in the following scheme:
29884 \begin_layout Standard
29892 \begin_layout Standard
29893 The text should not be longer than a line because it cannot be hyphenated.
29894 As LyX doesn't yet support
29900 directly, the text is written as mathematical text.
29907 must hereby be at the beginning of a line and appears in the output above
29909 An example where the text was inserted at the beginning of the second line:
29910 \begin_inset Formula
29912 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29913 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29921 \begin_layout Standard
29922 \begin_inset Newpage newpage
29928 \begin_layout Section
29930 \begin_inset Index idx
29933 \begin_layout Plain Layout
29940 \begin_inset Index idx
29943 \begin_layout Plain Layout
29944 Formula ! numbering|see
29948 \begin_layout Plain Layout
29959 \begin_layout Plain Layout
29974 \begin_layout Subsection
29978 \begin_layout Standard
29979 Numbered formulas can be created with the menu
29981 Insert\SpecialChar \menuseparator
29982 Math\SpecialChar \menuseparator
29984 \begin_inset space ~
29992 \begin_inset space ~
29998 Existing formulas can be numbered with the menu
30000 Edit\SpecialChar \menuseparator
30001 Math\SpecialChar \menuseparator
30003 \begin_inset space ~
30011 arg "math-number-toggle"
30015 The formula number is displayed in LyX behind the formula as number sign
30017 The number sign is replaced in the output by the formula number.
30020 \begin_layout Standard
30021 When numbering is turned on in multiline formulas, all lines will be numbered.
30022 But the numbering can be controlled with the menu
30024 Edit\SpecialChar \menuseparator
30025 Math\SpecialChar \menuseparator
30027 \begin_inset space ~
30031 \begin_inset space ~
30035 \begin_inset space ~
30043 arg "math-number-line-toggle"
30049 \begin_layout Standard
30050 Except for inline formulas, all formulas can be numbered with two different
30052 \begin_inset CommandInset ref
30054 reference "sec:Formula-Styles"
30061 \begin_layout Subsection
30063 \begin_inset Index idx
30066 \begin_layout Plain Layout
30067 Cross-references ! to formulas
30075 \begin_layout Standard
30076 All labeled formulas can be cross-referenced.
30077 A label is added by the menu
30079 Insert\SpecialChar \menuseparator
30082 or the toolbar button
30083 \begin_inset Graphics
30084 filename ../images/label-insert.png
30090 The cursor must hereby be inside a displayed formula.
30091 A dialog pops up displaying the prefix
30096 The label is inserted there behind the prefix.
30097 The predefined prefix means
30098 \begin_inset Quotes eld
30102 \begin_inset Quotes erd
30105 and makes it easier to find labels in large documents because it marks
30106 it as formula label to divide it from e.
30107 \begin_inset space \thinspace{}
30111 \begin_inset space \space{}
30115 To change a label, the menu
30117 Insert\SpecialChar \menuseparator
30123 \begin_layout Standard
30124 The name of the label is displayed in LyX within two parentheses behind
30126 A formula with a label is always numbered.
30129 \begin_layout Standard
30130 Cross-references are inserted via the menu
30132 Insert\SpecialChar \menuseparator
30135 or with the toolbar button
30136 \begin_inset Graphics
30137 filename ../images/dialog-show-new-inset_ref.png
30143 A formula cross-reference appears in the output as formula number.
30144 When in the cross-reference dialog window the format
30148 is chosen, the cross-reference appears in the output as formula number
30150 \begin_inset Newline newline
30153 By right-clicking on a cross-reference in LyX, one jumps to the formula
30154 that is referenced.
30157 \begin_layout Standard
30158 Here are as examples cross-references to formulas of the following subsections:
30159 \begin_inset Note Note
30162 \begin_layout Plain Layout
30163 Note the different cross-reference types.
30171 \begin_layout Standard
30173 \begin_inset CommandInset ref
30180 \begin_inset CommandInset ref
30188 \begin_inset CommandInset ref
30194 ) big Latin letters are used for the numbering in contrary to (
30195 \begin_inset CommandInset ref
30204 \begin_layout Standard
30205 \begin_inset VSpace medskip
30208 When the argument of
30216 \begin_layout Plain Layout
30224 \begin_inset CommandInset ref
30226 reference "sub:User-defined-Numbering"
30237 contains a box like in
30238 \begin_inset CommandInset ref
30240 reference "sub:Paragraph-Boxes"
30244 , the formula cannot be referenced.
30247 \begin_layout Subsection
30249 \begin_inset Index idx
30252 \begin_layout Plain Layout
30253 Formula numbering ! subnumbering
30261 \begin_layout Standard
30262 With the help of the commands
30266 begin{subequations}
30274 formulas can be subnumbered.
30275 Both commands are inserted in TeX-mode.
30278 \begin_layout Standard
30280 \begin_inset Formula
30291 \begin_layout Plain Layout
30295 addtocounter{equation}{-1}
30304 \begin_layout Plain Layout
30308 begin{subequations}
30314 \begin_inset VSpace -5mm
30318 \begin_inset Formula
30326 \begin_inset Formula
30336 \begin_layout Standard
30340 \begin_layout Plain Layout
30352 \begin_layout Standard
30353 To create the example, the following is done:
30356 \begin_layout Enumerate
30357 first formula is inserted
30360 \begin_layout Enumerate
30365 addtocounter{equation}{-1}
30367 begin{subequations}
30368 \begin_inset Index idx
30371 \begin_layout Plain Layout
30380 \begin_inset Newline newline
30385 is inserted after the first formula
30388 \begin_layout Enumerate
30389 second formula is inserted
30392 \begin_layout Enumerate
30393 third formula is inserted
30396 \begin_layout Enumerate
30403 is inserted after the third formula
30406 \begin_layout Standard
30407 Every formula between the commands
30419 is subnumbered as a, b,
30420 \begin_inset Newline linebreak
30423 c, \SpecialChar \ldots{}
30424 For multiline formulas every line will be subnumbered.
30425 All subnumbered formulas are treated as
30430 But as every numbered formula increases the counter
30434 by one, the command
30440 is needed to decrease it.
30441 Otherwise the formulas
30442 \begin_inset CommandInset ref
30449 \begin_inset CommandInset ref
30456 \begin_inset CommandInset ref
30462 would be numbered as
30463 \begin_inset CommandInset ref
30470 \begin_inset CommandInset ref
30477 \begin_inset CommandInset ref
30486 \begin_layout Standard
30487 By inserting the commands in TeX-mode, a space is created between the first
30490 \begin_inset space \thinspace{}
30493 mm vertical space is inserted after the command
30497 begin{subequations}
30500 When the formula style
30506 \begin_layout Plain Layout
30508 \begin_inset CommandInset ref
30510 reference "sec:Formula-Styles"
30522 \begin_inset space \thinspace{}
30525 mm space is inserted instead.
30528 \begin_layout Standard
30529 Here is an example for a multiline formula where the numbering was turned
30530 off for the second line:
30534 \begin_layout Plain Layout
30538 begin{subequations}
30544 \begin_inset Formula
30546 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
30547 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
30548 & = & B^{2}-2BZ+Z^{2}\label{eq:f}
30557 \begin_layout Plain Layout
30569 \begin_layout Subsection
30570 User-defined Numbering
30571 \begin_inset CommandInset label
30573 name "sub:User-defined-Numbering"
30578 \begin_inset Index idx
30581 \begin_layout Plain Layout
30582 Formula numbering ! user-defined
30590 \begin_layout Standard
30591 \begin_inset Index idx
30594 \begin_layout Plain Layout
30595 Formula numbering ! self-defined delimiters
30600 With the standard numbering parentheses are set around the formula number.
30601 To replace the parentheses for example by vertical bars, the following
30602 line is added to the LaTeX-preamble:
30605 \begin_layout Standard
30617 \begin_inset Note Note
30620 \begin_layout Plain Layout
30621 This macro is already declared in the LaTeX-preamble for testing.
30622 To activate it, remove the percent sign at the beginning.
30630 \begin_layout Standard
30631 To use other characters, the vertical bars besides the
30635 are replaced by one ore more characters.
30636 To get only the formula number the vertical bars are omitted.
30639 \begin_layout Standard
30640 \begin_inset VSpace bigskip
30643 When there should be an expression of your choice instead of the consecutive
30644 formula number in parentheses behind the formula, the command
30651 \begin_inset Index idx
30654 \begin_layout Plain Layout
30663 \begin_inset Formula
30665 A+B=C\tag{something}\label{eq:tag}
30670 In this example the command
30678 \begin_layout Plain Layout
30689 was inserted to the formula.
30692 \begin_layout Standard
30701 \begin_layout Plain Layout
30712 is inserted instead, the star prevents the parentheses around the expression:
30713 \begin_inset Formula
30715 A+B=C\tag*{something}
30723 \begin_layout Standard
30724 \begin_inset VSpace bigskip
30727 To restart the formula numbering with new document parts or sections, the
30728 following command is used:
30731 \begin_layout Standard
30736 @addtoreset{equation}{part}
30739 \begin_inset Index idx
30742 \begin_layout Plain Layout
30747 \begin_layout Plain Layout
30758 \begin_layout Plain Layout
30771 \begin_layout Plain Layout
30782 \begin_layout Plain Layout
30795 \begin_inset Newline newline
30799 \begin_inset Newline newline
30806 @addtoreset{equation}{section}
30809 \begin_layout Standard
30810 To be able to use these commands in TeX-mode, the
30811 \begin_inset Quotes eld
30815 \begin_inset Quotes erd
30818 character has to be made
30819 \begin_inset Quotes eld
30823 \begin_inset Quotes erd
30826 for LaTeX using the command
30840 So the command sequence in TeX-mode is:
30843 \begin_layout Standard
30849 \begin_inset Newline newline
30854 @addtoreset{equation}{section}
30855 \begin_inset Newline newline
30863 \begin_layout Standard
30864 In the LaTeX-preamble
30876 can be omitted as they are automatically internally inserted by LyX.
30879 \begin_layout Standard
30894 \begin_layout Plain Layout
30899 is part of the LaTeX-package
30904 \begin_inset Index idx
30907 \begin_layout Plain Layout
30908 Packages ! carlisle
30913 that is part of every LaTeX standard installation.
30919 \begin_inset Index idx
30922 \begin_layout Plain Layout
30923 Packages ! remreset
30928 has to be loaded in the LaTeX-preamble with the line
30931 \begin_layout Standard
30936 usepackage{remreset}
30939 \begin_layout Standard
30947 \begin_inset Index idx
30950 \begin_layout Plain Layout
30955 \begin_layout Plain Layout
30966 \begin_layout Plain Layout
30979 \begin_layout Plain Layout
30990 \begin_layout Plain Layout
31002 can be used with the same scheme as
31011 \begin_layout Standard
31012 \begin_inset VSpace bigskip
31015 Sometimes formulas should be numbered in the following form:
31018 \begin_layout Standard
31021 (section number.formula number)
31024 \begin_layout Standard
31025 The formula number should start with every section with
31026 \begin_inset Quotes eld
31030 \begin_inset Quotes erd
31036 \begin_layout Standard
31037 For this case there is the command
31044 \begin_inset Index idx
31047 \begin_layout Plain Layout
31055 , which is used with the following scheme:
31058 \begin_layout Standard
31063 numberwithin{counter}{sectioning}
31066 \begin_layout Standard
31067 Counter denotes what kind of numbering is affected, sectioning denotes what
31068 number is before the dot.
31071 \begin_layout Standard
31072 Thus in our case the following LaTeX-preamble or TeX-Code line is used:
31075 \begin_layout Standard
31080 numberwithin{equation}{section}
31083 \begin_layout Standard
31084 This is the result:
31088 \begin_layout Plain Layout
31092 numberwithin{equation}{section}
31098 \begin_inset Formula
31108 \begin_layout Standard
31110 \begin_inset space \thinspace{}
31114 \begin_inset space \space{}
31117 tables so that the number of the part is the sectioning,
31118 \begin_inset Newline newline
31125 numberwithin{table}{part}
31130 \begin_layout Standard
31131 To go back to the standard numbering or to prevent this kind of numbering
31132 when it is defined by the document class, the following command is inserted
31133 as TeX-Code or to the LaTeX-preamble:
31136 \begin_layout Standard
31146 \begin_inset Index idx
31149 \begin_layout Plain Layout
31163 \begin_layout Plain Layout
31179 \begin_inset Newline newline
31187 \begin_inset Newline newline
31199 \begin_layout Standard
31206 uses internally the command
31212 , described above, that also needs to be reverted.
31216 \begin_layout Plain Layout
31223 \begin_layout Plain Layout
31227 @removefromreset{equation}{section}
31230 \begin_layout Plain Layout
31242 \begin_layout Subsection
31243 Numbering with Roman Numbers and Letters
31244 \begin_inset Index idx
31247 \begin_layout Plain Layout
31248 Formula numbering ! with letters
31254 \begin_inset Index idx
31257 \begin_layout Plain Layout
31258 Formula numbering ! with Roman numbers
31266 \begin_layout Standard
31267 Formulas can also be numbered with Roman numbers and Latin letters.
31268 To number for example with small Roman numbers, the command
31271 \begin_layout Standard
31283 \begin_layout Standard
31284 is inserted before the formula in TeX-mode.
31292 \begin_inset Index idx
31295 \begin_layout Plain Layout
31303 redefines the predefined command
31319 \begin_layout Plain Layout
31326 has the same scheme like the command
31332 that is described in
31333 \begin_inset CommandInset ref
31335 reference "sub:The-Command-newcommand"
31348 is the formula counter.
31355 is used as prefix for a counter, the value of the counter is output as
31357 When a formula is numbered, LaTeX sets internally the command
31363 behind the formula.
31369 \begin_inset Index idx
31372 \begin_layout Plain Layout
31382 outputs the counter as small Roman number.
31385 \begin_layout Standard
31386 All formulas behind the command
31396 are now numbered Roman.
31397 To switch to numbering with big Roman numbers, the command is inserted
31411 \begin_inset Index idx
31414 \begin_layout Plain Layout
31426 \begin_inset Quotes eld
31430 \begin_inset Quotes erd
31433 with small Latin letters there is the command
31440 \begin_inset Index idx
31443 \begin_layout Plain Layout
31451 , for big ones there is the command
31458 \begin_inset Index idx
31461 \begin_layout Plain Layout
31474 \begin_layout Standard
31475 \begin_inset Note Greyedout
31478 \begin_layout Plain Layout
31483 Only maximal 26 formulas can be numbered with Latin letters in one document.
31491 \begin_layout Standard
31495 \begin_layout Plain Layout
31511 \begin_layout Standard
31512 \begin_inset Formula
31514 A=\textrm{small roman}
31523 \begin_layout Plain Layout
31537 \begin_inset Formula
31539 B=\textrm{big Roman}\label{eq:Rom}
31548 \begin_layout Plain Layout
31562 \begin_inset Formula
31564 C=\textrm{small Latin}
31573 \begin_layout Plain Layout
31587 \begin_inset Formula
31589 D=\textrm{big Latin}\label{eq:Lat}
31597 \begin_layout Standard
31598 To switch back to the default numbering, insert the command:
31601 \begin_layout Standard
31611 \begin_inset Index idx
31614 \begin_layout Plain Layout
31625 \begin_layout Standard
31629 \begin_layout Plain Layout
31643 \begin_inset Formula
31653 \begin_layout Standard
31654 \begin_inset VSpace medskip
31657 As you see, formulas are numbered serially independent from the numbering
31659 When then numbering should start with
31660 \begin_inset Quotes eld
31664 \begin_inset Quotes erd
31667 when the style is changed, new equation counters have to be defined.
31668 A description about this can be found in the file
31669 \begin_inset CommandInset href
31671 name "Formula-numbering.lyx"
31672 target "run:Formula-numbering.lyx"
31679 \begin_layout Section
31680 Chemical Symbols and Equations
31681 \begin_inset CommandInset label
31683 name "sub:Chemical-Symbols-and"
31688 \begin_inset Index idx
31691 \begin_layout Plain Layout
31692 Chemical characters ! Symbols
31698 \begin_inset Index idx
31701 \begin_layout Plain Layout
31708 \begin_inset Index idx
31711 \begin_layout Plain Layout
31720 \begin_layout Standard
31721 An example text from chemistry:
31724 \begin_layout Quote
31726 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
31729 -ion reacts with two
31730 \begin_inset Formula $\mathrm{Na^{+}}$
31733 -ions to sodium sulfate
31734 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
31738 The chemical equation for this is:
31739 \begin_inset Formula
31741 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
31749 \begin_layout Standard
31750 This chemical equation can directly be created as formula.
31751 To avoid that the symbols appear italic, everything is highlighted and
31752 changed by the shortcut
31758 to the upright font style.
31762 \begin_layout Plain Layout
31768 \begin_inset CommandInset ref
31770 reference "sub:Font-Styles"
31782 \begin_layout Standard
31783 A more convenient way to typeset chemical formulas is to use the command
31791 \begin_inset Index idx
31794 \begin_layout Plain Layout
31802 that is available when the LaTeX-package
31807 \begin_inset Index idx
31810 \begin_layout Plain Layout
31823 to a formula a new blue box appears where chemical formulas can be inserted
31824 in an intuitive way.
31827 \begin_layout Standard
31829 \begin_inset Tabular
31830 <lyxtabular version="3" rows="9" columns="2">
31831 <features tabularvalignment="middle">
31832 <column alignment="center" valignment="top" width="0">
31833 <column alignment="center" valignment="top" width="0">
31835 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31838 \begin_layout Plain Layout
31844 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31847 \begin_layout Plain Layout
31849 \begin_inset Note Note
31852 \begin_layout Plain Layout
31859 is only used as spacer.
31871 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31874 \begin_layout Plain Layout
31881 \begin_layout Plain Layout
31895 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31898 \begin_layout Plain Layout
31899 \begin_inset Formula $\raisebox{4.5mm}{}\ce{H2CO3}\raisebox{-2mm}{}$
31909 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31912 \begin_layout Plain Layout
31919 \begin_layout Plain Layout
31933 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31936 \begin_layout Plain Layout
31937 \begin_inset Formula $\raisebox{5mm}{}\ce{SO4^{2-}}\raisebox{-2mm}{}$
31947 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31950 \begin_layout Plain Layout
31957 \begin_layout Plain Layout
31971 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31974 \begin_layout Plain Layout
31975 \begin_inset Formula $\raisebox{4.5mm}{}\ce{(NH4)2S}\raisebox{-2mm}{}$
31985 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31988 \begin_layout Plain Layout
31995 \begin_layout Plain Layout
32009 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32012 \begin_layout Plain Layout
32013 \begin_inset Formula $\raisebox{4.5mm}{}\ce{KCr(SO4)2.12H2O}\raisebox{-2mm}{}$
32023 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32026 \begin_layout Plain Layout
32033 \begin_layout Plain Layout
32048 \begin_layout Plain Layout
32063 \begin_layout Plain Layout
32077 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32080 \begin_layout Plain Layout
32081 \begin_inset Formula $\raisebox{4.5mm}{}\ce{A-B\dbond C\tbond D}\raisebox{-2mm}{}$
32091 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32094 \begin_layout Plain Layout
32101 \begin_layout Plain Layout
32111 \begin_inset Formula $\downarrow$
32115 \begin_inset Formula $\to$
32123 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32126 \begin_layout Plain Layout
32127 \begin_inset Formula $\raisebox{5mm}{}\ce{_{90}^{227}Th+}\raisebox{-2mm}{}$
32137 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32140 \begin_layout Plain Layout
32147 \begin_layout Plain Layout
32160 \begin_layout Plain Layout
32173 \begin_layout Plain Layout
32186 \begin_layout Plain Layout
32199 \begin_layout Plain Layout
32213 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32216 \begin_layout Plain Layout
32217 \begin_inset Formula $\raisebox{4.5mm}{}\ce{CO2 + C <=> 2CO}\raisebox{-2mm}{}$
32227 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32230 \begin_layout Plain Layout
32237 \begin_layout Plain Layout
32250 \begin_layout Plain Layout
32263 \begin_layout Plain Layout
32276 \begin_layout Plain Layout
32293 \begin_layout Plain Layout
32307 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32310 \begin_layout Plain Layout
32311 \begin_inset Formula $\raisebox{5mm}{}\ce{CO2 + C ->[\alpha][\beta] 2CO}\raisebox{-4mm}{}$
32327 \begin_layout Standard
32328 \begin_inset Note Greyedout
32331 \begin_layout Plain Layout
32336 Inserting a formula to a
32342 box will lead to LaTeX errors.
32343 In this case TeX code has to be used like for
32357 \begin_layout Plain Layout
32378 \begin_layout Standard
32385 the command for equation
32386 \begin_inset space ~
32390 \begin_inset CommandInset ref
32392 reference "eq:chem-reaction"
32397 \begin_inset Newline newline
32408 \begin_layout Plain Layout
32421 \begin_layout Plain Layout
32434 \begin_layout Plain Layout
32447 \begin_layout Plain Layout
32460 \begin_layout Plain Layout
32473 \begin_layout Plain Layout
32485 \begin_layout Standard
32486 To create multiline chemical equations first a multiline formula is created
32488 \begin_inset CommandInset ref
32490 reference "sec:Multiline-Formulas"
32495 Afterwards the command
32501 is used in every small blue box of the formula.
32503 \begin_inset CommandInset ref
32505 reference "eq:TEOS-reaction-1"
32510 \begin_inset CommandInset ref
32512 reference "eq:TEOS-reaction-2"
32516 are an example of a multi-stage chemical reaction where every equation
32517 has its own number.
32518 \begin_inset Formula
32520 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
32521 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
32529 \begin_layout Standard
32540 package provides the command
32547 \begin_inset Index idx
32550 \begin_layout Plain Layout
32558 that has to be used for special cases.
32559 For more information about
32565 and more examples have a look at the documentation of
32570 \begin_inset CommandInset citation
32579 \begin_layout Section
32583 \begin_layout Standard
32584 LyX supports two types of commutative diagrams:
32592 that are explained in the following.
32595 \begin_layout Subsection
32597 \begin_inset Index idx
32600 \begin_layout Plain Layout
32609 \begin_layout Standard
32610 Diagrams of this type visualize relations by vertical and horizontal lines
32612 \begin_inset Formula
32614 \begin{CD}A@>>>B@>>>C\\
32625 \begin_layout Standard
32626 To get them, the command
32631 \begin_inset Index idx
32634 \begin_layout Plain Layout
32644 is inserted to a formula.
32645 A blue box appears with two dashed lines where further commands can be
32650 arg "newline-insert newline"
32653 a new line is created.
32654 Horizontal relations are inserted in odd, vertical in even formula lines.
32657 \begin_layout Standard
32658 To create the relations there are the following commands:
32661 \begin_layout Itemize
32666 creates a left arrow,
32677 \begin_layout Itemize
32682 creates an up arrow,
32690 a vertical equal sign
32693 \begin_layout Itemize
32699 is a placeholder for non-existent relations
32702 \begin_layout Standard
32703 All arrows can be labeled as follows:
32706 \begin_layout Itemize
32707 Is text inserted between the first and second < or >, resp., it is placed
32709 When it is inserted between the second and third one, it appears under
32713 \begin_layout Itemize
32714 When text for vertical arrows is inserted between the first and second A
32715 or V, resp., it is placed left beside the arrow.
32716 When it is inserted between the second and third one, it appears right
32718 If the text contains an A or V, these letters must be set into a TeX-brace.
32721 \begin_layout Standard
32722 As example a diagram with all possible relations:
32725 \begin_layout Standard
32726 \begin_inset Formula
32728 \begin{CD}A@>j>>B@>>k>C@=F\\
32739 \begin_layout Standard
32740 The command for this is:
32741 \begin_inset Newline newline
32752 \begin_layout Plain Layout
32761 A@>j>>B@>>k>C@=F Ctrl+Return
32762 \begin_inset Newline newline
32766 \begin_inset Phantom HPhantom
32769 \begin_layout Plain Layout
32778 \begin_layout Plain Layout
32797 \begin_inset Formula $\to$
32803 \begin_inset Newline newline
32807 \begin_inset Phantom HPhantom
32810 \begin_layout Plain Layout
32819 \begin_layout Plain Layout
32836 \begin_layout Subsection
32838 \begin_inset Index idx
32841 \begin_layout Plain Layout
32842 Diagrams ! xymatrix
32850 \begin_layout Standard
32851 To be able to use xymatrices, the LaTeX-package
32856 A xymatrix is created by inserting the command
32863 Then you are able to add new matrix columns and rows like for normal matrices,
32865 \begin_inset CommandInset ref
32867 reference "sec:Matrices"
32874 \begin_layout Standard
32875 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
32877 All possibilities to create commutative diagrams and decorations are explained
32882 that you find in the menu
32884 Help\SpecialChar \menuseparator
32886 \begin_inset space ~
32894 \begin_layout Subsection
32900 \begin_inset Index idx
32903 \begin_layout Plain Layout
32912 \begin_layout Standard
32917 -diagrams, the LaTeX-package
32926 -diagram is created by inserting the command
32933 Then you are able to add new matrix columns and rows like for normal matrices,
32935 \begin_inset CommandInset ref
32937 reference "sec:Matrices"
32944 \begin_layout Standard
32945 Examples how to create
32949 diagrams in LyX is given in the
32951 Feynman-diagram manual
32953 that you find in the menu
32955 Help\SpecialChar \menuseparator
32957 \begin_inset space ~
32965 \begin_layout Section
32966 User-defined Commands
32967 \begin_inset Index idx
32970 \begin_layout Plain Layout
32971 User-defined commands
32979 \begin_layout Standard
32980 \begin_inset Note Greyedout
32983 \begin_layout Plain Layout
32988 The names of user-defined commands and macros may only consist of Latin
32997 \begin_layout Subsection
33001 \begin_inset CommandInset label
33003 name "sub:The-Command-newcommand"
33008 \begin_inset Index idx
33011 \begin_layout Plain Layout
33012 User-defined commands !
33020 \begin_inset Index idx
33023 \begin_layout Plain Layout
33034 \begin_layout Standard
33035 Many LaTeX-commands are too long to be used frequently.
33036 But it is possible to define with the command
33042 new shorter commands.
33045 \begin_layout Standard
33046 The command scheme of
33055 \begin_layout Standard
33060 newcommand{new command name}[number of arguments][optional
33065 \begin_inset Newline newline
33069 \begin_inset Phantom HPhantom
33072 \begin_layout Plain Layout
33082 {command definition}
33085 \begin_layout Standard
33086 \begin_inset Note Greyedout
33089 \begin_layout Plain Layout
33094 Assure that the name of the new command is not already used in your document
33095 or by LaTeX-packages that you use.
33096 When you for example define the command
33108 , you get an error message because
33114 is already defined as command for
33115 \begin_inset Quotes eld
33119 \begin_inset Formula $\le$
33123 \begin_inset Quotes erd
33134 \begin_layout Standard
33135 The number of arguments is an integer in the range 0
33136 \begin_inset space \thinspace{}
33140 \begin_inset space \thinspace{}
33143 9 and specifies how many arguments the new command should have.
33144 With the optional value a value for an optional argument can be predefined.
33145 When this is done, the
33153 rgument of the new command is automatically an optional one.
33156 \begin_layout Standard
33157 Here are some examples:
33160 \begin_layout Itemize
33161 To define the command
33173 , the LaTeX-preamble line is:
33174 \begin_inset VSpace medskip
33178 \begin_inset Newline newline
33192 \begin_layout Itemize
33193 To define the command
33205 , the argument (that should be underlined) must be taken into account.
33206 For this the preamble line is:
33207 \begin_inset VSpace medskip
33211 \begin_inset Newline newline
33225 \begin_inset VSpace medskip
33229 \begin_inset Newline newline
33236 acts as argument placeholder, the
33240 behind it denotes that it is the placeholder for the first argument.
33243 \begin_layout Itemize
33251 \begin_inset space \thinspace{}
33255 \begin_inset space \space{}
33265 \begin_inset VSpace medskip
33269 \begin_inset Newline newline
33280 framebox#1#2{$#3$}}
33283 \begin_inset VSpace medskip
33287 \begin_inset Newline newline
33290 The two Dollar signs creates the extra formula needed for
33297 \begin_inset CommandInset ref
33299 reference "sub:Boxes-with-Frame"
33306 \begin_layout Itemize
33307 To create a new command for
33313 where the color for the box needn't to be specified, the argument for the
33314 color is defined optional:
33315 \begin_inset VSpace medskip
33319 \begin_inset Newline newline
33330 fcolorbox{#2}{#1}{$#3$}}
33333 \begin_inset VSpace medskip
33337 \begin_inset Newline newline
33340 When the color is not specified when using
33346 , the predefined color
33353 \begin_layout Standard
33354 A test of the new defined commands:
33357 \begin_layout Standard
33359 \begin_inset Tabular
33360 <lyxtabular version="3" rows="6" columns="2">
33361 <features tabularvalignment="middle">
33362 <column alignment="center" valignment="top" width="0">
33363 <column alignment="center" valignment="top" width="0">
33365 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33368 \begin_layout Plain Layout
33374 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33377 \begin_layout Plain Layout
33379 \begin_inset Note Note
33382 \begin_layout Plain Layout
33389 is only used as spacer.
33401 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33404 \begin_layout Plain Layout
33411 \begin_layout Plain Layout
33425 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33428 \begin_layout Plain Layout
33429 \begin_inset Formula $A\gr B$
33439 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33442 \begin_layout Plain Layout
33450 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33453 \begin_layout Plain Layout
33454 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
33464 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33467 \begin_layout Plain Layout
33471 \begin_inset Formula $\to$
33477 \begin_inset Formula $\to$
33488 \begin_layout Plain Layout
33502 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33505 \begin_layout Plain Layout
33506 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
33516 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33519 \begin_layout Plain Layout
33523 \begin_inset Formula $\to$
33534 \begin_layout Plain Layout
33548 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33551 \begin_layout Plain Layout
33552 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
33562 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33565 \begin_layout Plain Layout
33571 \begin_inset Formula $\to$
33582 \begin_layout Plain Layout
33596 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33599 \begin_layout Plain Layout
33600 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
33616 \begin_layout Subsection
33618 \begin_inset Index idx
33621 \begin_layout Plain Layout
33622 User-defined commands! Math macros
33628 \begin_inset Index idx
33631 \begin_layout Plain Layout
33640 \begin_layout Standard
33641 User-defined commands are especially convenient for complex expressions.
33642 When you are for example dealing in a document with quadratic equations,
33643 the same solution type occurs several times.
33644 The general form of a quadratic equation is
33645 \begin_inset Formula
33647 0=\lambda^{2}+p\lambda+q
33652 The general form of the solution is
33653 \begin_inset Formula
33655 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
33663 \begin_layout Standard
33664 To define a command for the solution formula where only the three parameters
33666 \begin_inset Formula $\lambda$
33670 \begin_inset Formula $p$
33674 \begin_inset Formula $q$
33677 need to be specified and the index of
33678 \begin_inset Formula $\lambda$
33681 can be given optionally, the LaTeX-preamble line is
33682 \begin_inset Newline newline
33698 \begin_inset Newline newline
33702 \begin_inset Phantom HPhantom
33705 \begin_layout Plain Layout
33719 frac{#3^{2}}{4}-#4}}
33722 \begin_layout Standard
33723 To create with this the solution formula, the command
33724 \begin_inset Newline newline
33734 \begin_inset Formula $\to$
33740 \begin_inset Formula $\to$
33747 is inserted to a formula
33752 \begin_layout Standard
33753 The definition of the new command is unintuitive because one has to know
33754 the schemes of all used LaTeX commands, e.
33755 \begin_inset space \thinspace{}
33759 \begin_inset space \space{}
33762 that a fraction is inserted in LaTeX as
33766 frac{numerator}{denominator}
33769 Furthermore one can easily forget a brace in the definition and cannot
33770 see in LyX what the new command is doing.
33771 To avoid these problems LyX offers the possibility to use math macros instead
33781 \begin_layout Standard
33782 A math macro is created by using the menu
33784 Insert\SpecialChar \menuseparator
33785 Math\SpecialChar \menuseparator
33788 or the toolbar button
33789 \begin_inset Graphics
33790 filename ../images/math-macro_newmacroname_newcommand.png
33796 The math macro toolbar appears together with the following box where the
33798 \begin_inset Newline newline
33802 \begin_inset space \hspace*{\fill}
33806 \begin_inset Graphics
33807 filename clipart/macrobox.png
33812 \begin_inset space \hspace*{\fill}
33816 \begin_inset Newline newline
33820 \begin_inset FormulaMacro
33821 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
33826 newmacroname is the default name of the macro that should be changed to
33827 something sensible.
33828 The wanted formula is inserted in the first blue box.
33829 An argument placeholder is inserted with the command
33836 \begin_inset space \thinspace{}
33840 \begin_inset space \space{}
33849 or by using the macro toolbar button
33850 \begin_inset Graphics
33851 filename ../images/math-macro-add-param.png
33857 Argument placeholders are displayed red.
33858 Maximum 9 arguments are possible.
33859 Optional arguments are created with the toolbar button
33860 \begin_inset Graphics
33861 filename ../images/math-macro-add-optional-param.png
33867 The first non-optional argument can be transformed to an optional one with
33869 \begin_inset Graphics
33870 filename ../images/math-macro-make-optional.png
33876 In the second blue box the appearance of the macro in LyX can be defined.
33877 Normally you want to see it as it is defined, so the box is kept empty.
33878 But when you have created a macro that needs lot of space on the screen,
33879 you can insert in the box for example
33880 \begin_inset Newline newline
33910 \begin_inset Newline newline
33915 For the macro only the arguments with the macro name in front of them will
33916 then be displayed in LyX, leading to a better overview.
33917 The formula appears in the output as defined in the first box.
33918 \begin_inset Newline newline
33921 The appearance of macros in formulas can furthermore be changed for single
33922 macros by setting the cursor in the macro and using the menu
33924 View\SpecialChar \menuseparator
33926 \begin_inset space ~
33930 \begin_inset space ~
33938 \begin_layout Standard
33939 To use a macro, the macro name is inserted as command to a formula, in our
33947 Our macro looks in LyX like this:
33948 \begin_inset Newline newline
33952 \begin_inset space \hspace*{\fill}
33956 \begin_inset Graphics
33957 filename clipart/macrouse.png
33962 \begin_inset space \hspace*{\fill}
33966 \begin_inset Newline newline
33969 Here is our macro example with the arguments
33970 \begin_inset Formula $x$
33974 \begin_inset Formula $\ln(x)$
33978 \begin_inset Formula $B$
33984 \begin_layout Standard
33985 \begin_inset Formula
33995 \begin_layout Standard
33996 LyX offers in the menu
33998 Tools\SpecialChar \menuseparator
33999 Preferences\SpecialChar \menuseparator
34000 Editing\SpecialChar \menuseparator
34003 different styles to edit macros.
34004 To find the style that suits you the most, choose a style and set the cursor
34005 in a macro formula to see the difference.
34008 \begin_layout Standard
34009 A math macro is transformed internally to a
34015 command when exporting the document.
34022 command is not placed in the LaTeX-preamble, therefore macros can only
34023 be used in formulas that are in the document below the macro definition
34027 \begin_layout Standard
34028 Math macros can also be directly be created from a
34035 When writing for example the command
34038 \begin_inset Newline newline
34047 xleftarrow[#2]{#1}}
34048 \begin_inset Newline newline
34053 in LyX as normal text, highlighting it completely and using then the shortcut
34058 , the command will be transformed to a math macro.
34059 Using this method you need to be careful that the
34065 command is typed correctly, otherwise you get a faulty macro leading to
34069 \begin_layout Standard
34070 Math macros currently yet have the problem that further formulas in macro
34071 definitions are handled wrongly.
34072 Therefore the example
34079 \begin_inset CommandInset ref
34081 reference "sub:The-Command-newcommand"
34085 cannot be created as macro.
34088 \begin_layout Standard
34089 When the cursor is in a macro definition box, you will see the macro toolbar
34093 \begin_layout Standard
34094 \begin_inset VSpace defskip
34100 \begin_layout Standard
34101 \begin_inset Graphics
34102 filename clipart/MacroToolbar.png
34107 \begin_inset Index idx
34110 \begin_layout Plain Layout
34119 \begin_layout Standard
34120 \begin_inset VSpace defskip
34126 \begin_layout Standard
34127 The macro toolbar contains from left to right the following buttons:
34130 \begin_layout Standard
34131 \begin_inset VSpace defskip
34137 \begin_layout Standard
34138 \begin_inset Tabular
34139 <lyxtabular version="3" rows="9" columns="2">
34140 <features islongtable="true" longtabularalignment="center">
34141 <column alignment="left" valignment="top" width="0">
34142 <column alignment="left" valignment="top" width="85col%">
34143 <row interlinespace="2.5mm">
34144 <cell alignment="center" valignment="top" usebox="none">
34147 \begin_layout Plain Layout
34148 \begin_inset Graphics
34149 filename ../images/math-macro-remove-param.png
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 Remove Last 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-add-param.png
34185 rotateOrigin center
34194 <cell alignment="center" valignment="top" usebox="none">
34197 \begin_layout Plain Layout
34200 Edit\SpecialChar \menuseparator
34201 Math\SpecialChar \menuseparator
34203 \begin_inset space ~
34206 Definition\SpecialChar \menuseparator
34213 <row interlinespace="2.5mm">
34214 <cell alignment="center" valignment="top" usebox="none">
34217 \begin_layout Plain Layout
34218 \begin_inset Graphics
34219 filename ../images/math-macro-make-optional.png
34220 rotateOrigin center
34229 <cell alignment="center" valignment="top" usebox="none">
34232 \begin_layout Plain Layout
34235 Edit\SpecialChar \menuseparator
34236 Math\SpecialChar \menuseparator
34238 \begin_inset space ~
34241 Definition\SpecialChar \menuseparator
34242 Make First Non-Optional into
34243 \begin_inset Newline newline
34247 \begin_inset Phantom HPhantom
34250 \begin_layout Plain Layout
34253 Edit\SpecialChar \menuseparator
34254 Math\SpecialChar \menuseparator
34256 \begin_inset space ~
34259 Definition\SpecialChar \menuseparator
34271 <row interlinespace="2.5mm">
34272 <cell alignment="center" valignment="top" usebox="none">
34275 \begin_layout Plain Layout
34276 \begin_inset Graphics
34277 filename ../images/math-macro-make-nonoptional.png
34278 rotateOrigin center
34287 <cell alignment="center" valignment="top" usebox="none">
34290 \begin_layout Plain Layout
34293 Edit\SpecialChar \menuseparator
34294 Math\SpecialChar \menuseparator
34296 \begin_inset space ~
34299 Definition\SpecialChar \menuseparator
34300 Make Last Optional into
34301 \begin_inset Newline newline
34305 \begin_inset Phantom HPhantom
34308 \begin_layout Plain Layout
34311 Edit\SpecialChar \menuseparator
34312 Math\SpecialChar \menuseparator
34314 \begin_inset space ~
34317 Definition\SpecialChar \menuseparator
34323 Non-Optional Argument
34329 <row interlinespace="2.5mm">
34330 <cell alignment="center" valignment="top" usebox="none">
34333 \begin_layout Plain Layout
34334 \begin_inset Graphics
34335 filename ../images/math-macro-remove-optional-param.png
34336 rotateOrigin center
34345 <cell alignment="center" valignment="top" usebox="none">
34348 \begin_layout Plain Layout
34351 Edit\SpecialChar \menuseparator
34352 Math\SpecialChar \menuseparator
34354 \begin_inset space ~
34357 Definition\SpecialChar \menuseparator
34358 Remove Optional Argument
34364 <row interlinespace="2.5mm">
34365 <cell alignment="center" valignment="top" usebox="none">
34368 \begin_layout Plain Layout
34369 \begin_inset Graphics
34370 filename ../images/math-macro-add-optional-param.png
34371 rotateOrigin center
34380 <cell alignment="center" valignment="top" usebox="none">
34383 \begin_layout Plain Layout
34386 Edit\SpecialChar \menuseparator
34387 Math\SpecialChar \menuseparator
34389 \begin_inset space ~
34392 Definition\SpecialChar \menuseparator
34393 Insert Optional Argument
34399 <row interlinespace="2.5mm">
34400 <cell alignment="center" valignment="top" usebox="none">
34403 \begin_layout Plain Layout
34404 \begin_inset Graphics
34405 filename ../images/math-macro-remove-greedy-param.png
34406 rotateOrigin center
34415 <cell alignment="center" valignment="top" usebox="none">
34418 \begin_layout Plain Layout
34421 Edit\SpecialChar \menuseparator
34422 Math\SpecialChar \menuseparator
34424 \begin_inset space ~
34427 Definition\SpecialChar \menuseparator
34428 Remove Last Argument
34429 \begin_inset Newline newline
34433 \begin_inset Phantom HPhantom
34436 \begin_layout Plain Layout
34439 Edit\SpecialChar \menuseparator
34440 Math\SpecialChar \menuseparator
34442 \begin_inset space ~
34445 Definition\SpecialChar \menuseparator
34451 Spitting Out To The Right
34457 <row interlinespace="2.5mm">
34458 <cell alignment="center" valignment="top" usebox="none">
34461 \begin_layout Plain Layout
34462 \begin_inset Graphics
34463 filename ../images/math-macro-append-greedy-param.png
34464 rotateOrigin center
34473 <cell alignment="center" valignment="top" usebox="none">
34476 \begin_layout Plain Layout
34479 Edit\SpecialChar \menuseparator
34480 Math\SpecialChar \menuseparator
34482 \begin_inset space ~
34485 Definition\SpecialChar \menuseparator
34487 \begin_inset Newline newline
34491 \begin_inset Phantom HPhantom
34494 \begin_layout Plain Layout
34497 Edit\SpecialChar \menuseparator
34498 Math\SpecialChar \menuseparator
34500 \begin_inset space ~
34503 Definition\SpecialChar \menuseparator
34509 Eating From The Right
34515 <row interlinespace="2.5mm">
34516 <cell alignment="center" valignment="top" usebox="none">
34519 \begin_layout Plain Layout
34520 \begin_inset Graphics
34521 filename ../images/math-macro-add-greedy-optional-param.png
34522 rotateOrigin center
34531 <cell alignment="center" valignment="top" usebox="none">
34534 \begin_layout Plain Layout
34537 Edit\SpecialChar \menuseparator
34538 Math\SpecialChar \menuseparator
34540 \begin_inset space ~
34543 Definition\SpecialChar \menuseparator
34544 Append Optional Argument
34545 \begin_inset Newline newline
34549 \begin_inset Phantom HPhantom
34552 \begin_layout Plain Layout
34555 Edit\SpecialChar \menuseparator
34556 Math\SpecialChar \menuseparator
34558 \begin_inset space ~
34561 Definition\SpecialChar \menuseparator
34567 Eating From The Right
34580 \begin_layout Section
34581 Computer Algebra Systems
34584 \begin_layout Standard
34585 LyX offers the exchange between mathematical expressions written in LyX's
34586 math editor and external applications or user defined scripts.
34587 Currently supported applications are
34604 Note that the set of supported mathematical constructs is limited only
34605 to very simple cases.
34608 \begin_layout Subsection
34612 \begin_layout Standard
34613 Write some expression in a formula, go to the
34615 Edit\SpecialChar \menuseparator
34616 Math\SpecialChar \menuseparator
34617 Use Computer Algebra System
34619 menu and choose the application you have installed on the computer.
34620 After that the result of computation should show on the right side of the
34621 expression together with the
34622 \begin_inset Quotes eld
34626 \begin_inset Quotes erd
34632 \begin_layout Standard
34633 Here are few simple examples (with results from
34637 ) to show what kind of computations can be performed:
34640 \begin_layout Itemize
34641 \begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$
34647 \begin_layout Itemize
34648 \begin_inset Formula $\frac{37.0}{3}=12.33333333333333$
34654 \begin_layout Itemize
34655 \begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$
34661 \begin_layout Itemize
34662 \begin_inset Formula $\det\left[\begin{array}{ccc}
34666 \end{array}\right]=-56$
34672 \begin_layout Itemize
34673 \begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$
34679 \begin_layout Subsection
34683 \begin_layout Standard
34684 Currently there is no keyboard shortcut for calling the algebra applications.
34685 One can easily bind a shortcut to the
34689 LyX function (see the
34697 \begin_inset space \thinspace{}
34701 \begin_inset space ~
34708 key inside the math editor.
34713 one would use this shortcut definition command:
34716 \begin_layout Standard
34719 command-alternatives break-paragraph;math-extern maxima
34722 \begin_layout Standard
34723 \begin_inset Newpage newpage
34729 \begin_layout Section
34731 \begin_inset Index idx
34734 \begin_layout Plain Layout
34743 \begin_layout Subsection
34745 \begin_inset Index idx
34748 \begin_layout Plain Layout
34757 \begin_layout Standard
34758 Negative numbers often look ugly in formulas because the minus sign before
34759 the number is set with the same length as the minus operator sign.
34760 When writing the negative number in normal text, the minus sign appears
34764 \begin_layout Standard
34765 Thus, the problem disappears when converting the minus sign to mathematical
34769 \begin_layout Standard
34770 An example to visualize the problem:
34773 \begin_layout Standard
34775 \begin_inset Tabular
34776 <lyxtabular version="3" rows="3" columns="2">
34777 <features tabularvalignment="middle">
34778 <column alignment="right" valignment="top" width="0">
34779 <column alignment="left" valignment="top" width="0">
34781 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34784 \begin_layout Plain Layout
34790 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
34793 \begin_layout Plain Layout
34801 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34804 \begin_layout Plain Layout
34810 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34813 \begin_layout Plain Layout
34814 \begin_inset Formula $x=-2$
34824 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34827 \begin_layout Plain Layout
34833 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34836 \begin_layout Plain Layout
34837 \begin_inset Formula $x=\textrm{-}2$
34853 \begin_layout Subsection
34854 Comma as decimal Separator
34855 \begin_inset Index idx
34858 \begin_layout Plain Layout
34867 \begin_layout Standard
34868 In LaTeX a comma inside a formula is used, according to the English convention,
34869 as number group separator.
34870 So there will be space added behind all commas in formulas.
34873 \begin_layout Standard
34874 To avoid this, the comma is highlighted and changed to mathematical text
34884 \begin_layout Standard
34885 To use all formula commas in the document as decimal separator, the file
34894 \begin_layout Plain Layout
34899 is part of the LaTeX-package
34904 \begin_inset Index idx
34907 \begin_layout Plain Layout
34912 \begin_layout Plain Layout
34932 \begin_inset Index idx
34935 \begin_layout Plain Layout
34941 is loaded with the LaTeX-preamble line
34944 \begin_layout Standard
34952 \begin_layout Subsection
34954 \begin_inset CommandInset label
34956 name "sub:Physical-Vectors"
34961 \begin_inset Index idx
34964 \begin_layout Plain Layout
34973 \begin_layout Standard
34974 Predefined vectors are offered by the LaTeX-package
34979 \begin_inset Index idx
34982 \begin_layout Plain Layout
34988 that is loaded with the LaTeX-preamble line
34991 \begin_layout Standard
34999 \begin_layout Standard
35003 \begin_layout Plain Layout
35013 \begin_inset Note Note
35016 \begin_layout Plain Layout
35017 The following table will only be displayed when the LaTeX-package
35029 \begin_layout Standard
35030 The following commands are defined:
35033 \begin_layout Standard
35035 \begin_inset Tabular
35036 <lyxtabular version="3" rows="4" columns="2">
35037 <features tabularvalignment="middle">
35038 <column alignment="center" valignment="top" width="0">
35039 <column alignment="center" valignment="top" width="0">
35041 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35044 \begin_layout Plain Layout
35050 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35053 \begin_layout Plain Layout
35061 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35064 \begin_layout Plain Layout
35074 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35077 \begin_layout Plain Layout
35078 \begin_inset Formula $\Bra{\psi}$
35088 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35091 \begin_layout Plain Layout
35101 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35104 \begin_layout Plain Layout
35105 \begin_inset Formula $\Ket{\psi}$
35115 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35118 \begin_layout Plain Layout
35130 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35133 \begin_layout Plain Layout
35134 \begin_inset Formula $\Braket{\psi|\phi}$
35150 \begin_layout Standard
35157 assures that all vertical bars are set in the size of the surrounding brackets:
35158 \begin_inset Formula
35160 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}
35169 \begin_layout Plain Layout
35179 \begin_inset Note Note
35182 \begin_layout Plain Layout
35183 The following will be displayed when the LaTeX-package
35195 \begin_layout Standard
35196 You need to install the LaTeX-package
35200 to see the rest of this subsection in the output.
35203 \begin_layout Standard
35207 \begin_layout Plain Layout
35219 \begin_layout Standard
35226 can also be achieved using the command
35232 , that is described in
35233 \begin_inset CommandInset ref
35235 reference "sub:Automatic-Bracket-Size"
35242 \begin_layout Subsection
35243 Self-defined Fractions
35244 \begin_inset CommandInset label
35246 name "sub:Self-defined-Fractions"
35251 \begin_inset Index idx
35254 \begin_layout Plain Layout
35255 Fractions ! self-defined
35263 \begin_layout Standard
35264 To define custom commands for fractions, the command
35271 \begin_inset Index idx
35274 \begin_layout Plain Layout
35282 is used in the following scheme:
35285 \begin_layout Standard
35298 bracket}{fraction bar thickness}{style}
35299 \begin_inset Newline newline
35303 \begin_inset Phantom HPhantom
35306 \begin_layout Plain Layout
35316 {numerator}{denominator}
35319 \begin_layout Standard
35320 The style is a number in the range of 0
35321 \begin_inset space \thinspace{}
35325 \begin_inset space \thinspace{}
35331 \begin_layout Standard
35333 \begin_inset Tabular
35334 <lyxtabular version="3" rows="5" columns="2">
35335 <features tabularvalignment="middle">
35336 <column alignment="center" valignment="top" width="0">
35337 <column alignment="center" valignment="top" width="0">
35339 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35342 \begin_layout Plain Layout
35348 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35351 \begin_layout Plain Layout
35359 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35362 \begin_layout Plain Layout
35368 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35371 \begin_layout Plain Layout
35372 display style formula
35379 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35382 \begin_layout Plain Layout
35388 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35391 \begin_layout Plain Layout
35399 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35402 \begin_layout Plain Layout
35408 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35411 \begin_layout Plain Layout
35419 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35422 \begin_layout Plain Layout
35428 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35431 \begin_layout Plain Layout
35445 \begin_layout Standard
35446 When no style is given, the size is adjusted to the surrounding environment
35447 like for the command
35456 \begin_layout Standard
35457 When no fraction bar thickness is given, the predefined value of 0.4
35458 \begin_inset space \thinspace{}
35464 \begin_layout Standard
35465 \begin_inset VSpace medskip
35468 For example, the commands
35481 \begin_inset CommandInset ref
35483 reference "sub:Fractions"
35487 are defined with the commands
35490 \begin_layout Standard
35499 genfrac{}{}{}{0}{#1}{#2}}
35502 \begin_layout Standard
35506 \begin_layout Standard
35515 genfrac{(}{)}{0pt}{1}{#1}{#2}}
35518 \begin_layout Standard
35519 \begin_inset VSpace medskip
35522 To define a fraction where the fraction bar thickness can be given as optional
35523 argument, the following line is inserted to the LaTeX-preamble:
35526 \begin_layout Standard
35535 genfrac{}{}{#1}{}{#2}{#3}}
35538 \begin_layout Standard
35540 \begin_inset Formula
35542 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
35543 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
35548 As one can see, the distance of the numerator and the denominator to the
35549 fraction bar is round about three times the bar thickness.
35552 \begin_layout Subsection
35554 \begin_inset Index idx
35557 \begin_layout Plain Layout
35566 \begin_layout Standard
35567 To cancel formulas or formula parts, the LaTeX-package
35572 \begin_inset Index idx
35575 \begin_layout Plain Layout
35581 has to be loaded with the LaTeX-preamble line
35584 \begin_layout Standard
35589 usepackage[samesize]{cancel}
35592 \begin_layout Standard
35596 \begin_layout Plain Layout
35606 \begin_inset Note Note
35609 \begin_layout Plain Layout
35610 The following table will only be displayed when the LaTeX-package
35622 \begin_layout Standard
35623 There are four ways to cancel formulas:
35626 \begin_layout Standard
35628 \begin_inset Tabular
35629 <lyxtabular version="3" rows="5" columns="2">
35630 <features tabularvalignment="middle">
35631 <column alignment="center" valignment="top" width="0">
35632 <column alignment="center" valignment="top" width="0">
35634 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35637 \begin_layout Plain Layout
35643 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35646 \begin_layout Plain Layout
35648 \begin_inset Note Note
35651 \begin_layout Plain Layout
35658 are used here as spacer.
35670 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35673 \begin_layout Plain Layout
35682 \begin_layout Plain Layout
35696 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35699 \begin_layout Plain Layout
35700 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
35710 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35713 \begin_layout Plain Layout
35722 \begin_layout Plain Layout
35736 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35739 \begin_layout Plain Layout
35740 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
35750 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35753 \begin_layout Plain Layout
35762 \begin_layout Plain Layout
35776 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35779 \begin_layout Plain Layout
35780 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
35790 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35793 \begin_layout Plain Layout
35797 \begin_inset Formula $\to$
35808 \begin_layout Plain Layout
35822 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35825 \begin_layout Plain Layout
35826 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
35842 \begin_layout Standard
35849 is especially suitable to visualize the reduction of fractions within formulas:
35850 \begin_inset Formula
35852 \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}}}
35860 \begin_layout Standard
35864 \begin_layout Plain Layout
35874 \begin_inset Note Note
35877 \begin_layout Plain Layout
35878 The following will be displayed when the LaTeX-package
35890 \begin_layout Standard
35891 You need to install the LaTeX-package
35895 to see the rest of this subsection in the output.
35898 \begin_layout Standard
35902 \begin_layout Plain Layout
35914 \begin_layout Subsection
35915 Formulas in Section Headings
35916 \begin_inset CommandInset label
35918 name "sub:Formulas-in-Section"
35923 \begin_inset Index idx
35926 \begin_layout Plain Layout
35927 Formula ! in section headings
35935 \begin_layout Standard
35936 When formulas are used in section headings, the following has to be taken
35940 \begin_layout Standard
35941 \begin_inset Note Greyedout
35944 \begin_layout Plain Layout
35950 \begin_inset Index idx
35953 \begin_layout Plain Layout
35954 Packages ! hyperref
35959 support is enabled in the document settings dialog under
35962 \begin_inset space ~
35967 , PDF-bookmarks are created for every section heading in the table of contents.
35968 If a section heading contains formulas, they are incorrectly displayed
35969 in the bookmark text, because formulas in bookmarks infringe the PDF convention
35978 \begin_layout Standard
35979 Both problems can be solved by inserting at the end of the section heading
35980 a short title with the menu
35982 Insert\SpecialChar \menuseparator
35984 \begin_inset space ~
35990 Short titles are used as alternative for multiline section headings to
35991 keep the table of contents clearly arranged.
35992 Only the short title appears in the table of contents and therefore also
35993 in the PDF-bookmark.
35996 \begin_layout Standard
35997 When formulas should be used in the table of contents but
36001 is used, one can use the following command in TeX-mode:
36004 \begin_layout Standard
36009 texorpdfstring{part}{alternative}
36010 \begin_inset Index idx
36013 \begin_layout Plain Layout
36024 \begin_layout Standard
36025 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
36026 This can be characters, formulas, footnotes, but also cross-references.
36027 The alternative is used instead of the part for the bookmark.
36030 \begin_layout Standard
36031 Here are two example headings:
36032 \begin_inset VSpace -3mm
36039 \begin_layout Plain Layout
36051 \begin_layout Subsubsection
36052 Heading without formula in table of contents
36053 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
36057 \begin_inset Argument
36060 \begin_layout Plain Layout
36061 Heading without formula in table of contents
36069 \begin_layout Subsubsection
36070 Heading with formula in table of contents
36074 \begin_layout Plain Layout
36084 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
36091 \begin_layout Plain Layout
36101 \begin_layout Standard
36105 \begin_layout Plain Layout
36114 In the first heading a short title was used, in the second one
36123 \begin_layout Standard
36124 To get the same formatting as for the other headings, the complete heading
36133 \begin_layout Plain Layout
36135 \begin_inset CommandInset ref
36137 reference "sub:Bold-Formulas"
36149 \begin_layout Subsection
36150 Formulas in multi-column Text
36151 \begin_inset Index idx
36154 \begin_layout Plain Layout
36155 Formula ! in multi-column text
36163 \begin_layout Standard
36164 Formulas in multi-column text are often too wide to fit into a column and
36165 thus need to be set over the whole page width.
36166 This is done by using the LaTeX-package
36174 \begin_layout Plain Layout
36179 is part of every LaTeX standard installation.
36185 \begin_inset Index idx
36188 \begin_layout Plain Layout
36189 Packages ! multicol
36194 , that is loaded with the LaTeX-preamble line
36197 \begin_layout Standard
36202 usepackage{multicol}
36205 \begin_layout Standard
36206 \begin_inset Note Greyedout
36209 \begin_layout Plain Layout
36210 Note herby that the setting
36213 \begin_inset space ~
36220 Document\SpecialChar \menuseparator
36226 \begin_inset space ~
36246 \begin_layout Standard
36247 Before the multi-column text the command
36250 \begin_layout Standard
36255 begin{multicols}{column number}
36258 \begin_layout Standard
36259 is written in TeX-mode.
36260 The column number is a number in the range of 2
36261 \begin_inset space \thinspace{}
36265 \begin_inset space \thinspace{}
36269 Before the formula the multi-column text is ended by inserting the command
36272 \begin_layout Standard
36280 \begin_layout Standard
36284 \begin_layout Standard
36285 Due to the command some space is automatically added before the formula.
36287 \begin_inset space \thinspace{}
36290 mm vertical space is inserted before the formula.
36291 When the formula style
36297 \begin_layout Plain Layout
36299 \begin_inset CommandInset ref
36301 reference "sec:Formula-Styles"
36313 \begin_inset space \thinspace{}
36316 mm space is inserted instead.
36319 \begin_layout Standard
36320 As example a multi-column text with a displayed formula:
36323 \begin_layout Standard
36329 \begin_layout Plain Layout
36333 begin{multicols}{2}
36338 Das Spektrum wird fouriertransformiert.
36339 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
36340 , Lösungsmittel) zu trennen.
36341 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
36342 nun das Aussehen des Ausgangssignals.
36343 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
36344 über alle Phasen integrieren muss.
36346 \begin_inset Formula $S$
36349 unser normiertes Ausgangssignal und
36350 \begin_inset Formula $P$
36353 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
36357 \begin_layout Plain Layout
36367 \begin_inset VSpace -6mm
36371 \begin_inset Formula
36373 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
36382 \begin_layout Plain Layout
36386 begin{multicols}{2}
36392 \begin_inset Formula $S_{0}$
36395 das Signal ohne Gradient ist und die Normierungsbedingung
36396 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
36400 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
36402 \begin_inset Formula $\nicefrac{\pi}{2}$
36406 \begin_inset space \thinspace{}
36409 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
36410 das Signal zusätzlich abschwächt.
36411 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
36413 \begin_inset Formula $T_{2}$
36419 \begin_layout Standard
36425 \begin_layout Plain Layout
36437 \begin_layout Subsection
36438 Formulas with Description of Variables
36439 \begin_inset Index idx
36442 \begin_layout Plain Layout
36443 Formula ! with description of variables
36451 \begin_layout Standard
36452 To describe variables within a formula, like in formula
36453 \begin_inset CommandInset ref
36455 reference "eq:within"
36464 \begin_inset Formula $n$
36468 \begin_inset space ~
36471 matrix is used with left aligned columns for the
36472 \begin_inset Formula $n$
36479 \begin_layout Plain Layout
36481 \begin_inset CommandInset ref
36483 reference "sec:Matrices"
36492 To set the description in a smaller size, before the matrix e.
36493 \begin_inset space \thinspace{}
36497 \begin_inset space \space{}
36510 \begin_layout Plain Layout
36512 \begin_inset CommandInset ref
36514 reference "sub:Font-Sizes"
36526 \begin_layout Standard
36527 When the formula style
36533 \begin_layout Plain Layout
36535 \begin_inset CommandInset ref
36537 reference "sec:Formula-Styles"
36558 \begin_layout Plain Layout
36565 only works in formulas with the style
36570 \begin_inset CommandInset ref
36572 reference "sub:Variable-Space"
36581 is inserted before and after the matrix to have the same separation of
36582 the matrix from the equation and the side margin.
36585 \begin_layout Standard
36586 When the formula style
36590 is used, the method described in
36591 \begin_inset CommandInset ref
36593 reference "sub:Flalign-Environment"
36597 is used to indent formulas.
36599 \begin_inset CommandInset ref
36601 reference "eq:within"
36605 consists of five columns whereas in the first two columns contain the equation,
36606 the third the matrix and the last one an empty TeX-brace.
36607 \begin_inset Formula
36609 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
36610 \rho & \textrm{density}\\
36611 V & \textrm{volume}\\
36612 g & \textrm{gravitational acceleration}
36613 \end{array} & & {}\label{eq:within}
36621 \begin_layout Subsection
36622 Upright small Greek Letters
36623 \begin_inset CommandInset label
36625 name "sub:Upright-small-Greek"
36630 \begin_inset Index idx
36633 \begin_layout Plain Layout
36634 Greek letters ! upright
36642 \begin_layout Standard
36643 Most of the math fonts only provide italic small Greek letters.
36644 But for symbols of elementary particles like pions and neutrinos, upright
36645 Greek letters are needed.
36654 \begin_layout Plain Layout
36659 is part of the LaTeX-package
36664 \begin_inset Index idx
36667 \begin_layout Plain Layout
36672 \begin_layout Plain Layout
36692 \begin_inset Index idx
36695 \begin_layout Plain Layout
36701 that is loaded with the LaTeX-preamble line
36704 \begin_layout Standard
36709 usepackage{upgreek}
36712 \begin_layout Standard
36718 \begin_layout Plain Layout
36728 \begin_inset Note Note
36731 \begin_layout Plain Layout
36732 The following table will only be displayed when the LaTeX-package
36741 They are created when the command for a small Greek letters is started
36747 For example the command
36754 \begin_inset Formula $\uptau$
36760 \begin_layout Standard
36761 With these commands reactions of elementary particles can be typeset:
36762 \begin_inset Formula
36764 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
36772 \begin_layout Standard
36773 The upright letters are more bold and wider than the italic ones.
36774 They should therefore not be used for units like
36775 \begin_inset Quotes eld
36779 \begin_inset Quotes erd
36785 \begin_layout Standard
36789 \begin_layout Plain Layout
36799 \begin_inset Note Note
36802 \begin_layout Plain Layout
36803 The following will be displayed when the LaTeX-package
36815 \begin_layout Standard
36816 You need to install the LaTeX-package
36820 to see the rest of this subsection in the output.
36823 \begin_layout Standard
36827 \begin_layout Plain Layout
36839 \begin_layout Subsection
36840 Text Characters in Formulas
36841 \begin_inset CommandInset label
36843 name "sub:Text-Characters-in"
36848 \begin_inset Index idx
36851 \begin_layout Plain Layout
36860 \begin_layout Standard
36861 In some cases you might want to insert text characters directly into formulas.
36862 When for example the centered dot · is often used in formulas like
36863 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
36866 , one would have to insert the command
36876 \begin_layout Plain Layout
36878 \begin_inset CommandInset ref
36880 reference "sub:Binary-Operators"
36889 all the time, because this character is defined in all encodings as text
36891 But the encoding can be changed by this LaTeX-preamble line:
36894 \begin_layout Standard
36899 Declare Inputtext{183}{
36909 f\SpecialChar \textcompwordmark{}
36913 \begin_layout Standard
36914 The character encoding (menu
36916 Document\SpecialChar \menuseparator
36917 Settings\SpecialChar \menuseparator
36920 ) specifies what character appears when a keyboard key is pressed.
36921 When the key for the character '·' is pressed, internally the command
36928 But this command is not available in a formula so that you would get LaTeX-erro
36930 With the changed encoding the right command is chosen automatically, depending
36931 on if the character was inserted into a formula or not.
36934 \begin_layout Standard
36935 The encoding of several characters is saved in definition files.
36936 Fore example the encoding
36940 is defined in the file
36944 that is in the installation folder of LaTeX.
36945 Encodings should only be changed via the LaTeX-preamble and not in the
36947 Otherwise own documents could not be edited by other LyX users working
36948 on other computers.
36951 \begin_layout Standard
36952 \begin_inset VSpace medskip
36955 Besides the centered dot, in this document the degree sign ° is defined
36956 with the following LaTeX-preamble line so that it can directly be inserted
36960 \begin_layout Standard
36965 DeclareInputtext{176}{
36975 f\SpecialChar \textcompwordmark{}
36979 \begin_layout Standard
36980 \begin_inset Newpage newpage
36986 \begin_layout Section
36989 \begin_inset Index idx
36992 \begin_layout Plain Layout
37001 \begin_layout Standard
37002 This section is a summary of the most important typographic rules, listed
37007 \begin_layout Plain Layout
37008 This collection was partly taken from the German semi-official dictionary
37010 \begin_inset Quotes eld
37014 \begin_inset Quotes erd
37018 \begin_inset CommandInset citation
37024 that lists some of the ISO rules.
37025 More rules are listed in
37026 \begin_inset CommandInset citation
37040 \begin_layout Itemize
37049 \begin_layout Plain Layout
37050 done with font styles, see
37051 \begin_inset CommandInset ref
37053 reference "sub:Font-Styles"
37062 , no matter if they appear in italic text: 30
37063 \begin_inset space \thinspace{}
37067 \begin_inset Newline newline
37070 Between the value and the unit is the smallest space, see
37071 \begin_inset CommandInset ref
37073 reference "sub:Predefined-Space"
37078 \begin_inset Newline newline
37081 This convention is automatically fulfilled when the command
37088 When it is entered to a formula, two boxes appear.
37089 In the first one the value is inserted, in the second one the unit, and
37091 \begin_inset Formula $\unit[30]{km/h}$
37095 \begin_inset space \thinspace{}
37105 is not a real LaTeX command but the command
37111 , therefore you cannot use it in TeX code.
37114 \begin_layout Itemize
37115 Percent and perthousand signs are set like physical units:
37116 \begin_inset Newline newline
37120 \begin_inset space \thinspace{}
37126 \begin_layout Itemize
37127 The degree sign follows directly on the value: 15°, but not when it is used
37129 \begin_inset space \thinspace{}
37135 \begin_layout Itemize
37136 In numbers with more than four digits the smallest space is inserted before
37137 every third digit to group them:
37147 \begin_inset space \thinspace{}
37151 \begin_inset space \thinspace{}
37157 \begin_layout Itemize
37158 For dimensions like 120×90×40
37159 \begin_inset space \thinspace{}
37162 cm the multiplication sign
37163 \begin_inset Quotes eld
37167 \begin_inset Quotes erd
37171 It is available either via the command
37179 Insert\SpecialChar \menuseparator
37180 Special Character\SpecialChar \menuseparator
37186 \begin_layout Itemize
37187 Functions with names consisting of several letters are set upright to avoid
37189 \begin_inset CommandInset ref
37191 reference "sub:Predefined-Functions"
37198 \begin_layout Itemize
37199 Indices consisting of several letters, are set upright:
37200 \begin_inset Formula $E_{\mathrm{kin}}$
37204 \begin_inset Newline newline
37207 Components of matrices are set italic:
37208 \begin_inset Formula $\hat{H}_{kl}$
37214 \begin_layout Itemize
37215 The differentiation/integration operator 'd', the Euler's number 'e' and
37216 the imaginary unit 'i' should be set upright, to avoid mixing them up with
37220 \begin_layout Itemize
37221 The character that denotes a
37225 transformation is inserted either by the command
37233 \begin_layout Plain Layout
37246 Insert\SpecialChar \menuseparator
37247 Special Character\SpecialChar \menuseparator
37248 Symbols\SpecialChar \menuseparator
37250 \begin_inset space ~
37256 \begin_inset Formula $\mathscr{F}$
37262 \begin_layout Standard
37263 \begin_inset Newpage newpage
37269 \begin_layout Section
37271 \begin_inset Index idx
37274 \begin_layout Plain Layout
37283 \begin_layout Standard
37284 Some characters and symbols can be created with several commands.
37285 Here is a list of the synonym commands:
37288 \begin_layout Standard
37289 \begin_inset VSpace bigskip
37293 \begin_inset space \hfill{}
37297 \begin_inset Tabular
37298 <lyxtabular version="3" rows="12" columns="2">
37299 <features tabularvalignment="middle">
37300 <column alignment="center" valignment="top" width="0pt">
37301 <column alignment="center" valignment="top" width="0pt">
37303 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37306 \begin_layout Plain Layout
37312 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37315 \begin_layout Plain Layout
37317 \begin_inset Note Note
37320 \begin_layout Plain Layout
37327 is only used as spacer.
37339 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37342 \begin_layout Plain Layout
37350 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37353 \begin_layout Plain Layout
37357 \begin_layout Plain Layout
37370 \begin_layout Plain Layout
37384 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37387 \begin_layout Plain Layout
37395 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37398 \begin_layout Plain Layout
37408 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37411 \begin_layout Plain Layout
37419 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37422 \begin_layout Plain Layout
37432 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37435 \begin_layout Plain Layout
37443 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37446 \begin_layout Plain Layout
37454 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37457 \begin_layout Plain Layout
37465 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37468 \begin_layout Plain Layout
37476 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37479 \begin_layout Plain Layout
37487 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37490 \begin_layout Plain Layout
37500 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37503 \begin_layout Plain Layout
37511 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37514 \begin_layout Plain Layout
37524 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37527 \begin_layout Plain Layout
37535 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37538 \begin_layout Plain Layout
37548 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37551 \begin_layout Plain Layout
37559 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37562 \begin_layout Plain Layout
37572 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37575 \begin_layout Plain Layout
37583 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37586 \begin_layout Plain Layout
37594 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37597 \begin_layout Plain Layout
37605 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37608 \begin_layout Plain Layout
37620 \begin_inset space \hfill{}
37624 \begin_inset Tabular
37625 <lyxtabular version="3" rows="12" columns="2">
37626 <features tabularvalignment="middle">
37627 <column alignment="center" valignment="top" width="0pt">
37628 <column alignment="center" valignment="top" width="0pt">
37630 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37633 \begin_layout Plain Layout
37639 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37642 \begin_layout Plain Layout
37650 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37653 \begin_layout Plain Layout
37661 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37664 \begin_layout Plain Layout
37676 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37679 \begin_layout Plain Layout
37687 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37690 \begin_layout Plain Layout
37700 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37703 \begin_layout Plain Layout
37711 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37714 \begin_layout Plain Layout
37724 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37727 \begin_layout Plain Layout
37735 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37738 \begin_layout Plain Layout
37746 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37749 \begin_layout Plain Layout
37757 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37760 \begin_layout Plain Layout
37768 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37771 \begin_layout Plain Layout
37779 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37782 \begin_layout Plain Layout
37792 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37795 \begin_layout Plain Layout
37803 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37806 \begin_layout Plain Layout
37816 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37819 \begin_layout Plain Layout
37827 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37830 \begin_layout Plain Layout
37840 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37843 \begin_layout Plain Layout
37851 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37854 \begin_layout Plain Layout
37864 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37867 \begin_layout Plain Layout
37875 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37878 \begin_layout Plain Layout
37888 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37891 \begin_layout Plain Layout
37899 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37902 \begin_layout Plain Layout
37916 \begin_inset space \hfill{}
37922 \begin_layout Standard
37923 \begin_inset Newpage newpage
37929 \begin_layout Bibliography
37930 \labelwidthstring References
37931 \begin_inset CommandInset bibitem
37932 LatexCommand bibitem
37944 The LaTeX Companion
37947 Addison Wesley, 2004
37950 \begin_layout Bibliography
37951 \labelwidthstring References
37952 \begin_inset CommandInset bibitem
37953 LatexCommand bibitem
37959 \begin_inset CommandInset href
37962 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
37966 of LaTeX's math abilities
37969 \begin_layout Bibliography
37970 \labelwidthstring References
37971 \begin_inset CommandInset bibitem
37972 LatexCommand bibitem
37978 \begin_inset CommandInset href
37981 target "ftp://ftp.ams.org/pub/tex/doc/amsmath/amsldoc.pdf"
37989 \begin_layout Plain Layout
38001 \begin_layout Bibliography
38002 \labelwidthstring References
38003 \begin_inset CommandInset bibitem
38004 LatexCommand bibitem
38010 \begin_inset CommandInset href
38013 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
38017 of all symbols available with LaTeX-packages
38020 \begin_layout Bibliography
38021 \labelwidthstring References
38022 \begin_inset CommandInset bibitem
38023 LatexCommand bibitem
38029 \begin_inset CommandInset href
38031 name "Documentation"
38032 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
38036 of the LaTeX-package
38041 \begin_inset Index idx
38044 \begin_layout Plain Layout
38045 Packages ! hyperref
38053 \begin_layout Bibliography
38054 \labelwidthstring References
38055 \begin_inset CommandInset bibitem
38056 LatexCommand bibitem
38062 \begin_inset CommandInset href
38064 name "Documentation"
38065 target "http://www.ctan.org/tex-archive/macros/latex/contrib/mhchem/mhchem.pdf"
38069 of the LaTeX-package
38074 \begin_inset Index idx
38077 \begin_layout Plain Layout
38086 \begin_layout Bibliography
38087 \labelwidthstring References
38088 \begin_inset CommandInset bibitem
38089 LatexCommand bibitem
38095 \begin_inset CommandInset href
38098 target "http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf"
38109 \begin_inset CommandInset ref
38111 reference "sub:Operator-Limits"
38116 \begin_inset Index idx
38119 \begin_layout Plain Layout
38130 \begin_layout Bibliography
38131 \labelwidthstring References
38132 \begin_inset CommandInset bibitem
38133 LatexCommand bibitem
38144 Auflage, Duden 2001
38147 \begin_layout Bibliography
38148 \labelwidthstring References
38149 \begin_inset CommandInset bibitem
38150 LatexCommand bibitem
38156 \begin_inset CommandInset href
38159 target "http://physics.nist.gov/Document/checklist.pdf"
38163 for reviewing manuscripts
38166 \begin_layout Standard
38167 \begin_inset CommandInset index_print
38168 LatexCommand printindex