1 #LyX 2.0 created this file. For more info see http://www.lyx.org/
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7 % DO NOT ALTER THIS PREAMBLE!!!
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9 % This preamble is designed to ensure that the file prints
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10 % out as advertised. If you mess with this preamble,
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11 % parts of this document may not print out as expected. If you
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12 % have problems LaTeXing this file, please contact
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13 % the documentation team
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14 % email: lyx-docs@lists.lyx.org
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16 % if pdflatex is used
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20 % set fonts for nicer pdf view
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21 \IfFileExists{lmodern.sty}
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22 {\usepackage{lmodern}}{}
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24 \fi % end if pdflatex is used
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26 % solves the following problem:
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27 % If the dection number consits of too many numerals the section heading
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28 % will be printed in the TOC without a space between it and the section number.
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29 % As solution more space between the number and the heading is inserted:
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30 \renewcommand{\l@subsection}{\@dottedtocline{2}{1.5em}{2.8em}}
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31 \renewcommand{\l@subsubsection}{\@dottedtocline{3}{4.3em}{3.6em}}
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33 % To be able to enter the character ° and · directly in LyX,
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35 \DeclareInputText{176}{\ifmmode^\circ\else\textdegree\fi}
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36 \DeclareInputText{183}{\ifmmode\cdot\else\textperiodcentered\fi}
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38 % increase link area for cross-references and autoname them,
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39 \AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}}
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40 \@ifundefined{extrasenglish}{\usepackage[english]{babel}}{}
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41 \addto\extrasenglish{%
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42 \renewcommand*{\equationautorefname}[1]{}
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43 \renewcommand{\sectionautorefname}{sec.\negthinspace}
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44 \renewcommand{\subsectionautorefname}{sec.\negthinspace}
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45 \renewcommand{\subsubsectionautorefname}{sec.\negthinspace}
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48 % don't load packages twice
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49 % see first footnote in sec. 9.3
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50 \@ifundefined{textcolor}{\usepackage{color}}{}
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52 % the pages of the TOC are numbered roman
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53 % and a PDF-bookmark for the TOC is added
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54 \pagenumbering{roman}
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55 \let\myTOC\tableofcontents
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56 \renewcommand{\tableofcontents}{%
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58 \pdfbookmark[1]{\contentsname}{}
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61 \pagenumbering{arabic}}
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63 % insert additional vertical space of 1.5 mm between footnotes,
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64 \let\myFoot\footnote
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65 \renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
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67 % provides caption formatting
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68 \setkomafont{captionlabel}{\bfseries}
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71 \usepackage[samesize]{cancel}
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73 % enables calculation of values
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76 % for multiple columns used in sec. 24.7
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77 \usepackage{multicol}
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79 % needed in sec. 19.4
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80 \usepackage{remreset}
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82 % for the Fourier transformation symbol
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83 \usepackage{mathrsfs}
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85 % define a color, used in sec.9.3
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86 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
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88 % declare operators (see sec. 10.4 and sec. 15.2)
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89 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
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90 \DeclareMathOperator{\sgn}{sgn}
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92 \newcommand{\spce}{\textvisiblespace}
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94 % example definitions for sec. 20.1
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95 \newcommand{\gr}{\Longrightarrow}
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96 \newcommand{\us}[1]{\underline{#1}}
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97 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
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98 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
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99 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
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101 % example macro from sec. 19.4
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102 %\def\tagform@#1{\maketag@@@{|#1|}}
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104 % macro from sec. 10.2
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105 \def\clap#1{\hbox to 0pt{\hss #1\hss}}
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106 \def\mathclap {\mathpalette \mathclapinternal}
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107 \def\mathclapinternal #1#2{\clap{$\mathsurround =0pt #1{#2}$}}
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110 % ------------------------------------
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111 % used to check for needed LaTeX packages
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112 \usepackage{ifthen}
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114 % check for package eurosym
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115 % used for the Euro symbol
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116 \newboolean{eurosym}
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117 \IfFileExists{eurosym.sty}
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118 {\usepackage[gennarrow]{eurosym}
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119 \setboolean{eurosym}{true}}
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120 {\setboolean{eurosym}{false}}
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122 % check for package braket
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123 % used for physical vectors
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124 \newboolean{braket}
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125 \IfFileExists{braket.sty}
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126 {\usepackage{braket}
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127 \setboolean{braket}{true}}
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128 {\setboolean{braket}{false}}
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130 % check for package cancel
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131 \newboolean{cancel}
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132 \IfFileExists{cancel.sty}
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133 {\usepackage{cancel}
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134 \setboolean{cancel}{true}}
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135 {\setboolean{cancel}{false}}
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137 % check for package upgreek
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138 \newboolean{upgreek}
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139 \IfFileExists{upgreek.sty}
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140 {\usepackage{upgreek}
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141 \setboolean{upgreek}{true}}
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142 {\setboolean{upgreek}{false}}
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144 \options bibliography=totoc,index=totoc,BCOR7.5mm,titlepage,captions=tableheading
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145 \use_default_options false
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146 \maintain_unincluded_children false
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148 \language_package default
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149 \inputencoding auto
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150 \fontencoding global
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153 \font_typewriter default
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154 \font_default_family default
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155 \use_non_tex_fonts false
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162 \default_output_format default
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164 \bibtex_command default
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165 \index_command default
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169 \pdf_title "LyX's Math Manual"
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170 \pdf_author "LyX Team, Uwe Stöhr"
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171 \pdf_subject "LyX-documentation about math"
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172 \pdf_keywords "LyX, Mathed"
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173 \pdf_bookmarks true
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174 \pdf_bookmarksnumbered true
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190 \use_bibtopic false
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204 \quotes_language english
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214 \html_css_as_file 0
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220 \begin_layout Title
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221 LyX's detailed Math manual
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224 \begin_layout Author
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229 \begin_layout Plain Layout
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231 If you have comments or error corrections, please send them to the LyX Documenta
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232 tion mailing list:
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235 \begin_inset CommandInset href
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237 name "lyx-docs@lists.lyx.org"
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238 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
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249 \begin_inset Note Note
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252 \begin_layout Plain Layout
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259 \begin_inset Newline newline
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263 \begin_inset Newline newline
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271 \begin_layout Standard
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272 \begin_inset CommandInset toc
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273 LatexCommand tableofcontents
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280 \begin_layout Standard
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281 \begin_inset Note Note
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284 \begin_layout Plain Layout
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285 To export this document to PDF, PS or DVI the LaTeX-packages
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287 braket, cancel, eurosym, mathdots, mhchem
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293 should be installed.
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294 If they are not installed the document can be exported anyway but the sections
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295 where the packages are required will not appear in the output.
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300 ; if it is not installed, this file cannot be exported.
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303 \begin_layout Plain Layout
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304 The latest PDF-version of this document can be found here:
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305 \begin_inset Newline newline
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310 http://wiki.lyx.org/LyX/DocumentationDevelopment#Math
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318 \begin_layout Standard
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319 \begin_inset Newpage newpage
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325 \begin_layout Section
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329 \begin_layout Standard
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330 This document explains LyX's math features and is furthermore a collection
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331 of LaTeX-commands used for mathematical characters and constructs.
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332 The explanations are designed for the usage of commands.
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333 It is therefore required that you have read the section
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336 \begin_inset space ~
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341 of the User's Guide.
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344 \begin_layout Standard
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345 Most of the characters and many constructs explained in this manual are
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346 also accessible via the menu
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350 \SpecialChar \menuseparator
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366 But everybody who has to write lots of formulas will notice that it is
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367 much faster to use commands instead of the math toolbar.
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368 Therefore this manual is focused on commands but also mentions the correspondin
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369 g toolbar buttons when available.
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372 \begin_layout Standard
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373 If not specially mentioned the commands are only available within formulas.
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374 To be able to use all commands explained in this document, the option
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376 Use AMS math package
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378 must be checked in the document settings (menu
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380 Document\SpecialChar \menuseparator
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381 Settings\SpecialChar \menuseparator
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383 \begin_inset space ~
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392 \begin_layout Plain Layout
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395 Use AMS math package automatically
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401 \begin_layout Plain Layout
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410 -math when math constructs are found that are supported by LyX.
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418 \begin_layout Standard
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419 This document doesn't list all
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423 \begin_layout Plain Layout
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436 \begin_layout Plain Layout
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441 \begin_layout Plain Layout
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450 -math commands is in the file
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453 \begin_inset CommandInset href
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456 target "ftp://ctan.tug.org/tex-archive/macros/amstex/doc/amsguide.ps"
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462 , which is part of every LaTeX standard installation.
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467 for lucidity reasons.
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470 \begin_layout Section
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471 General Instructions
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474 \begin_layout Standard
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475 To create an inline formula
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476 \begin_inset Index idx
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479 \begin_layout Plain Layout
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485 that is embedded into a text line, use one of the shortcuts
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491 or the toolbar button
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492 \begin_inset Graphics
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493 filename ../images/math-mode.png
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499 \begin_inset Newline newline
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502 To create a display style formula
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503 \begin_inset Index idx
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506 \begin_layout Plain Layout
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507 Formula ! display style
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512 which will appear bigger, has a different format, and will be in a separate
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513 paragraph, use one of these shortcuts:
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522 \begin_layout Standard
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523 To change a display style formula to an inline formula, set the cursor into
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524 the formula and use one of the shortcuts
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532 Edit\SpecialChar \menuseparator
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533 Math\SpecialChar \menuseparator
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534 Change formula type
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537 The same way is used to change an inline formula to a display style formula.
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540 \begin_layout Standard
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541 To display parts of an inline formula in the size of a display style formula,
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549 \begin_inset Index idx
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552 \begin_layout Plain Layout
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561 Then a new blue box appears in which the desired formula part is inserted.
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564 \begin_layout Standard
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565 Only inline formulas are allowed inside tables.
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568 \begin_layout Standard
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573 can be turned on in the menu
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575 View\SpecialChar \menuseparator
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579 When you click there on
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580 \begin_inset Quotes eld
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584 \begin_inset Quotes erd
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587 the toolbar will be shown permanently at the bottom; this state is visualized
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592 menu with a checkmark.
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593 When you click in this state again on
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594 \begin_inset Quotes eld
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598 \begin_inset Quotes erd
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609 is only shown when the cursor is within a formula; this state is visualized
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610 by the renaming of the menu entry from
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611 \begin_inset Quotes eld
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615 \begin_inset Quotes erd
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619 \begin_inset Quotes eld
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623 \begin_inset space ~
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627 \begin_inset Quotes erd
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633 \begin_layout Standard
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635 \begin_inset Index idx
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638 \begin_layout Plain Layout
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644 is invoked by pressing the toolbar button
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645 \begin_inset Graphics
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646 filename ../images/ert-insert.png
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651 or by using the menu
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653 Insert\SpecialChar \menuseparator
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658 \begin_layout Plain Layout
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674 \begin_inset Note Note
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677 \begin_layout Plain Layout
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678 In LyX there are three
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679 \begin_inset Quotes eld
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683 \begin_inset Quotes erd
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686 that appear in the output with sub- and superscript letters: TeX, LaTeX
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690 \begin_layout Plain Layout
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691 To avoid that these names are recognized as proper names, a TeX-brace pair
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700 \begin_layout Standard
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701 To change the LaTeX-preamble
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702 \begin_inset Index idx
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705 \begin_layout Plain Layout
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713 Document\SpecialChar \menuseparator
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714 Settings\SpecialChar \menuseparator
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719 \begin_layout Plain Layout
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735 \begin_layout Standard
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736 To edit matrices, case differentiations and multiline formulas subsequently,
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739 Edit\SpecialChar \menuseparator
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744 Edit\SpecialChar \menuseparator
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746 \begin_inset space \thinspace{}
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750 \begin_inset space \thinspace{}
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760 When lines and columns are swapped via the menu, the column or line where
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761 the cursor is in is exchanged with the column to the right or the line
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762 below, respectively.
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763 Is the cursor in the last column or row, the exchange is done with the
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764 column to the left or the line above.
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767 \begin_layout Standard
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768 To write text in formulas
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772 \begin_layout Plain Layout
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773 For multiline formulas the command
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780 \begin_inset CommandInset ref
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782 reference "sub:Text-in-multiline"
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796 \begin_inset Index idx
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799 \begin_layout Plain Layout
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806 \begin_inset Index idx
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809 \begin_layout Plain Layout
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816 This mode is invoked with the shortcut
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822 or by the insertion of the command
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829 \begin_inset Index idx
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832 \begin_layout Plain Layout
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841 The text appears black in LyX and can therefore be distinguished from the
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842 other formula parts which appear blue.
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843 In the output mathematical text is set upright, in contrary to other formula
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847 \begin_layout Subsection*
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851 \begin_layout Standard
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852 Most of the LaTeX-commands for math constructs have the following scheme:
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855 \begin_layout Standard
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860 commandname[optional
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871 \begin_layout Standard
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872 A command always starts with a backslash
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873 \begin_inset Quotes gld
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883 \begin_inset Quotes grd
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887 To omit optional arguments, also omit the associated brackets.
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888 The braces around the required arguments are named in this document as
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890 \begin_inset Index idx
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893 \begin_layout Plain Layout
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900 If you add in a formula a left brace to a command name, LyX automatically
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901 creates a TeX-brace.
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902 In all other cases TeX-braces are created in formulas with the command
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910 TeX-braces appear red in LyX, in contrary to normal braces which appear
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912 In TeX-mode no command is needed to get TeX-braces.
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913 TeX-braces don't appear in the output.
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916 \begin_layout Standard
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917 When commands without arguments, like commands for symbols are entered in
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918 TeX-mode, a space character must
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922 be behind the command to end it.
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923 This space doesn't appear in the output.
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924 When the space should appear in the output, the space must be followed
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925 by a protected space in normal text.
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928 \begin_layout Standard
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929 A protected space is inserted with
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932 arg "command-alternatives space-insert protected ; math-space"
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938 \begin_layout Subsection*
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939 \begin_inset Newpage newpage
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945 \begin_layout Itemize
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950 \begin_layout Plain Layout
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951 This visible space character can be created with the command
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958 \begin_inset Index idx
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961 \begin_layout Plain Layout
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969 , inserted in TeX-mode.
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978 \begin_layout Plain Layout
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988 \begin_inset space ~
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991 denotes a space character to be input.
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994 \begin_layout Itemize
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996 \begin_inset Formula $\to$
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999 denotes the usage of the corresponding arrow key on the keyboard.
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1004 key can often be used instead of
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1005 \begin_inset Formula $\to$
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1009 \begin_inset Formula $\downarrow$
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1017 \begin_inset Formula $\leftarrow$
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1021 \begin_inset Formula $\uparrow$
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1532 \begin_layout Standard
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1533 Indices are created with an underscore
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1534 \begin_inset Quotes eld
\r
1538 \begin_inset Quotes erd
\r
1541 or via the math toolbar button
\r
1542 \begin_inset Graphics
\r
1543 filename ../images/math-subscript.png
\r
1548 , exponents with a caret
\r
1549 \begin_inset Quotes eld
\r
1553 \begin_inset Quotes erd
\r
1556 or via the math toolbar button
\r
1557 \begin_inset Graphics
\r
1558 filename ../images/math-superscript.png
\r
1566 \begin_layout Standard
\r
1568 \begin_inset Tabular
\r
1569 <lyxtabular version="3" rows="4" columns="2">
\r
1570 <features tabularvalignment="middle">
\r
1571 <column alignment="center" valignment="top" width="0pt">
\r
1572 <column alignment="center" valignment="top" width="0pt">
\r
1574 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
1577 \begin_layout Plain Layout
\r
1583 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
1586 \begin_layout Plain Layout
\r
1588 \begin_inset Note Note
\r
1591 \begin_layout Plain Layout
\r
1598 is only used as spacer.
\r
1610 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
1613 \begin_layout Plain Layout
\r
1619 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
1622 \begin_layout Plain Layout
\r
1623 \begin_inset Formula $B_{V}$
\r
1633 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
1636 \begin_layout Plain Layout
\r
1642 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
1645 \begin_layout Plain Layout
\r
1646 \begin_inset Formula $\raisebox{5mm}{}B^{V}$
\r
1656 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
1659 \begin_layout Plain Layout
\r
1664 \begin_layout Plain Layout
\r
1678 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
1681 \begin_layout Plain Layout
\r
1682 \begin_inset Formula $\raisebox{5mm}{}B^{A}$
\r
1698 \begin_layout Standard
\r
1699 As the caret is in some languages an accent, vowels will be accentuated
\r
1700 in this case and not set as exponents
\r
1704 \begin_layout Plain Layout
\r
1705 Depending on the used keyboard settings this can also happen for characters
\r
1706 other than vowels.
\r
1712 To get exponents in this case, press
\r
1716 after the caret as in the last example.
\r
1719 \begin_layout Subsection
\r
1721 \begin_inset CommandInset label
\r
1722 LatexCommand label
\r
1723 name "sub:Fractions"
\r
1728 \begin_inset Index idx
\r
1731 \begin_layout Plain Layout
\r
1740 \begin_layout Standard
\r
1741 Fractions are generated with the command
\r
1748 \begin_inset Index idx
\r
1751 \begin_layout Plain Layout
\r
1759 or via the math toolbar button
\r
1760 \begin_inset Graphics
\r
1761 filename ../images/math/frac.png
\r
1767 The font size is adjusted automatically, depending on whether the fraction
\r
1768 is in an inline or display style formula.
\r
1769 With the math toolbar button
\r
1770 \begin_inset Graphics
\r
1771 filename ../images/math/frac-square.png
\r
1776 you can select different fraction types.
\r
1779 \begin_layout Standard
\r
1787 \begin_inset Index idx
\r
1790 \begin_layout Plain Layout
\r
1798 a fraction can be created that always has the size of a display style formula.
\r
1806 \begin_inset Index idx
\r
1809 \begin_layout Plain Layout
\r
1817 the fraction appears always with the size of an inline formula.
\r
1821 \begin_layout Standard
\r
1822 A line with the fraction
\r
1823 \begin_inset Formula $\frac{1}{2}$
\r
1826 that was created with the command
\r
1835 \begin_layout Standard
\r
1836 A line with the fraction
\r
1837 \begin_inset Formula $\dfrac{1}{2}$
\r
1840 that was created with the command
\r
1849 \begin_layout Standard
\r
1851 \begin_inset Tabular
\r
1852 <lyxtabular version="3" rows="4" columns="2">
\r
1853 <features tabularvalignment="middle">
\r
1854 <column alignment="center" valignment="top" width="0pt">
\r
1855 <column alignment="center" valignment="top" width="0pt">
\r
1857 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
1860 \begin_layout Plain Layout
\r
1866 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
1869 \begin_layout Plain Layout
\r
1871 \begin_inset Note Note
\r
1874 \begin_layout Plain Layout
\r
1881 is only used as spacer.
\r
1893 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
1896 \begin_layout Plain Layout
\r
1903 \begin_layout Plain Layout
\r
1913 \begin_inset Formula $\downarrow$
\r
1921 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
1924 \begin_layout Plain Layout
\r
1925 \begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$
\r
1935 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
1938 \begin_layout Plain Layout
\r
1945 \begin_layout Plain Layout
\r
1955 \begin_inset Formula $\downarrow$
\r
1963 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
1966 \begin_layout Plain Layout
\r
1967 \begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$
\r
1977 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
1980 \begin_layout Plain Layout
\r
1987 \begin_layout Plain Layout
\r
2002 \begin_layout Plain Layout
\r
2012 \begin_inset Formula $\downarrow$
\r
2016 \begin_inset Formula $\downarrow\downarrow$
\r
2024 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
2027 \begin_layout Plain Layout
\r
2028 \begin_inset Formula $\raisebox{8mm}{}\dfrac{e^{\frac{1}{2}}}{3}\raisebox{-4mm}{}$
\r
2044 \begin_layout Standard
\r
2045 \begin_inset VSpace bigskip
\r
2049 \begin_inset Newpage newpage
\r
2052 For nested fractions the command
\r
2059 \begin_inset Index idx
\r
2062 \begin_layout Plain Layout
\r
2071 Here is an example:
\r
2072 \begin_inset VSpace -3mm
\r
2078 \begin_layout Standard
\r
2079 \begin_inset Formula
\r
2081 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
\r
2082 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}
\r
2090 \begin_layout Standard
\r
2091 The command for the example above is:
\r
2094 \begin_layout Standard
\r
2103 \begin_layout Plain Layout
\r
2113 \begin_inset Formula $\downarrow$
\r
2122 \begin_layout Plain Layout
\r
2137 \begin_layout Plain Layout
\r
2147 \begin_inset Formula $\downarrow$
\r
2151 \begin_inset Formula $\downarrow$
\r
2157 \begin_layout Standard
\r
2158 \begin_inset VSpace medskip
\r
2164 \begin_layout Standard
\r
2171 sets the fraction always in the size of a displayed formula, also when
\r
2172 it is part of another fraction.
\r
2175 \begin_layout Standard
\r
2176 It is possible to specify the alignment of the numerator.
\r
2183 is used to left align it, the command
\r
2189 to right-align it.
\r
2196 centers the numerator.
\r
2197 These fractions demonstrate the different alignments:
\r
2200 \begin_layout Standard
\r
2203 \begin_inset Formula
\r
2205 \cfrac[l]{A}{B+C}\,,\,\cfrac{A}{B+C}\,,\,\cfrac[r]{A}{B+C}
\r
2213 \begin_layout Standard
\r
2214 \begin_inset Note Greyedout
\r
2217 \begin_layout Plain Layout
\r
2234 are no real LaTeX commands but represent the command
\r
2238 cfrac[alignment]{numerator}{denominator}
\r
2241 Therefore you cannot use them in TeX code.
\r
2249 \begin_layout Standard
\r
2250 \begin_inset VSpace medskip
\r
2253 It is often advantageous to combine
\r
2266 \begin_inset Formula
\r
2268 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}
\r
2276 \begin_layout Standard
\r
2277 For inline fractions with a sloped fraction stroke you can use the command
\r
2285 \begin_inset Index idx
\r
2288 \begin_layout Plain Layout
\r
2297 \begin_inset Formula $\nicefrac{5}{31}$
\r
2307 \begin_inset Index idx
\r
2310 \begin_layout Plain Layout
\r
2319 \begin_inset Formula $\unitfrac{5}{31}$
\r
2322 There is furthermore the command
\r
2328 that offers to write a fraction in combination with a number:
\r
2329 \begin_inset Formula $\unitfrac[2]{1}{3}$
\r
2335 \begin_layout Standard
\r
2336 \begin_inset Note Greyedout
\r
2339 \begin_layout Plain Layout
\r
2350 is not a real LaTeX command but the command
\r
2351 \begin_inset Newline newline
\r
2358 unitfrac[number]{numerator}{denominator}
\r
2361 Therefore you cannot use it in TeX code.
\r
2369 \begin_layout Standard
\r
2370 How to define own fractions where the fraction stroke can be changed, is
\r
2372 \begin_inset CommandInset ref
\r
2374 reference "sub:Self-defined-Fractions"
\r
2381 \begin_layout Standard
\r
2382 \begin_inset Newpage newpage
\r
2388 \begin_layout Subsection
\r
2390 \begin_inset Index idx
\r
2393 \begin_layout Plain Layout
\r
2402 \begin_layout Standard
\r
2403 Square roots are created with
\r
2410 \begin_inset Index idx
\r
2413 \begin_layout Plain Layout
\r
2421 or the math toolbar button
\r
2422 \begin_inset Graphics
\r
2423 filename ../images/math/sqrt.png
\r
2428 , all other roots with the command
\r
2435 \begin_inset Index idx
\r
2438 \begin_layout Plain Layout
\r
2446 or with the math toolbar button
\r
2447 \begin_inset Graphics
\r
2448 filename ../images/math/root.png
\r
2456 \begin_layout Standard
\r
2458 \begin_inset Tabular
\r
2459 <lyxtabular version="3" rows="3" columns="2">
\r
2460 <features tabularvalignment="middle">
\r
2461 <column alignment="center" valignment="top" width="0pt">
\r
2462 <column alignment="center" valignment="top" width="0pt">
\r
2464 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
2467 \begin_layout Plain Layout
\r
2473 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
2476 \begin_layout Plain Layout
\r
2478 \begin_inset Note Note
\r
2481 \begin_layout Plain Layout
\r
2488 is only used as spacer.
\r
2500 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
2503 \begin_layout Plain Layout
\r
2510 \begin_layout Plain Layout
\r
2524 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
2527 \begin_layout Plain Layout
\r
2528 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$
\r
2538 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
2541 \begin_layout Plain Layout
\r
2548 \begin_layout Plain Layout
\r
2558 \begin_inset Formula $\downarrow$
\r
2566 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
2569 \begin_layout Plain Layout
\r
2570 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$
\r
2586 \begin_layout Standard
\r
2587 A square root can also be created with
\r
2593 when the root index field is left empty.
\r
2596 \begin_layout Standard
\r
2597 With certain indices the distance to the root is too small, like in this
\r
2599 \begin_inset Formula $\sqrt[\beta]{B}$
\r
2603 \begin_inset Newline newline
\r
2607 \begin_inset Formula $\beta$
\r
2611 To avoid this, the commands
\r
2618 \begin_inset Index idx
\r
2621 \begin_layout Plain Layout
\r
2636 \begin_inset Index idx
\r
2639 \begin_layout Plain Layout
\r
2647 are used with the following scheme:
\r
2650 \begin_layout Standard
\r
2655 leftroot{distance}
\r
2664 \begin_layout Standard
\r
2665 Distance is the number of Big Points (unit bp;
\r
2666 \begin_inset Formula $\mathrm{72\, bp=1\, inch}$
\r
2669 ), that the index should be moved to the left or top, resp..
\r
2670 The commands are written to the index.
\r
2671 This way the command
\r
2672 \begin_inset Newline newline
\r
2682 \begin_inset Formula $\to$
\r
2688 \begin_inset Formula $\to$
\r
2697 \begin_layout Plain Layout
\r
2707 \begin_inset Formula $\to$
\r
2711 \begin_inset Newline newline
\r
2716 produces a correct typeset formula:
\r
2717 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
\r
2723 \begin_layout Subsection
\r
2724 Binomial Coefficients
\r
2725 \begin_inset Index idx
\r
2728 \begin_layout Plain Layout
\r
2729 Binomial coefficients
\r
2737 \begin_layout Standard
\r
2738 Binomial coefficients are inserted with the command
\r
2745 \begin_inset Index idx
\r
2748 \begin_layout Plain Layout
\r
2756 or with the submenu of the math toolbar button
\r
2757 \begin_inset Graphics
\r
2758 filename ../images/math/frac-square.png
\r
2764 As with fractions (
\r
2776 there are the commands
\r
2783 \begin_inset Index idx
\r
2786 \begin_layout Plain Layout
\r
2801 \begin_inset Index idx
\r
2804 \begin_layout Plain Layout
\r
2813 For other brackets around binomial coeficients there are the commands
\r
2820 \begin_inset Index idx
\r
2823 \begin_layout Plain Layout
\r
2838 \begin_inset Index idx
\r
2841 \begin_layout Plain Layout
\r
2852 \begin_layout Standard
\r
2854 \begin_inset Tabular
\r
2855 <lyxtabular version="3" rows="6" columns="2">
\r
2856 <features tabularvalignment="middle">
\r
2857 <column alignment="center" valignment="top" width="0pt">
\r
2858 <column alignment="center" valignment="top" width="0pt">
\r
2860 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
2863 \begin_layout Plain Layout
\r
2869 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
2872 \begin_layout Plain Layout
\r
2874 \begin_inset Note Note
\r
2877 \begin_layout Plain Layout
\r
2884 is only used as spacer.
\r
2896 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
2899 \begin_layout Plain Layout
\r
2906 \begin_layout Plain Layout
\r
2916 \begin_inset Formula $\downarrow$
\r
2924 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
2927 \begin_layout Plain Layout
\r
2928 \begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$
\r
2938 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
2941 \begin_layout Plain Layout
\r
2948 \begin_layout Plain Layout
\r
2958 \begin_inset Formula $\downarrow$
\r
2966 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
2969 \begin_layout Plain Layout
\r
2970 \begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$
\r
2980 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
2983 \begin_layout Plain Layout
\r
2990 \begin_layout Plain Layout
\r
3000 \begin_inset Formula $\downarrow$
\r
3008 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
3011 \begin_layout Plain Layout
\r
3012 \begin_inset Formula $\raisebox{5mm}{}\tbinom{A}{B}\raisebox{-2.5mm}{}$
\r
3022 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
3025 \begin_layout Plain Layout
\r
3032 \begin_layout Plain Layout
\r
3042 \begin_inset Formula $\downarrow$
\r
3050 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
3053 \begin_layout Plain Layout
\r
3054 \begin_inset Formula $\raisebox{5mm}{}{A \brack B}\raisebox{-2.5mm}{}$
\r
3064 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
3067 \begin_layout Plain Layout
\r
3074 \begin_layout Plain Layout
\r
3084 \begin_inset Formula $\downarrow$
\r
3092 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
3095 \begin_layout Plain Layout
\r
3096 \begin_inset Formula $\raisebox{5mm}{}{A \brace B}\raisebox{-2.5mm}{}$
\r
3112 \begin_layout Subsection
\r
3113 Case Differentiations
\r
3114 \begin_inset Index idx
\r
3117 \begin_layout Plain Layout
\r
3118 Case differentiations
\r
3126 \begin_layout Standard
\r
3128 \begin_inset Tabular
\r
3129 <lyxtabular version="3" rows="3" columns="2">
\r
3130 <features tabularvalignment="middle">
\r
3131 <column alignment="center" valignment="top" width="0pt">
\r
3132 <column alignment="center" valignment="top" width="0pt">
\r
3134 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
3137 \begin_layout Plain Layout
\r
3143 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
3146 \begin_layout Plain Layout
\r
3154 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
3157 \begin_layout Plain Layout
\r
3164 \begin_layout Plain Layout
\r
3174 \begin_inset Formula $\to$
\r
3178 \begin_inset Index idx
\r
3181 \begin_layout Plain Layout
\r
3194 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
3197 \begin_layout Plain Layout
\r
3198 \begin_inset Formula $\begin{cases}
\r
3199 A & B>0\end{cases}$
\r
3209 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
3212 \begin_layout Plain Layout
\r
3219 \begin_layout Plain Layout
\r
3231 arg "newline-insert newline"
\r
3239 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
3242 \begin_layout Plain Layout
\r
3243 \begin_inset Formula $\begin{cases}
\r
3244 A & \textrm{for }x>0\\
\r
3245 B & \textrm{for }x=0
\r
3262 \begin_layout Standard
\r
3269 or pressing the math toolbar button
\r
3270 \begin_inset Graphics
\r
3271 filename ../images/math/cases.png
\r
3276 you can create new lines with the shortcut
\r
3279 arg "newline-insert newline"
\r
3282 or the table toolbar button
\r
3283 \begin_inset Graphics
\r
3284 filename ../images/tabular-feature_append-row.png
\r
3292 \begin_layout Standard
\r
3299 is also available via the menu
\r
3301 Insert\SpecialChar \menuseparator
\r
3302 Math\SpecialChar \menuseparator
\r
3308 \begin_layout Subsection
\r
3310 \begin_inset Index idx
\r
3313 \begin_layout Plain Layout
\r
3322 \begin_layout Standard
\r
3330 \begin_inset Index idx
\r
3333 \begin_layout Plain Layout
\r
3341 every character can be displayed canceled.
\r
3342 The characters are quasi accentuated by a slash.
\r
3345 \begin_layout Standard
\r
3347 \begin_inset Tabular
\r
3348 <lyxtabular version="3" rows="4" columns="2">
\r
3349 <features tabularvalignment="middle">
\r
3350 <column alignment="center" valignment="top" width="0pt">
\r
3351 <column alignment="center" valignment="top" width="0pt">
\r
3353 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
3356 \begin_layout Plain Layout
\r
3362 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
3365 \begin_layout Plain Layout
\r
3373 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
3376 \begin_layout Plain Layout
\r
3384 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
3387 \begin_layout Plain Layout
\r
3388 \begin_inset Formula $\not=$
\r
3398 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
3401 \begin_layout Plain Layout
\r
3411 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
3414 \begin_layout Plain Layout
\r
3415 \begin_inset Formula $\not\le$
\r
3425 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
3428 \begin_layout Plain Layout
\r
3438 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
3441 \begin_layout Plain Layout
\r
3442 \begin_inset Formula $\not\parallel$
\r
3458 \begin_layout Standard
\r
3459 The last example shows that not all negations look good.
\r
3460 Therefore there are special commands for some negations (see
\r
3461 \begin_inset CommandInset ref
\r
3463 reference "sub:Mathematical-Symbols"
\r
3468 \begin_inset CommandInset ref
\r
3470 reference "sec:Relations"
\r
3477 \begin_layout Subsection
\r
3479 \begin_inset CommandInset label
\r
3480 LatexCommand label
\r
3481 name "sub:Placeholders"
\r
3486 \begin_inset Index idx
\r
3489 \begin_layout Plain Layout
\r
3496 \begin_inset Index idx
\r
3499 \begin_layout Plain Layout
\r
3500 Chemical characters ! Isotopes
\r
3506 \begin_inset Index idx
\r
3509 \begin_layout Plain Layout
\r
3514 \begin_layout Plain Layout
\r
3521 Chemical characters
\r
3525 \begin_layout Plain Layout
\r
3540 \begin_layout Standard
\r
3541 When displaying e.
\r
3542 \begin_inset space \thinspace{}
\r
3546 \begin_inset space \space{}
\r
3553 \begin_layout Plain Layout
\r
3554 Typesetting isotopes and chemical symbols is described in
\r
3555 \begin_inset CommandInset ref
\r
3557 reference "sub:Chemical-Symbols-and"
\r
3566 the following problem occurs:
\r
3569 \begin_layout Standard
\r
3571 \begin_inset Tabular
\r
3572 <lyxtabular version="3" rows="2" columns="2">
\r
3573 <features tabularvalignment="middle">
\r
3574 <column alignment="center" valignment="top" width="0pt">
\r
3575 <column alignment="center" valignment="top" width="0pt">
\r
3577 <cell alignment="center" valignment="top" usebox="none">
\r
3580 \begin_layout Plain Layout
\r
3581 Indices created with sub- and superscripts:
\r
3586 <cell alignment="center" valignment="top" usebox="none">
\r
3589 \begin_layout Plain Layout
\r
3590 \begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
\r
3600 <cell alignment="center" valignment="top" usebox="none">
\r
3603 \begin_layout Plain Layout
\r
3609 <cell alignment="center" valignment="top" usebox="none">
\r
3612 \begin_layout Plain Layout
\r
3613 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
\r
3627 \begin_inset Note Note
\r
3630 \begin_layout Plain Layout
\r
3637 is only used as spacer.
\r
3645 \begin_layout Standard
\r
3646 The shorter index is by default placed below or above the first character
\r
3647 of the longer index.
\r
3648 To avoid this there is the command
\r
3655 \begin_inset Index idx
\r
3658 \begin_layout Plain Layout
\r
3666 or the math toolbar button
\r
3667 \begin_inset space \thinspace{}
\r
3674 \begin_layout Plain Layout
\r
3675 can be found in the submenu of the toolbar button
\r
3676 \begin_inset Graphics
\r
3677 filename ../images/math/space.png
\r
3688 \begin_inset Graphics
\r
3689 filename ../images/math/phantom.png
\r
3694 that creates one or more phantom characters.
\r
3701 a small blue box appears that is superposed with two red arrows.
\r
3702 The arrows indicate that the complete width and height of the box content
\r
3703 will be created as placeholder.
\r
3704 Phantom characters are accordingly placeholders with the size of the characters.
\r
3707 \begin_layout Standard
\r
3709 \begin_inset Tabular
\r
3710 <lyxtabular version="3" rows="4" columns="2">
\r
3711 <features tabularvalignment="middle">
\r
3712 <column alignment="center" valignment="top" width="0">
\r
3713 <column alignment="center" valignment="top" width="0">
\r
3715 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
3718 \begin_layout Plain Layout
\r
3724 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
3727 \begin_layout Plain Layout
\r
3729 \begin_inset Note Note
\r
3732 \begin_layout Plain Layout
\r
3739 is only used as spacer.
\r
3751 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
3754 \begin_layout Plain Layout
\r
3759 \begin_layout Plain Layout
\r
3774 \begin_layout Plain Layout
\r
3784 \begin_inset Formula $\to$
\r
3791 \begin_layout Plain Layout
\r
3805 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
3808 \begin_layout Plain Layout
\r
3809 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
\r
3819 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
3822 \begin_layout Plain Layout
\r
3827 \begin_layout Plain Layout
\r
3842 \begin_layout Plain Layout
\r
3852 \begin_inset Formula $\to$
\r
3859 \begin_layout Plain Layout
\r
3873 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
3876 \begin_layout Plain Layout
\r
3877 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
\r
3887 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
3890 \begin_layout Plain Layout
\r
3897 \begin_layout Plain Layout
\r
3912 \begin_layout Plain Layout
\r
3922 \begin_inset Formula $\to$
\r
3929 \begin_layout Plain Layout
\r
3943 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
3946 \begin_layout Plain Layout
\r
3947 \begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
\r
3963 \begin_layout Standard
\r
3964 Furthermore there are the commands
\r
3971 \begin_inset Index idx
\r
3974 \begin_layout Plain Layout
\r
3983 \begin_inset space ~
\r
3987 \begin_inset Graphics
\r
3988 filename ../images/math/vphantom.png
\r
4000 \begin_inset Index idx
\r
4003 \begin_layout Plain Layout
\r
4012 \begin_inset space ~
\r
4016 \begin_inset Graphics
\r
4017 filename ../images/math/hphantom.png
\r
4029 creates only space for the maximal height of the characters in the box
\r
4030 but not for its width.
\r
4037 creates only space for the width of the box content.
\r
4038 Therefore the boxes of both commands have only one red arrow.
\r
4041 \begin_layout Standard
\r
4042 For example the command
\r
4052 \begin_layout Plain Layout
\r
4067 creates space for the height of the integral sign,
\r
4071 \begin_layout Plain Layout
\r
4078 creates an integral sign, see
\r
4079 \begin_inset CommandInset ref
\r
4081 reference "sub:Big-Operators"
\r
4090 because this is the larger character.
\r
4091 An example application is in
\r
4092 \begin_inset CommandInset ref
\r
4094 reference "sub:Multiline-Brackets"
\r
4101 \begin_layout Standard
\r
4102 Placeholders can also be used for text when they are inserted via the menu
\r
4105 Insert\SpecialChar \menuseparator
\r
4106 Formatting\SpecialChar \menuseparator
\r
4112 \begin_layout Standard
\r
4113 This is a sentence.
\r
4114 \begin_inset Newline newline
\r
4118 \begin_inset Phantom Phantom
\r
4121 \begin_layout Plain Layout
\r
4130 \begin_layout Subsection
\r
4132 \begin_inset Index idx
\r
4135 \begin_layout Plain Layout
\r
4142 \begin_inset Index idx
\r
4145 \begin_layout Plain Layout
\r
4146 Formula ! underlined
\r
4154 \begin_layout Standard
\r
4156 \begin_inset Tabular
\r
4157 <lyxtabular version="3" rows="4" columns="2">
\r
4158 <features tabularvalignment="middle">
\r
4159 <column alignment="center" valignment="top" width="0pt">
\r
4160 <column alignment="center" valignment="top" width="0pt">
\r
4162 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
4165 \begin_layout Plain Layout
\r
4171 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
4174 \begin_layout Plain Layout
\r
4176 \begin_inset Note Note
\r
4179 \begin_layout Plain Layout
\r
4186 is only used as spacer.
\r
4198 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
4201 \begin_layout Plain Layout
\r
4208 \begin_layout Plain Layout
\r
4218 \begin_inset Index idx
\r
4221 \begin_layout Plain Layout
\r
4234 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
4237 \begin_layout Plain Layout
\r
4238 \begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
\r
4248 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
4251 \begin_layout Plain Layout
\r
4258 \begin_layout Plain Layout
\r
4268 \begin_inset Index idx
\r
4271 \begin_layout Plain Layout
\r
4284 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
4287 \begin_layout Plain Layout
\r
4288 \begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
\r
4298 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
4301 \begin_layout Plain Layout
\r
4308 \begin_layout Plain Layout
\r
4323 \begin_layout Plain Layout
\r
4337 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
4340 \begin_layout Plain Layout
\r
4341 \begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
\r
4357 \begin_layout Standard
\r
4358 In the last example it doesn't matter if first
\r
4373 \begin_layout Standard
\r
4374 To double underline use
\r
4383 \begin_layout Standard
\r
4384 It is possible to place up to 6 lines above or below characters.
\r
4387 \begin_layout Standard
\r
4388 \begin_inset VSpace bigskip
\r
4391 Custom lines can be created using the command
\r
4398 \begin_inset Index idx
\r
4401 \begin_layout Plain Layout
\r
4409 which has the following scheme:
\r
4412 \begin_layout Standard
\r
4417 rule[vertical offset]{length}{thickness}
\r
4420 \begin_layout Standard
\r
4421 The optional vertical offset shifts the line upwards (or downwards, when
\r
4422 the value is negative).
\r
4423 The units listed in
\r
4424 \begin_inset CommandInset ref
\r
4426 reference "tab:Available-units"
\r
4430 can be used for the values.
\r
4431 Here are two example lines created with the commands
\r
4432 \begin_inset Newline newline
\r
4439 rule[-2ex]{3cm}{2pt}
\r
4450 \begin_layout Standard
\r
4451 This is a sentence
\r
4452 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
\r
4458 \begin_layout Standard
\r
4465 can also be used for text when a line is inserted via the menu
\r
4467 Insert\SpecialChar \menuseparator
\r
4468 Formatting\SpecialChar \menuseparator
\r
4470 \begin_inset space ~
\r
4478 \begin_layout Standard
\r
4479 This is a sentence
\r
4480 \begin_inset CommandInset line
\r
4491 \begin_layout Subsection
\r
4493 \begin_inset CommandInset label
\r
4494 LatexCommand label
\r
4495 name "sub:Ellipses"
\r
4500 \begin_inset Index idx
\r
4503 \begin_layout Plain Layout
\r
4512 \begin_layout Standard
\r
4513 There are different types of ellipses available.
\r
4517 \begin_layout Plain Layout
\r
4518 In the math toolbar in the submenu of the button
\r
4519 \begin_inset Graphics
\r
4520 filename ../images/math/ldots.png
\r
4530 For listings dots at the baseline are used (
\r
4537 \begin_inset Index idx
\r
4540 \begin_layout Plain Layout
\r
4548 ), while for operations dots are needed that are on the same height as the
\r
4556 \begin_inset Index idx
\r
4559 \begin_layout Plain Layout
\r
4568 When using the command
\r
4575 \begin_inset Index idx
\r
4578 \begin_layout Plain Layout
\r
4586 , LaTeX decides on the basis of the next character what type is used.
\r
4589 \begin_layout Standard
\r
4591 \begin_inset Tabular
\r
4592 <lyxtabular version="3" rows="9" columns="2">
\r
4593 <features tabularvalignment="middle">
\r
4594 <column alignment="center" valignment="top" width="0pt">
\r
4595 <column alignment="center" valignment="top" width="0pt">
\r
4597 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
4600 \begin_layout Plain Layout
\r
4606 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
4609 \begin_layout Plain Layout
\r
4617 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
4620 \begin_layout Plain Layout
\r
4625 \begin_layout Plain Layout
\r
4640 \begin_layout Plain Layout
\r
4654 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
4657 \begin_layout Plain Layout
\r
4658 \begin_inset Formula $A_{1},\dots,A_{n}$
\r
4668 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
4671 \begin_layout Plain Layout
\r
4676 \begin_layout Plain Layout
\r
4691 \begin_layout Plain Layout
\r
4705 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
4708 \begin_layout Plain Layout
\r
4709 \begin_inset Formula $A_{1}+\dots+A_{n}$
\r
4719 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
4722 \begin_layout Plain Layout
\r
4727 \begin_layout Plain Layout
\r
4742 \begin_layout Plain Layout
\r
4756 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
4759 \begin_layout Plain Layout
\r
4760 \begin_inset Formula $A_{1},\ldots,A_{n}$
\r
4770 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
4773 \begin_layout Plain Layout
\r
4778 \begin_layout Plain Layout
\r
4793 \begin_layout Plain Layout
\r
4807 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
4810 \begin_layout Plain Layout
\r
4811 \begin_inset Formula $A_{1}+\cdots+A_{n}$
\r
4821 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
4824 \begin_layout Plain Layout
\r
4832 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
4835 \begin_layout Plain Layout
\r
4836 \begin_inset Formula $\vdots$
\r
4846 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
4849 \begin_layout Plain Layout
\r
4857 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
4860 \begin_layout Plain Layout
\r
4861 \begin_inset Formula $\ddots$
\r
4871 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
4874 \begin_layout Plain Layout
\r
4882 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
4885 \begin_layout Plain Layout
\r
4886 \begin_inset Formula $\iddots$
\r
4896 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
4899 \begin_layout Plain Layout
\r
4901 \begin_inset space \thinspace{}
\r
4904 matrix with the different dots
\r
4909 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
4912 \begin_layout Plain Layout
\r
4913 \begin_inset Formula $\begin{array}{ccc}
\r
4914 A_{11} & \cdots & A_{1m}\\
\r
4915 \vdots & \ddots & \vdots\\
\r
4916 A_{n1} & \cdots & A_{nm}
\r
4933 \begin_layout Standard
\r
4934 The ellipses available in menu
\r
4936 Insert\SpecialChar \menuseparator
\r
4938 \begin_inset space ~
\r
4952 \begin_layout Standard
\r
4953 \begin_inset VSpace medskip
\r
4962 , one of the options
\r
4964 Use mathdots package (automatically)
\r
4966 must be set in the document settings under
\r
4969 \begin_inset space ~
\r
4975 \begin_inset Newline newline
\r
4980 Use mathdots package
\r
4982 will improve the appearance of all dots in the documents if their font
\r
4983 style or size is not the default.
\r
4986 \begin_layout Standard
\r
4987 \begin_inset VSpace medskip
\r
4990 Specially for matrices there are ellipses that span over several columns.
\r
4991 They are created with the command
\r
4998 \begin_inset Index idx
\r
5001 \begin_layout Plain Layout
\r
5009 , that has the following scheme:
\r
5012 \begin_layout Standard
\r
5017 hdotsfor[distance]{number of columns}
\r
5020 \begin_layout Standard
\r
5021 The number of columns specifies how many columns should be spanned.
\r
5022 Distance is a factor for the distance between the dots.
\r
5025 \begin_layout Standard
\r
5026 In the following matrix the command
\r
5032 was inserted in the first box of the second line, to get an ellipsis with
\r
5033 a dot distance twice as long as with the command
\r
5040 \begin_inset Formula
\r
5042 \left(\begin{array}{cccc}
\r
5046 \end{array}\right)
\r
5051 Note that the matrix fields that should be spanned must be empty, otherwise
\r
5052 you get LaTeX-errors.
\r
5055 \begin_layout Standard
\r
5056 \begin_inset VSpace bigskip
\r
5059 Furthermore you can fill with the command
\r
5066 \begin_inset Index idx
\r
5069 \begin_layout Plain Layout
\r
5077 the rest of a line with dots.
\r
5078 The effect of these commands is the same as with
\r
5085 \begin_inset CommandInset ref
\r
5087 reference "sub:Variable-Space"
\r
5094 \begin_layout Standard
\r
5095 For example the command
\r
5103 \begin_layout Plain Layout
\r
5117 \begin_layout Standard
\r
5118 \begin_inset Formula $A\dotfill B$
\r
5124 \begin_layout Standard
\r
5131 there is for a line the command
\r
5138 \begin_inset Index idx
\r
5141 \begin_layout Plain Layout
\r
5152 \begin_layout Standard
\r
5153 \begin_inset Formula $A\hrulefill B$
\r
5159 \begin_layout Standard
\r
5160 To use the commands for text, they have to be inserted in TeX-mode.
\r
5163 \begin_layout Section
\r
5165 \begin_inset CommandInset label
\r
5166 LatexCommand label
\r
5167 name "sec:Matrices"
\r
5172 \begin_inset Index idx
\r
5175 \begin_layout Plain Layout
\r
5184 \begin_layout Standard
\r
5185 Matrices can be inserted via the math toolbar button
\r
5186 \begin_inset Graphics
\r
5187 filename ../images/dialog-show_mathmatrix.png
\r
5194 Insert\SpecialChar \menuseparator
\r
5195 Math\SpecialChar \menuseparator
\r
5199 In the matrix dialog you can specify the number of columns and rows, the
\r
5200 alignment and the decoration.
\r
5201 The vertical alignment is only of importance for matrices in inline formulas:
\r
5204 \begin_layout Standard
\r
5205 The first matrix is top
\r
5206 \begin_inset Formula $\begin{array}[t]{cccc}
\r
5213 , the second middle
\r
5214 \begin_inset Formula $\begin{array}{cccc}
\r
5221 and the third bottom
\r
5222 \begin_inset Formula $\begin{array}[b]{cccc}
\r
5232 \begin_layout Standard
\r
5233 The horizontal alignment specifies how the column entries should be aligned.
\r
5234 It is set by entering a letter for every column.
\r
5239 denotes left aligned,
\r
5248 To create for example a 4
\r
5253 \begin_inset space ~
\r
5256 matrix where the first column is left aligned, the second and third are
\r
5257 centered and the last one is right aligned, one enters for the horizontal
\r
5263 Normally in a matrix all columns are centered, therefore the default for
\r
5264 every column is a
\r
5271 \begin_layout Standard
\r
5272 Horizontal alignment:
\r
5275 \begin_layout Standard
\r
5281 \begin_inset Formula $\begin{array}{lll}
\r
5293 \begin_inset Formula $\begin{array}{ccc}
\r
5305 \begin_inset Formula $\begin{array}{rrr}
\r
5315 \begin_layout Standard
\r
5316 To add or delete rows and columns subsequently, the math toolbar buttons
\r
5318 \begin_inset Graphics
\r
5319 filename ../images/tabular-feature_append-row.png
\r
5325 \begin_inset Graphics
\r
5326 filename ../images/tabular-feature_delete-row.png
\r
5332 \begin_inset space \thinspace{}
\r
5337 Edit\SpecialChar \menuseparator
\r
5341 New rows can also be created with
\r
5344 arg "newline-insert newline"
\r
5350 \begin_layout Standard
\r
5351 \begin_inset VSpace bigskip
\r
5358 adds parentheses in the selected style around the matrix.
\r
5359 Alternatively, parentheses can can either be created with the commands
\r
5367 \begin_inset Index idx
\r
5370 \begin_layout Plain Layout
\r
5385 \begin_inset Index idx
\r
5388 \begin_layout Plain Layout
\r
5399 \begin_inset space ~
\r
5405 \begin_inset CommandInset ref
\r
5407 reference "sub:Automatic-Bracket-Size"
\r
5411 , or by using the following commands:
\r
5412 \begin_inset VSpace medskip
\r
5418 \begin_layout Standard
\r
5419 \begin_inset space \hfill{}
\r
5423 \begin_inset Tabular
\r
5424 <lyxtabular version="3" rows="4" columns="2">
\r
5425 <features tabularvalignment="middle">
\r
5426 <column alignment="center" valignment="top" width="0">
\r
5427 <column alignment="center" valignment="top" width="0">
\r
5429 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
5432 \begin_layout Plain Layout
\r
5438 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
5441 \begin_layout Plain Layout
\r
5443 \begin_inset Note Note
\r
5446 \begin_layout Plain Layout
\r
5453 is only used as spacer.
\r
5465 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
5468 \begin_layout Plain Layout
\r
5475 \begin_layout Plain Layout
\r
5489 \begin_inset space \thinspace{}
\r
5497 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
5500 \begin_layout Plain Layout
\r
5501 \begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
\r
5502 0 & \textrm{-}\mathrm{i}\\
\r
5504 \end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
\r
5514 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
5517 \begin_layout Plain Layout
\r
5524 \begin_layout Plain Layout
\r
5538 \begin_inset space \thinspace{}
\r
5546 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
5549 \begin_layout Plain Layout
\r
5550 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
\r
5551 0 & \textrm{-}\mathrm{i}\\
\r
5553 \end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
\r
5563 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
5566 \begin_layout Plain Layout
\r
5573 \begin_layout Plain Layout
\r
5587 \begin_inset space \thinspace{}
\r
5595 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
5598 \begin_layout Plain Layout
\r
5599 \begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
\r
5600 0 & \textrm{-}\mathrm{i}\\
\r
5602 \end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
\r
5616 \begin_inset space \hfill{}
\r
5620 \begin_inset Tabular
\r
5621 <lyxtabular version="3" rows="4" columns="2">
\r
5622 <features tabularvalignment="middle">
\r
5623 <column alignment="center" valignment="top" width="0">
\r
5624 <column alignment="center" valignment="top" width="0">
\r
5626 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
5629 \begin_layout Plain Layout
\r
5635 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
5638 \begin_layout Plain Layout
\r
5646 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
5649 \begin_layout Plain Layout
\r
5656 \begin_layout Plain Layout
\r
5670 \begin_inset space \thinspace{}
\r
5678 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
5681 \begin_layout Plain Layout
\r
5682 \begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
\r
5683 0 & \textrm{-}\mathrm{i}\\
\r
5685 \end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
\r
5695 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
5698 \begin_layout Plain Layout
\r
5705 \begin_layout Plain Layout
\r
5719 \begin_inset space \thinspace{}
\r
5727 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
5730 \begin_layout Plain Layout
\r
5731 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
\r
5732 0 & \textrm{-}\mathrm{i}\\
\r
5734 \end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
\r
5744 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
5747 \begin_layout Plain Layout
\r
5754 \begin_layout Plain Layout
\r
5768 \begin_inset space \thinspace{}
\r
5776 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
5779 \begin_layout Plain Layout
\r
5780 \begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
\r
5781 0 & \textrm{-}\mathrm{i}\\
\r
5783 \end{array}\end{matrix}\raisebox{-5.3mm}{}$
\r
5797 \begin_inset space \hfill{}
\r
5803 \begin_layout Standard
\r
5804 \begin_inset VSpace medskip
\r
5808 \begin_inset space \thinspace{}
\r
5812 \begin_inset space \space{}
\r
5821 is inserted, a blue box appears between two vertical lines where the matrix
\r
5823 \begin_inset Newline newline
\r
5826 Note that decorated matrices ignore the vertical alignment.
\r
5829 \begin_layout Standard
\r
5830 \begin_inset VSpace bigskip
\r
5833 As all multiline formulas are matrices, the length
\r
5840 \begin_inset Index idx
\r
5843 \begin_layout Plain Layout
\r
5851 that is described in
\r
5852 \begin_inset CommandInset ref
\r
5854 reference "sub:Column-Separation"
\r
5858 can also be used to change the column separation of matrices.
\r
5861 \begin_layout Standard
\r
5862 To change the row separation, the command
\r
5869 \begin_inset Index idx
\r
5872 \begin_layout Plain Layout
\r
5881 It is used as follows:
\r
5884 \begin_layout Standard
\r
5891 arraystretch}{stretch factor}
\r
5892 \begin_inset Index idx
\r
5895 \begin_layout Plain Layout
\r
5906 \begin_layout Standard
\r
5913 assigns the stretch factor to the predefined command
\r
5921 \begin_inset space \thinspace{}
\r
5925 \begin_inset space \space{}
\r
5928 the row separation, use the factor 2.
\r
5929 This is then used for all following matrices.
\r
5930 To go back to the original separation, assign the factor 1 to
\r
5939 \begin_layout Standard
\r
5940 To set matrices into a text line, the command
\r
5947 \begin_inset Index idx
\r
5950 \begin_layout Plain Layout
\r
5959 When it is inserted a blue box with two dashed lines appears.
\r
5960 In this box the matrix is inserted.
\r
5963 \begin_layout Standard
\r
5965 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
\r
5967 \end{smallmatrix}\right)$
\r
5973 \begin_layout Section
\r
5974 Brackets and Delimiters
\r
5975 \begin_inset Index idx
\r
5978 \begin_layout Plain Layout
\r
5985 \begin_inset Index idx
\r
5988 \begin_layout Plain Layout
\r
5997 \begin_layout Subsection
\r
5998 Vertical Brackets and Delimiters
\r
5999 \begin_inset Index idx
\r
6002 \begin_layout Plain Layout
\r
6003 Brackets ! vertical
\r
6011 \begin_layout Standard
\r
6012 \begin_inset space \hfill{}
\r
6016 \begin_inset Tabular
\r
6017 <lyxtabular version="3" rows="9" columns="2">
\r
6018 <features tabularvalignment="middle">
\r
6019 <column alignment="center" valignment="top" width="0pt">
\r
6020 <column alignment="center" valignment="top" width="0pt">
\r
6022 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
6025 \begin_layout Plain Layout
\r
6031 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
6034 \begin_layout Plain Layout
\r
6042 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
6045 \begin_layout Plain Layout
\r
6051 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
6054 \begin_layout Plain Layout
\r
6055 \begin_inset Formula $($
\r
6065 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
6068 \begin_layout Plain Layout
\r
6074 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
6077 \begin_layout Plain Layout
\r
6078 \begin_inset Formula $\{$
\r
6088 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
6091 \begin_layout Plain Layout
\r
6097 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
6100 \begin_layout Plain Layout
\r
6101 \begin_inset Formula $[$
\r
6111 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
6114 \begin_layout Plain Layout
\r
6122 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
6125 \begin_layout Plain Layout
\r
6126 \begin_inset Formula $\langle$
\r
6136 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
6139 \begin_layout Plain Layout
\r
6147 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
6150 \begin_layout Plain Layout
\r
6151 \begin_inset Formula $\lceil$
\r
6161 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
6164 \begin_layout Plain Layout
\r
6172 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
6175 \begin_layout Plain Layout
\r
6176 \begin_inset Formula $\lfloor$
\r
6186 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
6189 \begin_layout Plain Layout
\r
6195 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
6198 \begin_layout Plain Layout
\r
6199 \begin_inset Formula $/$
\r
6209 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
6212 \begin_layout Plain Layout
\r
6218 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
6221 \begin_layout Plain Layout
\r
6222 \begin_inset Formula $|$
\r
6236 \begin_inset space \hfill{}
\r
6240 \begin_inset Tabular
\r
6241 <lyxtabular version="3" rows="9" columns="2">
\r
6242 <features tabularvalignment="middle">
\r
6243 <column alignment="center" valignment="top" width="0pt">
\r
6244 <column alignment="center" valignment="top" width="0pt">
\r
6246 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
6249 \begin_layout Plain Layout
\r
6255 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
6258 \begin_layout Plain Layout
\r
6266 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
6269 \begin_layout Plain Layout
\r
6275 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
6278 \begin_layout Plain Layout
\r
6279 \begin_inset Formula $)$
\r
6289 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
6292 \begin_layout Plain Layout
\r
6298 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
6301 \begin_layout Plain Layout
\r
6302 \begin_inset Formula $\}$
\r
6312 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
6315 \begin_layout Plain Layout
\r
6321 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
6324 \begin_layout Plain Layout
\r
6325 \begin_inset Formula $]$
\r
6335 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
6338 \begin_layout Plain Layout
\r
6346 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
6349 \begin_layout Plain Layout
\r
6350 \begin_inset Formula $\rangle$
\r
6360 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
6363 \begin_layout Plain Layout
\r
6371 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
6374 \begin_layout Plain Layout
\r
6375 \begin_inset Formula $\rceil$
\r
6385 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
6388 \begin_layout Plain Layout
\r
6396 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
6399 \begin_layout Plain Layout
\r
6400 \begin_inset Formula $\rfloor$
\r
6410 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
6413 \begin_layout Plain Layout
\r
6423 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
6426 \begin_layout Plain Layout
\r
6427 \begin_inset Formula $\backslash$
\r
6437 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
6440 \begin_layout Plain Layout
\r
6448 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
6451 \begin_layout Plain Layout
\r
6452 \begin_inset Formula $\|$
\r
6466 \begin_inset space \hfill{}
\r
6472 \begin_layout Standard
\r
6475 \begin_inset Note Greyedout
\r
6478 \begin_layout Plain Layout
\r
6483 In TeX-mode the command
\r
6490 \begin_inset Index idx
\r
6493 \begin_layout Plain Layout
\r
6501 must be used for the backslash, because the command
\r
6509 produces a line break there.
\r
6517 \begin_layout Standard
\r
6518 For all characters listed above the size can be adjusted with the commands
\r
6519 described in the following two subsections.
\r
6520 When using these commands, the characters < and > can directly be used
\r
6521 instead of the commands
\r
6536 \begin_layout Subsubsection
\r
6537 Manual Bracket Size
\r
6538 \begin_inset CommandInset label
\r
6539 LatexCommand label
\r
6540 name "sub:Manual-Bracket-Size"
\r
6545 \begin_inset Index idx
\r
6548 \begin_layout Plain Layout
\r
6549 Bracket size ! manual
\r
6557 \begin_layout Standard
\r
6558 The bracket size can be specified manually by the LaTeX-commands
\r
6565 \begin_inset Index idx
\r
6568 \begin_layout Plain Layout
\r
6601 denotes the smallest and
\r
6607 the largest bracket size.
\r
6610 \begin_layout Standard
\r
6611 These commands are used to emphasize levels of brackets:
\r
6614 \begin_layout Standard
\r
6616 \begin_inset Tabular
\r
6617 <lyxtabular version="3" rows="2" columns="2">
\r
6618 <features tabularvalignment="middle">
\r
6619 <column alignment="center" valignment="top" width="0pt">
\r
6620 <column alignment="center" valignment="top" width="0pt">
\r
6622 <cell alignment="center" valignment="top" usebox="none">
\r
6625 \begin_layout Plain Layout
\r
6626 all brackets in the same size:
\r
6631 <cell alignment="center" valignment="top" usebox="none">
\r
6634 \begin_layout Plain Layout
\r
6635 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
\r
6645 <cell alignment="center" valignment="top" usebox="none">
\r
6648 \begin_layout Plain Layout
\r
6649 this looks better:
\r
6654 <cell alignment="center" valignment="top" usebox="none">
\r
6657 \begin_layout Plain Layout
\r
6658 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
\r
6672 \begin_inset Note Note
\r
6675 \begin_layout Plain Layout
\r
6682 is only used as spacer.
\r
6690 \begin_layout Standard
\r
6691 For the second formula the command
\r
6701 \begin_layout Plain Layout
\r
6715 \begin_layout Standard
\r
6716 Here is an overview about all bracket sizes:
\r
6719 \begin_layout Standard
\r
6739 \begin_layout Plain Layout
\r
6756 \begin_layout Plain Layout
\r
6769 \begin_layout Plain Layout
\r
6785 \begin_layout Standard
\r
6787 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
\r
6793 \begin_layout Standard
\r
6800 -commands there is the variant
\r
6807 \begin_inset Index idx
\r
6810 \begin_layout Plain Layout
\r
6818 that adds a bit more space between the bracket and its content, and the
\r
6832 \begin_inset Index idx
\r
6835 \begin_layout Plain Layout
\r
6845 , that don't add additional space.
\r
6850 at the end of the command
\r
6856 is for a left bracket; for a right bracket this will be replaced by an
\r
6862 A left or right bracket can each be an opening or closing bracket.
\r
6865 \begin_layout Standard
\r
6866 In the following table is a comparison of the variants:
\r
6869 \begin_layout Standard
\r
6871 \begin_inset Tabular
\r
6872 <lyxtabular version="3" rows="5" columns="2">
\r
6873 <features tabularvalignment="middle">
\r
6874 <column alignment="center" valignment="middle" width="0">
\r
6875 <column alignment="center" valignment="middle" width="0">
\r
6877 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
6880 \begin_layout Plain Layout
\r
6886 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
6889 \begin_layout Plain Layout
\r
6891 \begin_inset Note Note
\r
6894 \begin_layout Plain Layout
\r
6901 is only used as spacer.
\r
6913 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
6916 \begin_layout Plain Layout
\r
6931 \begin_layout Plain Layout
\r
6949 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
6952 \begin_layout Plain Layout
\r
6953 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
\r
6963 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
6966 \begin_layout Plain Layout
\r
6981 \begin_layout Plain Layout
\r
6999 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
7002 \begin_layout Plain Layout
\r
7003 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
\r
7013 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
7016 \begin_layout Plain Layout
\r
7031 \begin_layout Plain Layout
\r
7049 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
7052 \begin_layout Plain Layout
\r
7053 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
\r
7063 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
7066 \begin_layout Plain Layout
\r
7078 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
7081 \begin_layout Plain Layout
\r
7082 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
\r
7098 \begin_layout Subsubsection
\r
7099 Automatic Bracket Size
\r
7100 \begin_inset CommandInset label
\r
7101 LatexCommand label
\r
7102 name "sub:Automatic-Bracket-Size"
\r
7107 \begin_inset Index idx
\r
7110 \begin_layout Plain Layout
\r
7111 Bracket size ! automatic
\r
7119 \begin_layout Standard
\r
7120 Brackets with variable size can be inserted with the commands
\r
7127 \begin_inset Index idx
\r
7130 \begin_layout Plain Layout
\r
7145 \begin_inset Index idx
\r
7148 \begin_layout Plain Layout
\r
7156 or via the math toolbar button
\r
7157 \begin_inset Graphics
\r
7158 filename ../images/dialog-show_mathdelimiter.png
\r
7176 the wanted bracket must be inserted.
\r
7177 The bracket size will then automatically be calculated for the output.
\r
7180 \begin_layout Standard
\r
7182 normal bracket: The command
\r
7192 \begin_layout Plain Layout
\r
7202 \begin_inset Formula $\downarrow$
\r
7209 \begin_layout Plain Layout
\r
7221 \begin_inset Formula
\r
7231 \begin_layout Standard
\r
7233 multiline bracket: The command
\r
7245 \begin_layout Plain Layout
\r
7255 \begin_inset Formula $\downarrow$
\r
7262 \begin_layout Plain Layout
\r
7276 \begin_inset Formula
\r
7278 \ln\left(\frac{A}{C}\right)
\r
7286 \begin_layout Standard
\r
7302 \begin_inset space ~
\r
7308 This has the advantage that you can see in LyX immediately the real bracket
\r
7309 size and that the matching right bracket will be created too.
\r
7310 \begin_inset Newline newline
\r
7313 The command for the last example would then be:
\r
7327 \begin_layout Plain Layout
\r
7337 \begin_inset Formula $\downarrow$
\r
7343 \begin_layout Standard
\r
7344 To omit a left or right bracket, a dot is inserted for the omitted bracket.
\r
7345 For example the command
\r
7355 \begin_layout Plain Layout
\r
7365 \begin_inset Formula $\downarrow$
\r
7372 \begin_layout Plain Layout
\r
7388 \begin_inset Formula
\r
7390 \left.\frac{A}{B}\right\}
\r
7409 will be converted by LyX to brackets in the right size when the document
\r
7410 is reloaded and an omitted bracket will appear as dashed line.
\r
7413 \begin_layout Standard
\r
7414 \begin_inset VSpace bigskip
\r
7417 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
\r
7425 \begin_inset Index idx
\r
7428 \begin_layout Plain Layout
\r
7436 is additionally available for all brackets and limits.
\r
7437 With this command the height of the following character is adapted to the
\r
7438 one of the surrounding brackets, what is e.
\r
7439 \begin_inset space \thinspace{}
\r
7443 \begin_inset space \space{}
\r
7446 needed for physical vectors:
\r
7447 \begin_inset Formula
\r
7449 \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle
\r
7454 For physical vectors there is a special LaTeX-package, described in
\r
7455 \begin_inset CommandInset ref
\r
7457 reference "sub:Physical-Vectors"
\r
7464 \begin_layout Subsection
\r
7465 Horizontal Brackets
\r
7466 \begin_inset Index idx
\r
7469 \begin_layout Plain Layout
\r
7470 Brackets ! horizontal
\r
7478 \begin_layout Standard
\r
7480 \begin_inset Tabular
\r
7481 <lyxtabular version="3" rows="4" columns="2">
\r
7482 <features tabularvalignment="middle">
\r
7483 <column alignment="center" valignment="top" width="0pt">
\r
7484 <column alignment="center" valignment="top" width="0pt">
\r
7486 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
7489 \begin_layout Plain Layout
\r
7491 \begin_inset Note Note
\r
7494 \begin_layout Plain Layout
\r
7501 is only used as spacer.
\r
7511 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
7514 \begin_layout Plain Layout
\r
7522 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
7525 \begin_layout Plain Layout
\r
7529 \begin_layout Plain Layout
\r
7544 \begin_layout Plain Layout
\r
7557 \begin_layout Plain Layout
\r
7570 \begin_layout Plain Layout
\r
7583 \begin_layout Plain Layout
\r
7591 \begin_inset Index idx
\r
7594 \begin_layout Plain Layout
\r
7607 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
7610 \begin_layout Plain Layout
\r
7611 \begin_inset Formula $\overbrace{A+B}^{3}$
\r
7621 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
7624 \begin_layout Plain Layout
\r
7628 \begin_layout Plain Layout
\r
7643 \begin_layout Plain Layout
\r
7656 \begin_layout Plain Layout
\r
7669 \begin_layout Plain Layout
\r
7677 \begin_inset Index idx
\r
7680 \begin_layout Plain Layout
\r
7693 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
7696 \begin_layout Plain Layout
\r
7697 \begin_inset Formula $\underbrace{A+B}_{5}$
\r
7707 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
7710 \begin_layout Plain Layout
\r
7717 \begin_layout Plain Layout
\r
7732 \begin_layout Plain Layout
\r
7745 \begin_layout Plain Layout
\r
7758 \begin_layout Plain Layout
\r
7771 \begin_layout Plain Layout
\r
7784 \begin_layout Plain Layout
\r
7797 \begin_layout Plain Layout
\r
7811 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
7814 \begin_layout Plain Layout
\r
7815 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
\r
7831 \begin_layout Standard
\r
7832 In the last example it doesn't matter if
\r
7844 is inserted at first.
\r
7847 \begin_layout Standard
\r
7848 \begin_inset VSpace bigskip
\r
7851 When brackets are needed that overlap each other, multiline formulas, as
\r
7853 \begin_inset CommandInset ref
\r
7855 reference "sec:Multiline-Formulas"
\r
7860 \begin_inset Formula
\r
7862 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
\r
7863 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
\r
7868 In the first row the formula is inserted together with the first brace.
\r
7869 It is hereby important that the space command
\r
7873 \begin_layout Plain Layout
\r
7874 Space commands are explained in
\r
7875 \begin_inset CommandInset ref
\r
7877 reference "sub:Predefined-Space"
\r
7892 is inserted before the first
\r
7893 \begin_inset Formula $d$
\r
7896 , because the brace that ends behind the
\r
7897 \begin_inset Formula $q$
\r
7900 prevents that the following
\r
7901 \begin_inset Quotes eld
\r
7905 \begin_inset Quotes erd
\r
7908 is surrounded by space.
\r
7912 \begin_layout Plain Layout
\r
7913 because a bracket is not handled as a character, see
\r
7914 \begin_inset CommandInset ref
\r
7916 reference "sub:Binary-Operators"
\r
7925 In the second row the second brace is inserted.
\r
7926 As it should begin before the
\r
7927 \begin_inset Formula $b$
\r
7930 , first the command
\r
7942 \begin_layout Plain Layout
\r
7950 \begin_inset CommandInset ref
\r
7952 reference "sub:Placeholders"
\r
7961 This space is needed because the
\r
7962 \begin_inset Quotes eld
\r
7966 \begin_inset Quotes erd
\r
7969 is also surrounded by space in the formula.
\r
7970 The brace is placed under the command
\r
7974 hphantom{bbqq+dddd}
\r
7979 \begin_layout Standard
\r
7980 It gets more complicated when brackets overlap each other, like in the following
\r
7985 \begin_layout Plain Layout
\r
7997 \begin_inset Formula
\r
7999 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
\r
8000 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd
\r
8009 \begin_layout Plain Layout
\r
8020 The first formula row is the same as the second row of the previous example,
\r
8021 with the difference that the brace is above.
\r
8022 The second row contains the formula together with the second brace.
\r
8023 To avoid that there is space between the upper brace in the first row and
\r
8024 the formula, the row spacing needs to be reduced.
\r
8025 This is not easily possible due to a bug in LyX
\r
8029 \begin_layout Plain Layout
\r
8030 \begin_inset CommandInset href
\r
8032 name "LyX-bug #1505"
\r
8033 target "http://www.lyx.org/trac/ticket/1505"
\r
8043 As a solution for the problem, the global formula row separation
\r
8050 \begin_inset Index idx
\r
8053 \begin_layout Plain Layout
\r
8061 must be changed to -6
\r
8062 \begin_inset space \thinspace{}
\r
8065 pt before the formula with the command
\r
8080 is set back after the formula to the standard value of 3
\r
8081 \begin_inset space \thinspace{}
\r
8084 pt using the same command.
\r
8085 More about the row separation in formulas is explained in
\r
8086 \begin_inset CommandInset ref
\r
8088 reference "sub:Line-Separation"
\r
8095 \begin_layout Section
\r
8097 \begin_inset Index idx
\r
8100 \begin_layout Plain Layout
\r
8109 \begin_layout Standard
\r
8110 Arrows can be inserted via the math toolbar button
\r
8111 \begin_inset Graphics
\r
8112 filename ../images/math/leftarrow.png
\r
8117 or the commands listed in the following subsections.
\r
8120 \begin_layout Subsection
\r
8122 \begin_inset Index idx
\r
8125 \begin_layout Plain Layout
\r
8126 Arrows ! horizontal
\r
8134 \begin_layout Standard
\r
8135 \begin_inset space \hfill{}
\r
8139 \begin_inset Tabular
\r
8140 <lyxtabular version="3" rows="8" columns="2">
\r
8141 <features tabularvalignment="middle">
\r
8142 <column alignment="center" valignment="top" width="0pt">
\r
8143 <column alignment="center" valignment="top" width="0pt">
\r
8145 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
8148 \begin_layout Plain Layout
\r
8154 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
8157 \begin_layout Plain Layout
\r
8165 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
8168 \begin_layout Plain Layout
\r
8176 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
8179 \begin_layout Plain Layout
\r
8180 \begin_inset Formula $\gets$
\r
8190 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
8193 \begin_layout Plain Layout
\r
8201 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
8204 \begin_layout Plain Layout
\r
8205 \begin_inset Formula $\Leftarrow$
\r
8215 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
8218 \begin_layout Plain Layout
\r
8226 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
8229 \begin_layout Plain Layout
\r
8230 \begin_inset Formula $\longleftarrow$
\r
8240 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
8243 \begin_layout Plain Layout
\r
8251 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
8254 \begin_layout Plain Layout
\r
8255 \begin_inset Formula $\Longleftarrow$
\r
8265 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
8268 \begin_layout Plain Layout
\r
8276 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
8279 \begin_layout Plain Layout
\r
8280 \begin_inset Formula $\leftharpoonup$
\r
8290 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
8293 \begin_layout Plain Layout
\r
8301 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
8304 \begin_layout Plain Layout
\r
8305 \begin_inset Formula $\leftharpoondown$
\r
8315 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
8318 \begin_layout Plain Layout
\r
8326 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
8329 \begin_layout Plain Layout
\r
8330 \begin_inset Formula $\hookleftarrow$
\r
8344 \begin_inset space \hfill{}
\r
8348 \begin_inset Tabular
\r
8349 <lyxtabular version="3" rows="8" columns="2">
\r
8350 <features tabularvalignment="middle">
\r
8351 <column alignment="center" valignment="top" width="0pt">
\r
8352 <column alignment="center" valignment="top" width="0pt">
\r
8354 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
8357 \begin_layout Plain Layout
\r
8363 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
8366 \begin_layout Plain Layout
\r
8374 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
8377 \begin_layout Plain Layout
\r
8385 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
8388 \begin_layout Plain Layout
\r
8389 \begin_inset Formula $\to$
\r
8399 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
8402 \begin_layout Plain Layout
\r
8410 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
8413 \begin_layout Plain Layout
\r
8414 \begin_inset Formula $\Rightarrow$
\r
8424 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
8427 \begin_layout Plain Layout
\r
8435 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
8438 \begin_layout Plain Layout
\r
8439 \begin_inset Formula $\longrightarrow$
\r
8449 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
8452 \begin_layout Plain Layout
\r
8460 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
8463 \begin_layout Plain Layout
\r
8464 \begin_inset Formula $\Longrightarrow$
\r
8474 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
8477 \begin_layout Plain Layout
\r
8485 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
8488 \begin_layout Plain Layout
\r
8489 \begin_inset Formula $\rightharpoonup$
\r
8499 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
8502 \begin_layout Plain Layout
\r
8510 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
8513 \begin_layout Plain Layout
\r
8514 \begin_inset Formula $\rightharpoondown$
\r
8524 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
8527 \begin_layout Plain Layout
\r
8535 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
8538 \begin_layout Plain Layout
\r
8539 \begin_inset Formula $\hookrightarrow$
\r
8553 \begin_inset space \hfill{}
\r
8559 \begin_layout Standard
\r
8560 \begin_inset space \hfill{}
\r
8564 \begin_inset Tabular
\r
8565 <lyxtabular version="3" rows="6" columns="2">
\r
8566 <features tabularvalignment="middle">
\r
8567 <column alignment="center" valignment="top" width="0pt">
\r
8568 <column alignment="center" valignment="top" width="0pt">
\r
8570 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
8573 \begin_layout Plain Layout
\r
8579 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
8582 \begin_layout Plain Layout
\r
8590 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
8593 \begin_layout Plain Layout
\r
8601 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
8604 \begin_layout Plain Layout
\r
8605 \begin_inset Formula $\leftrightarrow$
\r
8615 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
8618 \begin_layout Plain Layout
\r
8626 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
8629 \begin_layout Plain Layout
\r
8630 \begin_inset Formula $\Leftrightarrow$
\r
8640 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
8643 \begin_layout Plain Layout
\r
8646 longleftrightarrow
\r
8651 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
8654 \begin_layout Plain Layout
\r
8655 \begin_inset Formula $\longleftrightarrow$
\r
8665 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
8668 \begin_layout Plain Layout
\r
8671 Longleftrightarrow
\r
8676 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
8679 \begin_layout Plain Layout
\r
8680 \begin_inset Formula $\Longleftrightarrow$
\r
8690 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
8693 \begin_layout Plain Layout
\r
8701 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
8704 \begin_layout Plain Layout
\r
8705 \begin_inset Formula $\rightleftharpoons$
\r
8719 \begin_inset space \hspace{}
\r
8724 \begin_inset space \hfill{}
\r
8728 \begin_inset Tabular
\r
8729 <lyxtabular version="3" rows="5" columns="2">
\r
8730 <features tabularvalignment="middle">
\r
8731 <column alignment="center" valignment="top" width="0pt">
\r
8732 <column alignment="center" valignment="top" width="0pt">
\r
8734 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
8737 \begin_layout Plain Layout
\r
8743 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
8746 \begin_layout Plain Layout
\r
8754 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
8757 \begin_layout Plain Layout
\r
8765 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
8768 \begin_layout Plain Layout
\r
8769 \begin_inset Formula $\mapsto$
\r
8779 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
8782 \begin_layout Plain Layout
\r
8790 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
8793 \begin_layout Plain Layout
\r
8794 \begin_inset Formula $\longmapsto$
\r
8804 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
8807 \begin_layout Plain Layout
\r
8815 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
8818 \begin_layout Plain Layout
\r
8819 \begin_inset Formula $\leadsto$
\r
8829 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
8832 \begin_layout Plain Layout
\r
8840 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
8843 \begin_layout Plain Layout
\r
8844 \begin_inset Formula $\dasharrow$
\r
8858 \begin_inset space \hfill{}
\r
8864 \begin_layout Standard
\r
8865 \begin_inset VSpace medskip
\r
8868 Arrows used as accents like e.
\r
8869 \begin_inset space \thinspace{}
\r
8873 \begin_inset space \space{}
\r
8876 vector arrows are listed in
\r
8877 \begin_inset CommandInset ref
\r
8879 reference "sec:Accents"
\r
8886 \begin_layout Standard
\r
8887 \begin_inset VSpace bigskip
\r
8890 Furthermore there are the labeled arrows
\r
8891 \begin_inset Index idx
\r
8894 \begin_layout Plain Layout
\r
8907 \begin_inset Index idx
\r
8910 \begin_layout Plain Layout
\r
8925 \begin_inset Index idx
\r
8928 \begin_layout Plain Layout
\r
8935 \begin_layout Plain Layout
\r
8950 When inserting one of these commands in a formula, an arrow with two blue
\r
8951 boxes appear where the label can be inserted.
\r
8952 The length of the arrow adapts to the label width.
\r
8955 \begin_layout Standard
\r
8957 \begin_inset Tabular
\r
8958 <lyxtabular version="3" rows="3" columns="2">
\r
8959 <features tabularvalignment="middle">
\r
8960 <column alignment="center" valignment="top" width="0pt">
\r
8961 <column alignment="center" valignment="top" width="0pt">
\r
8963 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
8966 \begin_layout Plain Layout
\r
8972 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
8975 \begin_layout Plain Layout
\r
8977 \begin_inset Note Note
\r
8980 \begin_layout Plain Layout
\r
8987 is only used as spacer.
\r
8999 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
9002 \begin_layout Plain Layout
\r
9009 \begin_layout Plain Layout
\r
9019 \begin_inset Formula $\downarrow$
\r
9023 \begin_inset Formula $\to$
\r
9031 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
9034 \begin_layout Plain Layout
\r
9035 \begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
\r
9045 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
9048 \begin_layout Plain Layout
\r
9055 \begin_layout Plain Layout
\r
9065 \begin_inset Formula $\downarrow$
\r
9069 \begin_inset Formula $\to$
\r
9077 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
9080 \begin_layout Plain Layout
\r
9081 \begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
\r
9097 \begin_layout Subsection
\r
9098 Vertical and diagonal Arrows
\r
9099 \begin_inset Index idx
\r
9102 \begin_layout Plain Layout
\r
9109 \begin_inset Index idx
\r
9112 \begin_layout Plain Layout
\r
9121 \begin_layout Standard
\r
9122 \begin_inset space \hfill{}
\r
9126 \begin_inset Tabular
\r
9127 <lyxtabular version="3" rows="7" columns="2">
\r
9128 <features tabularvalignment="middle">
\r
9129 <column alignment="center" valignment="top" width="0pt">
\r
9130 <column alignment="center" valignment="top" width="0pt">
\r
9132 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
9135 \begin_layout Plain Layout
\r
9141 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
9144 \begin_layout Plain Layout
\r
9152 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
9155 \begin_layout Plain Layout
\r
9163 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
9166 \begin_layout Plain Layout
\r
9167 \begin_inset Formula $\uparrow$
\r
9177 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
9180 \begin_layout Plain Layout
\r
9188 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
9191 \begin_layout Plain Layout
\r
9192 \begin_inset Formula $\Uparrow$
\r
9202 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
9205 \begin_layout Plain Layout
\r
9213 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
9216 \begin_layout Plain Layout
\r
9217 \begin_inset Formula $\updownarrow$
\r
9227 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
9230 \begin_layout Plain Layout
\r
9238 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
9241 \begin_layout Plain Layout
\r
9242 \begin_inset Formula $\Updownarrow$
\r
9252 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
9255 \begin_layout Plain Layout
\r
9263 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
9266 \begin_layout Plain Layout
\r
9267 \begin_inset Formula $\Downarrow$
\r
9277 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
9280 \begin_layout Plain Layout
\r
9288 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
9291 \begin_layout Plain Layout
\r
9292 \begin_inset Formula $\downarrow$
\r
9306 \begin_inset space \hfill{}
\r
9310 \begin_inset Tabular
\r
9311 <lyxtabular version="3" rows="5" columns="2">
\r
9312 <features tabularvalignment="middle">
\r
9313 <column alignment="center" valignment="top" width="0pt">
\r
9314 <column alignment="center" valignment="top" width="0pt">
\r
9316 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
9319 \begin_layout Plain Layout
\r
9325 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
9328 \begin_layout Plain Layout
\r
9336 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
9339 \begin_layout Plain Layout
\r
9347 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
9350 \begin_layout Plain Layout
\r
9351 \begin_inset Formula $\nearrow$
\r
9361 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
9364 \begin_layout Plain Layout
\r
9372 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
9375 \begin_layout Plain Layout
\r
9376 \begin_inset Formula $\searrow$
\r
9386 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
9389 \begin_layout Plain Layout
\r
9397 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
9400 \begin_layout Plain Layout
\r
9401 \begin_inset Formula $\swarrow$
\r
9411 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
9414 \begin_layout Plain Layout
\r
9422 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
9425 \begin_layout Plain Layout
\r
9426 \begin_inset Formula $\nwarrow$
\r
9440 \begin_inset space \hfill{}
\r
9446 \begin_layout Standard
\r
9447 \begin_inset VSpace medskip
\r
9450 Vertical arrows can be used also as delimiters together with the commands
\r
9452 \begin_inset CommandInset ref
\r
9454 reference "sub:Manual-Bracket-Size"
\r
9459 \begin_inset CommandInset ref
\r
9461 reference "sub:Automatic-Bracket-Size"
\r
9468 \begin_layout Section
\r
9470 \begin_inset CommandInset label
\r
9471 LatexCommand label
\r
9472 name "sec:Accents"
\r
9477 \begin_inset Index idx
\r
9480 \begin_layout Plain Layout
\r
9489 \begin_layout Standard
\r
9490 Accents can be inserted via the math toolbar button
\r
9491 \begin_inset Graphics
\r
9492 filename ../images/math/hat.png
\r
9497 or the commands listed in the following subsections.
\r
9500 \begin_layout Subsection
\r
9501 Accents for one Character
\r
9505 \begin_layout Plain Layout
\r
9518 \begin_layout Plain Layout
\r
9519 accents in text see
\r
9520 \begin_inset CommandInset ref
\r
9522 reference "sub:Accents-in-Text"
\r
9535 \begin_layout Plain Layout
\r
9543 \begin_inset Note Note
\r
9546 \begin_layout Plain Layout
\r
9553 is used to avoid that the footnote appears in the PDF-bookmark.
\r
9556 \begin_layout Plain Layout
\r
9564 \begin_inset CommandInset ref
\r
9566 reference "sub:Formulas-in-Section"
\r
9576 \begin_inset CommandInset label
\r
9577 LatexCommand label
\r
9578 name "sub:Accents-for-one"
\r
9583 \begin_inset Index idx
\r
9586 \begin_layout Plain Layout
\r
9587 Accents ! for one character
\r
9595 \begin_layout Standard
\r
9596 \begin_inset space \hfill{}
\r
9600 \begin_inset Tabular
\r
9601 <lyxtabular version="3" rows="8" columns="2">
\r
9602 <features tabularvalignment="middle">
\r
9603 <column alignment="center" valignment="top" width="0pt">
\r
9604 <column alignment="center" valignment="top" width="0pt">
\r
9606 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
9609 \begin_layout Plain Layout
\r
9615 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
9618 \begin_layout Plain Layout
\r
9620 \begin_inset Note Note
\r
9623 \begin_layout Plain Layout
\r
9630 is only used as spacer.
\r
9642 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
9645 \begin_layout Plain Layout
\r
9652 \begin_layout Plain Layout
\r
9666 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
9669 \begin_layout Plain Layout
\r
9670 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
\r
9680 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
9683 \begin_layout Plain Layout
\r
9690 \begin_layout Plain Layout
\r
9704 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
9707 \begin_layout Plain Layout
\r
9708 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
\r
9718 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
9721 \begin_layout Plain Layout
\r
9728 \begin_layout Plain Layout
\r
9742 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
9745 \begin_layout Plain Layout
\r
9746 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
\r
9756 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
9759 \begin_layout Plain Layout
\r
9766 \begin_layout Plain Layout
\r
9780 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
9783 \begin_layout Plain Layout
\r
9784 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
\r
9794 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
9797 \begin_layout Plain Layout
\r
9804 \begin_layout Plain Layout
\r
9814 \begin_inset Index idx
\r
9817 \begin_layout Plain Layout
\r
9828 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
9831 \begin_layout Plain Layout
\r
9832 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
\r
9842 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
9845 \begin_layout Plain Layout
\r
9852 \begin_layout Plain Layout
\r
9866 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
9869 \begin_layout Plain Layout
\r
9870 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
\r
9880 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
9883 \begin_layout Plain Layout
\r
9890 \begin_layout Plain Layout
\r
9904 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
9907 \begin_layout Plain Layout
\r
9908 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
\r
9922 \begin_inset space \hfill{}
\r
9926 \begin_inset Tabular
\r
9927 <lyxtabular version="3" rows="7" columns="2">
\r
9928 <features tabularvalignment="middle">
\r
9929 <column alignment="center" valignment="top" width="0pt">
\r
9930 <column alignment="center" valignment="top" width="0pt">
\r
9932 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
9935 \begin_layout Plain Layout
\r
9941 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
9944 \begin_layout Plain Layout
\r
9952 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
9955 \begin_layout Plain Layout
\r
9962 \begin_layout Plain Layout
\r
9976 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
9979 \begin_layout Plain Layout
\r
9980 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
\r
9990 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
9993 \begin_layout Plain Layout
\r
10000 \begin_layout Plain Layout
\r
10014 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
10015 \begin_inset Text
\r
10017 \begin_layout Plain Layout
\r
10018 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
\r
10028 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
10029 \begin_inset Text
\r
10031 \begin_layout Plain Layout
\r
10038 \begin_layout Plain Layout
\r
10052 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
10053 \begin_inset Text
\r
10055 \begin_layout Plain Layout
\r
10056 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
\r
10066 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
10067 \begin_inset Text
\r
10069 \begin_layout Plain Layout
\r
10076 \begin_layout Plain Layout
\r
10090 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
10091 \begin_inset Text
\r
10093 \begin_layout Plain Layout
\r
10094 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
\r
10104 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
10105 \begin_inset Text
\r
10107 \begin_layout Plain Layout
\r
10114 \begin_layout Plain Layout
\r
10128 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
10129 \begin_inset Text
\r
10131 \begin_layout Plain Layout
\r
10132 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
\r
10142 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
10143 \begin_inset Text
\r
10145 \begin_layout Plain Layout
\r
10152 \begin_layout Plain Layout
\r
10166 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
10167 \begin_inset Text
\r
10169 \begin_layout Plain Layout
\r
10170 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
\r
10184 \begin_inset space \hfill{}
\r
10190 \begin_layout Standard
\r
10191 \begin_inset VSpace bigskip
\r
10197 \begin_layout Standard
\r
10198 You can directly insert accents like é to formulas.
\r
10199 LyX will transform them to the corresponding accent command.
\r
10201 \begin_inset Index idx
\r
10204 \begin_layout Plain Layout
\r
10210 it is better to insert a quotation mark before the vowel.
\r
10211 These two characters are then treated by LaTeX as
\r
10215 character when the formula part with the umlaut is marked as German.
\r
10222 , with this method
\r
10223 \begin_inset Quotes eld
\r
10227 \begin_inset Quotes erd
\r
10230 umlauts are created as demonstrated in the following example:
\r
10233 \begin_layout Standard
\r
10234 \begin_inset VSpace -2mm
\r
10240 \begin_layout Standard
\r
10242 \begin_inset Tabular
\r
10243 <lyxtabular version="3" rows="3" columns="2">
\r
10244 <features tabularvalignment="middle">
\r
10245 <column alignment="center" valignment="top" width="0">
\r
10246 <column alignment="center" valignment="top" width="0">
\r
10248 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
10249 \begin_inset Text
\r
10251 \begin_layout Plain Layout
\r
10257 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
10258 \begin_inset Text
\r
10260 \begin_layout Plain Layout
\r
10262 \begin_inset Note Note
\r
10265 \begin_layout Plain Layout
\r
10273 \begin_inset space \thinspace{}
\r
10276 pt space are only used as spacer.
\r
10288 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
10289 \begin_inset Text
\r
10291 \begin_layout Plain Layout
\r
10294 \begin_inset Quotes grd
\r
10302 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
10303 \begin_inset Text
\r
10305 \begin_layout Plain Layout
\r
10306 \begin_inset space \hspace{}
\r
10313 \begin_inset Formula $"i$
\r
10323 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
10324 \begin_inset Text
\r
10326 \begin_layout Plain Layout
\r
10333 \begin_layout Plain Layout
\r
10347 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
10348 \begin_inset Text
\r
10350 \begin_layout Plain Layout
\r
10351 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
\r
10367 \begin_layout Standard
\r
10368 Another advantage to
\r
10374 is that umlauts can directly be converted to mathematical text because
\r
10375 the accent commands above are
\r
10381 in mathematical text
\r
10384 To convert an accented character to mathematical text, only the character
\r
10385 under the accent may be converted.
\r
10386 This applies also for all other conversions, e.
\r
10387 \begin_inset space \thinspace{}
\r
10391 \begin_inset space \space{}
\r
10394 to italic or bold.
\r
10397 \begin_layout Standard
\r
10398 In mathematical text, umlauts and other accented characters can directly
\r
10402 \begin_layout Subsection
\r
10403 Accents for several Characters
\r
10404 \begin_inset Index idx
\r
10407 \begin_layout Plain Layout
\r
10408 Accents ! for several characters
\r
10416 \begin_layout Standard
\r
10417 \begin_inset space \hfill{}
\r
10421 \begin_inset Tabular
\r
10422 <lyxtabular version="3" rows="5" columns="2">
\r
10423 <features tabularvalignment="middle">
\r
10424 <column alignment="center" valignment="top" width="0pt">
\r
10425 <column alignment="center" valignment="top" width="0pt">
\r
10427 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
10428 \begin_inset Text
\r
10430 \begin_layout Plain Layout
\r
10436 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
10437 \begin_inset Text
\r
10439 \begin_layout Plain Layout
\r
10441 \begin_inset Note Note
\r
10444 \begin_layout Plain Layout
\r
10451 is only used as spacer.
\r
10463 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
10464 \begin_inset Text
\r
10466 \begin_layout Plain Layout
\r
10473 \begin_layout Plain Layout
\r
10487 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
10488 \begin_inset Text
\r
10490 \begin_layout Plain Layout
\r
10491 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
\r
10501 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
10502 \begin_inset Text
\r
10504 \begin_layout Plain Layout
\r
10511 \begin_layout Plain Layout
\r
10525 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
10526 \begin_inset Text
\r
10528 \begin_layout Plain Layout
\r
10529 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
\r
10539 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
10540 \begin_inset Text
\r
10542 \begin_layout Plain Layout
\r
10545 overleftrightarrow
\r
10549 \begin_layout Plain Layout
\r
10563 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
10564 \begin_inset Text
\r
10566 \begin_layout Plain Layout
\r
10567 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
\r
10577 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
10578 \begin_inset Text
\r
10580 \begin_layout Plain Layout
\r
10583 underleftrightarrow
\r
10587 \begin_layout Plain Layout
\r
10601 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
10602 \begin_inset Text
\r
10604 \begin_layout Plain Layout
\r
10605 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
\r
10619 \begin_inset space \hfill{}
\r
10623 \begin_inset Tabular
\r
10624 <lyxtabular version="3" rows="5" columns="2">
\r
10625 <features tabularvalignment="middle">
\r
10626 <column alignment="center" valignment="top" width="0pt">
\r
10627 <column alignment="center" valignment="top" width="0pt">
\r
10629 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
10630 \begin_inset Text
\r
10632 \begin_layout Plain Layout
\r
10638 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
10639 \begin_inset Text
\r
10641 \begin_layout Plain Layout
\r
10649 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
10650 \begin_inset Text
\r
10652 \begin_layout Plain Layout
\r
10659 \begin_layout Plain Layout
\r
10673 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
10674 \begin_inset Text
\r
10676 \begin_layout Plain Layout
\r
10677 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
\r
10687 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
10688 \begin_inset Text
\r
10690 \begin_layout Plain Layout
\r
10697 \begin_layout Plain Layout
\r
10711 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
10712 \begin_inset Text
\r
10714 \begin_layout Plain Layout
\r
10715 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
\r
10725 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
10726 \begin_inset Text
\r
10728 \begin_layout Plain Layout
\r
10735 \begin_layout Plain Layout
\r
10749 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
10750 \begin_inset Text
\r
10752 \begin_layout Plain Layout
\r
10753 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
\r
10763 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
10764 \begin_inset Text
\r
10766 \begin_layout Plain Layout
\r
10773 \begin_layout Plain Layout
\r
10787 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
10788 \begin_inset Text
\r
10790 \begin_layout Plain Layout
\r
10791 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
\r
10805 \begin_inset space \hfill{}
\r
10811 \begin_layout Standard
\r
10812 \begin_inset VSpace medskip
\r
10815 With these commands as many characters as you like can be accented.
\r
10828 will only be set in the output with a length of three characters, as shown
\r
10829 in the following example:
\r
10830 \begin_inset Formula
\r
10832 \widetilde{A+B=C-D}
\r
10840 \begin_layout Standard
\r
10841 With the commands
\r
10848 \begin_inset Index idx
\r
10851 \begin_layout Plain Layout
\r
10866 \begin_inset Index idx
\r
10869 \begin_layout Plain Layout
\r
10877 described in the previous subsection it is also possible to accent several
\r
10887 \begin_layout Plain Layout
\r
10897 \begin_inset Formula $\downarrow$
\r
10903 \begin_inset Formula
\r
10905 \underset{***}{A=B}
\r
10913 \begin_layout Standard
\r
10914 \begin_inset Newpage newpage
\r
10920 \begin_layout Section
\r
10922 \begin_inset CommandInset label
\r
10923 LatexCommand label
\r
10929 \begin_inset Index idx
\r
10932 \begin_layout Plain Layout
\r
10933 Space ! horizontal
\r
10941 \begin_layout Subsection
\r
10943 \begin_inset CommandInset label
\r
10944 LatexCommand label
\r
10945 name "sub:Predefined-Space"
\r
10950 \begin_inset Index idx
\r
10953 \begin_layout Plain Layout
\r
10954 Space ! horizontal ! predefined
\r
10962 \begin_layout Standard
\r
10963 Sometimes it is necessary to insert horizontal space into a formula.
\r
10964 This is done by inserting a protected space (shortcut
\r
10965 \begin_inset Info
\r
10967 arg "command-alternatives space-insert protected ; math-space"
\r
10972 \begin_inset Quotes eld
\r
10981 \begin_layout Plain Layout
\r
10993 \begin_inset Quotes erd
\r
10996 appears and by pressing
\r
11000 several times one can select one of eight different space sizes.
\r
11001 The spaces can also be inserted using the math toolbar button
\r
11002 \begin_inset Graphics
\r
11003 filename ../images/math/space.png
\r
11008 or special commands.
\r
11009 Independent from the inserted command, one can select the size again by
\r
11017 \begin_layout Standard
\r
11020 \begin_inset VSpace -5mm
\r
11024 \begin_inset Tabular
\r
11025 <lyxtabular version="3" rows="3" columns="7">
\r
11026 <features tabularvalignment="middle">
\r
11027 <column alignment="center" valignment="middle" width="6.8cm">
\r
11028 <column alignment="center" valignment="top" width="0">
\r
11029 <column alignment="center" valignment="top" width="0">
\r
11030 <column alignment="center" valignment="top" width="0">
\r
11031 <column alignment="center" valignment="top" width="0">
\r
11032 <column alignment="center" valignment="top" width="0">
\r
11033 <column alignment="center" valignment="top" width="0">
\r
11035 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
11036 \begin_inset Text
\r
11038 \begin_layout Plain Layout
\r
11044 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
11045 \begin_inset Text
\r
11047 \begin_layout Plain Layout
\r
11055 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
11056 \begin_inset Text
\r
11058 \begin_layout Plain Layout
\r
11066 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
11067 \begin_inset Text
\r
11069 \begin_layout Plain Layout
\r
11077 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
11078 \begin_inset Text
\r
11080 \begin_layout Plain Layout
\r
11088 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
11089 \begin_inset Text
\r
11091 \begin_layout Plain Layout
\r
11099 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
11100 \begin_inset Text
\r
11102 \begin_layout Plain Layout
\r
11112 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
11113 \begin_inset Text
\r
11115 \begin_layout Plain Layout
\r
11120 keystrokes after inserting the protected space
\r
11125 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
11126 \begin_inset Text
\r
11128 \begin_layout Plain Layout
\r
11134 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
11135 \begin_inset Text
\r
11137 \begin_layout Plain Layout
\r
11143 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
11144 \begin_inset Text
\r
11146 \begin_layout Plain Layout
\r
11152 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
11153 \begin_inset Text
\r
11155 \begin_layout Plain Layout
\r
11161 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
11162 \begin_inset Text
\r
11164 \begin_layout Plain Layout
\r
11170 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
11171 \begin_inset Text
\r
11173 \begin_layout Plain Layout
\r
11181 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
11182 \begin_inset Text
\r
11184 \begin_layout Plain Layout
\r
11190 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
11191 \begin_inset Text
\r
11193 \begin_layout Plain Layout
\r
11194 \begin_inset Formula $A\, B$
\r
11202 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
11203 \begin_inset Text
\r
11205 \begin_layout Plain Layout
\r
11206 \begin_inset Formula $A\: B$
\r
11214 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
11215 \begin_inset Text
\r
11217 \begin_layout Plain Layout
\r
11218 \begin_inset Formula $A\; B$
\r
11226 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
11227 \begin_inset Text
\r
11229 \begin_layout Plain Layout
\r
11230 \begin_inset Formula $A\quad B$
\r
11238 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
11239 \begin_inset Text
\r
11241 \begin_layout Plain Layout
\r
11242 \begin_inset Formula $A\qquad B$
\r
11250 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
11251 \begin_inset Text
\r
11253 \begin_layout Plain Layout
\r
11254 \begin_inset Formula $A\! B$
\r
11270 \begin_layout Standard
\r
11271 The last size seem to produce no space.
\r
11272 It is displayed red in LyX contrary to the other sizes, because it is a
\r
11274 There are two more negative spaces:
\r
11277 \begin_layout Standard
\r
11279 \begin_inset Tabular
\r
11280 <lyxtabular version="3" rows="3" columns="3">
\r
11281 <features tabularvalignment="middle">
\r
11282 <column alignment="center" valignment="middle" width="6.8cm">
\r
11283 <column alignment="center" valignment="top" width="0pt">
\r
11284 <column alignment="center" valignment="top" width="0pt">
\r
11286 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
11287 \begin_inset Text
\r
11289 \begin_layout Plain Layout
\r
11295 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
11296 \begin_inset Text
\r
11298 \begin_layout Plain Layout
\r
11306 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
11307 \begin_inset Text
\r
11309 \begin_layout Plain Layout
\r
11319 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
11320 \begin_inset Text
\r
11322 \begin_layout Plain Layout
\r
11327 keystrokes after inserting the protected space
\r
11332 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
11333 \begin_inset Text
\r
11335 \begin_layout Plain Layout
\r
11341 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
11342 \begin_inset Text
\r
11344 \begin_layout Plain Layout
\r
11352 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
11353 \begin_inset Text
\r
11355 \begin_layout Plain Layout
\r
11361 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
11362 \begin_inset Text
\r
11364 \begin_layout Plain Layout
\r
11365 \begin_inset Formula $A\negmedspace B$
\r
11373 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
11374 \begin_inset Text
\r
11376 \begin_layout Plain Layout
\r
11377 \begin_inset Formula $A\negthickspace B$
\r
11393 \begin_layout Standard
\r
11394 Negative spaces can lead to characters overlapping each other.
\r
11395 Thus they can be used to enforce ligatures, which are e.
\r
11396 \begin_inset space \thinspace{}
\r
11400 \begin_inset space \space{}
\r
11403 useful for summation operators:
\r
11406 \begin_layout Standard
\r
11408 \begin_inset Tabular
\r
11409 <lyxtabular version="3" rows="3" columns="2">
\r
11410 <features tabularvalignment="middle">
\r
11411 <column alignment="center" valignment="top" width="0">
\r
11412 <column alignment="center" valignment="top" width="0">
\r
11414 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
11415 \begin_inset Text
\r
11417 \begin_layout Plain Layout
\r
11423 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
11424 \begin_inset Text
\r
11426 \begin_layout Plain Layout
\r
11428 \begin_inset Note Note
\r
11431 \begin_layout Plain Layout
\r
11438 is only used as spacer.
\r
11450 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
11451 \begin_inset Text
\r
11453 \begin_layout Plain Layout
\r
11462 \begin_layout Plain Layout
\r
11476 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
11477 \begin_inset Text
\r
11479 \begin_layout Plain Layout
\r
11480 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
\r
11490 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
11491 \begin_inset Text
\r
11493 \begin_layout Plain Layout
\r
11504 \begin_layout Plain Layout
\r
11518 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
11519 \begin_inset Text
\r
11521 \begin_layout Plain Layout
\r
11522 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
\r
11538 \begin_layout Standard
\r
11539 Relations like for example equal signs, are always surrounded by space.
\r
11540 To suppress this, the equal sign is placed into a TeX-brace.
\r
11541 The following example demonstrates this:
\r
11544 \begin_layout Standard
\r
11546 \begin_inset Tabular
\r
11547 <lyxtabular version="3" rows="2" columns="2">
\r
11548 <features tabularvalignment="middle">
\r
11549 <column alignment="center" valignment="top" width="0pt">
\r
11550 <column alignment="center" valignment="top" width="0pt">
\r
11552 <cell alignment="center" valignment="top" usebox="none">
\r
11553 \begin_inset Text
\r
11555 \begin_layout Plain Layout
\r
11561 <cell alignment="center" valignment="top" usebox="none">
\r
11562 \begin_inset Text
\r
11564 \begin_layout Plain Layout
\r
11565 \begin_inset Formula $A=B$
\r
11575 <cell alignment="center" valignment="top" usebox="none">
\r
11576 \begin_inset Text
\r
11578 \begin_layout Plain Layout
\r
11579 \begin_inset Note Note
\r
11582 \begin_layout Plain Layout
\r
11589 is only used as spacer.
\r
11595 \begin_inset Formula $\raisebox{5mm}{}$
\r
11598 equation without space
\r
11603 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
\r
11604 \begin_inset Text
\r
11606 \begin_layout Plain Layout
\r
11607 \begin_inset Formula $A{=}B$
\r
11623 \begin_layout Standard
\r
11625 The command for the last formula is:
\r
11630 \begin_inset Formula $\to$
\r
11636 \begin_layout Standard
\r
11637 \begin_inset VSpace bigskip
\r
11640 Spaces are needed for physical units, because the space between the value
\r
11641 and the unit is the smallest one and not a normal space.
\r
11642 For units in text, the smallest space is inserted via the menu
\r
11644 Insert\SpecialChar \menuseparator
\r
11645 Formatting\SpecialChar \menuseparator
\r
11647 \begin_inset space ~
\r
11653 \begin_inset Info
\r
11655 arg "space-insert thin"
\r
11661 \begin_layout Standard
\r
11662 An example to visualize the difference:
\r
11665 \begin_layout Standard
\r
11666 \begin_inset Tabular
\r
11667 <lyxtabular version="3" rows="2" columns="2">
\r
11668 <features tabularvalignment="middle">
\r
11669 <column alignment="left" valignment="top" width="0">
\r
11670 <column alignment="left" valignment="top" width="0">
\r
11672 <cell alignment="center" valignment="top" usebox="none">
\r
11673 \begin_inset Text
\r
11675 \begin_layout Plain Layout
\r
11677 \begin_inset Formula $\cdot$
\r
11685 <cell alignment="center" valignment="top" usebox="none">
\r
11686 \begin_inset Text
\r
11688 \begin_layout Plain Layout
\r
11689 space between value and unit
\r
11696 <cell alignment="center" valignment="top" usebox="none">
\r
11697 \begin_inset Text
\r
11699 \begin_layout Plain Layout
\r
11701 \begin_inset space \thinspace{}
\r
11705 \begin_inset Formula $\cdot$
\r
11713 <cell alignment="center" valignment="top" usebox="none">
\r
11714 \begin_inset Text
\r
11716 \begin_layout Plain Layout
\r
11717 smallest space between value and unit
\r
11730 \begin_layout Subsection
\r
11735 \begin_layout Plain Layout
\r
11745 \begin_inset Foot
\r
11748 \begin_layout Plain Layout
\r
11749 for vertical space in formulas see
\r
11750 \begin_inset CommandInset ref
\r
11752 reference "sub:Line-Separation"
\r
11765 \begin_layout Plain Layout
\r
11773 \begin_inset Note Note
\r
11776 \begin_layout Plain Layout
\r
11779 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
\r
11782 \begin_layout Plain Layout
\r
11785 texorpdfstring is in section
\r
11786 \begin_inset CommandInset ref
\r
11788 reference "sub:Formulas-in-Section"
\r
11798 \begin_inset CommandInset label
\r
11799 LatexCommand label
\r
11800 name "sub:Variable-Space"
\r
11805 \begin_inset Index idx
\r
11808 \begin_layout Plain Layout
\r
11809 Space ! horizontal ! variable
\r
11817 \begin_layout Standard
\r
11818 Space with a defined length can be inserted with the command
\r
11825 \begin_inset Index idx
\r
11828 \begin_layout Plain Layout
\r
11838 \begin_inset Quotes eld
\r
11847 \begin_layout Plain Layout
\r
11859 \begin_inset Quotes erd
\r
11863 The length can be specified by left-clicking on the
\r
11864 \begin_inset Quotes eld
\r
11873 \begin_layout Plain Layout
\r
11885 \begin_inset Quotes erd
\r
11889 The length may also be negative.
\r
11890 To insert as much space as is available, the command
\r
11897 \begin_inset Index idx
\r
11900 \begin_layout Plain Layout
\r
11911 \begin_layout Standard
\r
11912 \begin_inset VSpace -1mm
\r
11918 \begin_layout Standard
\r
11920 \begin_inset Tabular
\r
11921 <lyxtabular version="3" rows="4" columns="2">
\r
11922 <features tabularvalignment="middle">
\r
11923 <column alignment="center" valignment="top" width="0">
\r
11924 <column alignment="center" valignment="top" width="0">
\r
11926 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
11927 \begin_inset Text
\r
11929 \begin_layout Plain Layout
\r
11937 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
11938 \begin_inset Text
\r
11940 \begin_layout Plain Layout
\r
11948 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
11949 \begin_inset Text
\r
11951 \begin_layout Plain Layout
\r
11958 \begin_layout Plain Layout
\r
11968 \begin_inset Formula $\to$
\r
11974 \begin_inset space \thinspace{}
\r
11982 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
11983 \begin_inset Text
\r
11985 \begin_layout Plain Layout
\r
11986 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
\r
11996 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
11997 \begin_inset Text
\r
11999 \begin_layout Plain Layout
\r
12006 \begin_layout Plain Layout
\r
12016 \begin_inset Formula $\to$
\r
12022 \begin_inset space \thinspace{}
\r
12030 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
12031 \begin_inset Text
\r
12033 \begin_layout Plain Layout
\r
12034 \begin_inset Formula $A\hspace{-1mm}A\not=A$
\r
12044 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
12045 \begin_inset Text
\r
12047 \begin_layout Plain Layout
\r
12054 \begin_layout Plain Layout
\r
12068 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
12069 \begin_inset Text
\r
12071 \begin_layout Plain Layout
\r
12072 \begin_inset Formula $A=A\hfill B=B$
\r
12088 \begin_layout Standard
\r
12089 In the last example the available space is given by the longest column entry
\r
12091 In an inline formula the space depends on the length of the line in which
\r
12099 Thus, when the line uses the full width, no space will be created.
\r
12106 only has an effect on displayed formulas when the formula style
\r
12111 (Formula styles are explained in
\r
12112 \begin_inset CommandInset ref
\r
12114 reference "sec:Formula-Styles"
\r
12121 \begin_layout Standard
\r
12128 , there are the commands
\r
12140 that fill the space with a pattern, see
\r
12141 \begin_inset CommandInset ref
\r
12143 reference "sub:Ellipses"
\r
12150 \begin_layout Standard
\r
12151 For text, variable space can be inserted via the menu
\r
12153 Insert\SpecialChar \menuseparator
\r
12154 Formatting\SpecialChar \menuseparator
\r
12156 \begin_inset space ~
\r
12164 \begin_layout Standard
\r
12165 This is a line with
\r
12166 \begin_inset space \hspace{}
\r
12171 \begin_inset space \thinspace{}
\r
12177 \begin_layout Standard
\r
12178 This is a line with
\r
12179 \begin_inset space \hfill{}
\r
12185 \begin_layout Subsection
\r
12186 Space besides inline Formulas
\r
12187 \begin_inset Index idx
\r
12190 \begin_layout Plain Layout
\r
12191 Space ! besides inline formulas
\r
12199 \begin_layout Standard
\r
12200 The space that surrounds inline formulas can be adjusted with the length
\r
12208 \begin_inset Index idx
\r
12211 \begin_layout Plain Layout
\r
12220 The value of a length is set with the command
\r
12227 \begin_inset Index idx
\r
12230 \begin_layout Plain Layout
\r
12238 which has the following scheme:
\r
12241 \begin_layout Standard
\r
12246 setlength{length name}{value}
\r
12249 \begin_layout Standard
\r
12257 \begin_inset space \thinspace{}
\r
12263 \begin_layout Standard
\r
12270 mathsurround}{5mm}
\r
12273 \begin_layout Standard
\r
12274 is inserted in TeX-mode.
\r
12276 \begin_inset space \thinspace{}
\r
12279 mm space will now be set around all inline formulas:
\r
12283 \begin_layout Plain Layout
\r
12289 mathsurround}{5mm}
\r
12297 \begin_layout Standard
\r
12298 This is a line with an inline formula
\r
12299 \begin_inset Formula $A=B$
\r
12303 \begin_inset space \thinspace{}
\r
12306 mm surrounding space.
\r
12310 \begin_layout Plain Layout
\r
12316 mathsurround}{0pt}
\r
12324 \begin_layout Standard
\r
12325 To return to the predefined value,
\r
12331 is set to the value 0
\r
12332 \begin_inset space \thinspace{}
\r
12338 \begin_layout Section
\r
12340 \begin_inset Index idx
\r
12343 \begin_layout Plain Layout
\r
12350 \begin_inset Index idx
\r
12353 \begin_layout Plain Layout
\r
12358 \begin_layout Plain Layout
\r
12369 \begin_layout Plain Layout
\r
12384 \begin_layout Standard
\r
12385 Boxes for text are described in chapter
\r
12386 \family typewriter
\r
12390 \family typewriter
\r
12392 \begin_inset space ~
\r
12400 \begin_layout Subsection
\r
12402 \begin_inset CommandInset label
\r
12403 LatexCommand label
\r
12404 name "sub:Boxes-with-Frame"
\r
12409 \begin_inset Index idx
\r
12412 \begin_layout Plain Layout
\r
12413 Boxes ! with frame
\r
12421 \begin_layout Standard
\r
12422 It is possible to frame a formula or part of one with the commands
\r
12429 \begin_inset Index idx
\r
12432 \begin_layout Plain Layout
\r
12447 \begin_inset Index idx
\r
12450 \begin_layout Plain Layout
\r
12461 \begin_layout Standard
\r
12462 When one of these commands is inserted in a formula, a blue box appears
\r
12463 within a frame to enter formula parts.
\r
12470 an additional formula has to be created by
\r
12474 within this box, because the box content will otherwise be treated as mathemati
\r
12482 is used, a new formula is automatically created inside the frame.
\r
12485 \begin_layout Standard
\r
12492 is not suitable to frame displayed formulas because the formula will always
\r
12493 be set in the size of the text.
\r
12500 is in contrary not suitable to frame inline formulas, because the formula
\r
12501 will always be set in the size of a displayed formula.
\r
12504 \begin_layout Standard
\r
12518 \begin_inset Index idx
\r
12521 \begin_layout Plain Layout
\r
12529 where additionally the frame width and the alignment can be specified.
\r
12536 is used in the following scheme:
\r
12539 \begin_layout Standard
\r
12544 framebox[frame width][position]{box content}
\r
12547 \begin_layout Standard
\r
12548 The position can either be
\r
12565 right aligns the formula in the box.
\r
12566 When no position is given, the formula will be centered.
\r
12567 \begin_inset Newline newline
\r
12570 If no width is given, also no position can be given.
\r
12571 In this case the frame width is adjusted to the box content like for
\r
12580 \begin_layout Standard
\r
12581 When the command
\r
12587 is inserted, a box appears containing three blue boxes.
\r
12588 The first two boxes are surrounded by brackets and denote the two optional
\r
12590 The third box is for formula parts like for
\r
12599 \begin_layout Standard
\r
12600 \begin_inset Newpage newpage
\r
12606 \begin_layout Standard
\r
12608 \begin_inset Tabular
\r
12609 <lyxtabular version="3" rows="5" columns="2">
\r
12610 <features tabularvalignment="middle">
\r
12611 <column alignment="center" valignment="top" width="0">
\r
12612 <column alignment="center" valignment="top" width="0">
\r
12614 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
12615 \begin_inset Text
\r
12617 \begin_layout Plain Layout
\r
12623 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
12624 \begin_inset Text
\r
12626 \begin_layout Plain Layout
\r
12628 \begin_inset Note Note
\r
12631 \begin_layout Plain Layout
\r
12638 is only used as spacer.
\r
12650 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
12651 \begin_inset Text
\r
12653 \begin_layout Plain Layout
\r
12660 \begin_layout Plain Layout
\r
12679 \begin_layout Plain Layout
\r
12693 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
12694 \begin_inset Text
\r
12696 \begin_layout Plain Layout
\r
12697 \begin_inset Formula $\raisebox{6mm}{}\fbox{\ensuremath{\int A=B}}\raisebox{-4mm}{}$
\r
12707 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
12708 \begin_inset Text
\r
12710 \begin_layout Plain Layout
\r
12717 \begin_layout Plain Layout
\r
12732 \begin_layout Plain Layout
\r
12746 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
12747 \begin_inset Text
\r
12749 \begin_layout Plain Layout
\r
12750 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
\r
12760 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
12761 \begin_inset Text
\r
12763 \begin_layout Plain Layout
\r
12770 \begin_layout Plain Layout
\r
12784 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
12785 \begin_inset Text
\r
12787 \begin_layout Plain Layout
\r
12788 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
\r
12798 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
12799 \begin_inset Text
\r
12801 \begin_layout Plain Layout
\r
12808 \begin_layout Plain Layout
\r
12818 \begin_inset Formula $\to$
\r
12822 \begin_inset Formula $\to$
\r
12835 \begin_layout Plain Layout
\r
12845 \begin_inset Formula $\downarrow$
\r
12853 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
12854 \begin_inset Text
\r
12856 \begin_layout Plain Layout
\r
12857 \begin_inset Formula $\raisebox{6mm}{}$
\r
12861 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
\r
12865 \begin_inset Formula $\raisebox{-4mm}{}$
\r
12881 \begin_layout Standard
\r
12882 The frame thickness can also be adjusted.
\r
12883 To do this the following commands have to be inserted in TeX-mode before
\r
12887 \begin_layout Standard
\r
12897 \begin_inset Quotes eld
\r
12901 \begin_inset Quotes erd
\r
12915 \begin_inset Quotes eld
\r
12919 \begin_inset Quotes erd
\r
12925 \begin_layout Standard
\r
12926 \begin_inset Quotes eld
\r
12930 \begin_inset Quotes erd
\r
12933 specifies the minimal distance between the frame and the first character
\r
12935 An example for this is the following framed formula:
\r
12939 \begin_layout Plain Layout
\r
12951 \begin_inset Formula
\r
12958 Before this formula the commands
\r
12961 \begin_layout Standard
\r
12983 \begin_layout Standard
\r
12984 were inserted in TeX-mode.
\r
12985 The given values are used for all following boxes.
\r
12988 \begin_layout Standard
\r
12989 To return to the standard frame size, the command
\r
12992 \begin_layout Standard
\r
13017 \begin_layout Plain Layout
\r
13031 \begin_layout Standard
\r
13032 is inserted in TeX-mode before the next formula.
\r
13035 \begin_layout Subsection
\r
13036 Boxes without Frame
\r
13037 \begin_inset CommandInset label
\r
13038 LatexCommand label
\r
13039 name "sub:Boxes-without-Frame"
\r
13044 \begin_inset Index idx
\r
13047 \begin_layout Plain Layout
\r
13048 Boxes ! without frame
\r
13056 \begin_layout Standard
\r
13057 For boxes without a frame there are the following box commands:
\r
13064 \begin_inset Index idx
\r
13067 \begin_layout Plain Layout
\r
13082 \begin_inset Index idx
\r
13085 \begin_layout Plain Layout
\r
13100 \begin_inset Index idx
\r
13103 \begin_layout Plain Layout
\r
13114 \begin_layout Standard
\r
13121 a box can be super- or subscripted.
\r
13122 But in contrary to normal super- and subscripting, the characters in the
\r
13123 box keep their font size.
\r
13130 is used in the following scheme:
\r
13133 \begin_layout Standard
\r
13138 raisebox{height}{box content}
\r
13141 \begin_layout Standard
\r
13142 When the box should contain a formula, an extra formula is needed like for
\r
13153 \begin_inset Note Greyedout
\r
13156 \begin_layout Plain Layout
\r
13167 this extra formula is created by pressing
\r
13171 twice instead of once because LyX doesn't yet support
\r
13185 \begin_layout Standard
\r
13187 \begin_inset Tabular
\r
13188 <lyxtabular version="3" rows="4" columns="2">
\r
13189 <features tabularvalignment="middle">
\r
13190 <column alignment="center" valignment="top" width="0">
\r
13191 <column alignment="center" valignment="top" width="0">
\r
13193 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
13194 \begin_inset Text
\r
13196 \begin_layout Plain Layout
\r
13202 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
13203 \begin_inset Text
\r
13205 \begin_layout Plain Layout
\r
13213 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
13214 \begin_inset Text
\r
13216 \begin_layout Plain Layout
\r
13220 \begin_inset Formula $\to$
\r
13226 \begin_inset Formula $\to$
\r
13234 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
13235 \begin_inset Text
\r
13237 \begin_layout Plain Layout
\r
13238 \begin_inset Formula $H\raisebox{2mm}{al}lo$
\r
13248 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
13249 \begin_inset Text
\r
13251 \begin_layout Plain Layout
\r
13255 \begin_inset Formula $\to$
\r
13261 \begin_inset Formula $\to$
\r
13269 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
13270 \begin_inset Text
\r
13272 \begin_layout Plain Layout
\r
13273 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
\r
13283 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
13284 \begin_inset Text
\r
13286 \begin_layout Plain Layout
\r
13290 \begin_inset Formula $\to$
\r
13309 \begin_layout Plain Layout
\r
13323 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
13324 \begin_inset Text
\r
13326 \begin_layout Plain Layout
\r
13327 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
\r
13343 \begin_layout Standard
\r
13350 is equivalent to
\r
13362 is equivalent to
\r
13368 , with the difference that there is no frame.
\r
13371 \begin_layout Subsection
\r
13373 \begin_inset CommandInset label
\r
13374 LatexCommand label
\r
13375 name "sub:Colored-Boxes"
\r
13380 \begin_inset Index idx
\r
13383 \begin_layout Plain Layout
\r
13392 \begin_layout Standard
\r
13393 To be able to use all commands explained in this section, the LaTeX-package
\r
13399 \begin_inset Foot
\r
13402 \begin_layout Plain Layout
\r
13403 The LaTeX-package
\r
13407 is part of every LaTeX standard installation.
\r
13413 \begin_inset Index idx
\r
13416 \begin_layout Plain Layout
\r
13422 has to be loaded in the LaTeX-preamble with the line
\r
13423 \begin_inset Foot
\r
13426 \begin_layout Plain Layout
\r
13427 When text is colored somewhere in the document with a predefined color,
\r
13428 LyX loads the LaTeX-package
\r
13433 Thus it is possible that the package is loaded twice, but this does not
\r
13440 \begin_inset Note Note
\r
13443 \begin_layout Plain Layout
\r
13444 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
\r
13453 \begin_layout Standard
\r
13458 usepackage{color}
\r
13461 \begin_layout Standard
\r
13462 \begin_inset VSpace medskip
\r
13465 To color boxes, the command
\r
13472 \begin_inset Index idx
\r
13475 \begin_layout Plain Layout
\r
13483 is used in the following scheme:
\r
13486 \begin_layout Standard
\r
13491 colorbox{color}{box content}
\r
13494 \begin_layout Standard
\r
13495 The box content can also be a box and a
\r
13501 can also be part of another box (see the 2nd and 3rd example).
\r
13502 When the box should contain a formula, an extra formula has to be created,
\r
13503 the same way as for
\r
13510 \begin_inset Foot
\r
13513 \begin_layout Plain Layout
\r
13514 This also applies for the command
\r
13528 \begin_layout Standard
\r
13529 One of the following predefined colors can be chosen:
\r
13532 \begin_layout Standard
\r
13566 \begin_layout Standard
\r
13568 \begin_inset Tabular
\r
13569 <lyxtabular version="3" rows="4" columns="2">
\r
13570 <features tabularvalignment="middle">
\r
13571 <column alignment="center" valignment="top" width="0">
\r
13572 <column alignment="center" valignment="top" width="0">
\r
13574 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
13575 \begin_inset Text
\r
13577 \begin_layout Plain Layout
\r
13583 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
13584 \begin_inset Text
\r
13586 \begin_layout Plain Layout
\r
13588 \begin_inset Note Note
\r
13591 \begin_layout Plain Layout
\r
13598 is only used as spacer.
\r
13610 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
13611 \begin_inset Text
\r
13613 \begin_layout Plain Layout
\r
13617 \begin_inset Formula $\to$
\r
13627 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
13628 \begin_inset Text
\r
13630 \begin_layout Plain Layout
\r
13631 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
\r
13641 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
13642 \begin_inset Text
\r
13644 \begin_layout Plain Layout
\r
13648 \begin_inset Formula $\to$
\r
13659 \begin_layout Plain Layout
\r
13673 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
13674 \begin_inset Text
\r
13676 \begin_layout Plain Layout
\r
13677 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
\r
13687 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
13688 \begin_inset Text
\r
13690 \begin_layout Plain Layout
\r
13697 \begin_layout Plain Layout
\r
13709 \begin_inset Formula $\to$
\r
13728 \begin_layout Plain Layout
\r
13742 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
13743 \begin_inset Text
\r
13745 \begin_layout Plain Layout
\r
13746 \begin_inset Formula $\raisebox{7mm}{}\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}\raisebox{-5mm}{}$
\r
13762 \begin_layout Standard
\r
13769 only colors the box but not the characters in the box.
\r
13770 To color all characters, the whole formula is highlighted and the desired
\r
13771 color is chosen in the
\r
13774 \begin_inset space ~
\r
13780 The dialog can be called with the toolbar button
\r
13781 \begin_inset Graphics
\r
13782 filename ../images/dialog-show_character.png
\r
13789 Edit\SpecialChar \menuseparator
\r
13791 \begin_inset space ~
\r
13794 Style\SpecialChar \menuseparator
\r
13798 The formula number then has the same color as the formula.
\r
13799 When the formula number should get another color than the formula characters,
\r
13800 the color must be changed within the formula.
\r
13803 \begin_layout Standard
\r
13807 \begin_layout Standard
\r
13810 \begin_inset Formula
\r
13812 \int A=B\label{eq:red}
\r
13820 \begin_inset Formula
\r
13822 \textcolor{red}{\int A=B}\label{eq:redgreen}
\r
13830 \begin_layout Standard
\r
13832 \begin_inset CommandInset ref
\r
13833 LatexCommand eqref
\r
13834 reference "eq:red"
\r
13838 is completely colored red.
\r
13839 \begin_inset Newline newline
\r
13843 \begin_inset CommandInset ref
\r
13844 LatexCommand eqref
\r
13845 reference "eq:redgreen"
\r
13849 was first completely colored green to set the color for the formula number.
\r
13850 Subsequently the formula characters were colored red.
\r
13853 \begin_layout Standard
\r
13854 \begin_inset VSpace bigskip
\r
13857 To color the frame different than the rest of the box, the command
\r
13864 \begin_inset Index idx
\r
13867 \begin_layout Plain Layout
\r
13875 is used in the following scheme:
\r
13878 \begin_layout Standard
\r
13883 fcolorbox{frame color}{color}{box content}
\r
13886 \begin_layout Standard
\r
13893 is an extension of the command
\r
13900 The frame width is set, like for
\r
13923 \begin_layout Plain Layout
\r
13935 \begin_inset Formula
\r
13937 \fcolorbox{cyan}{magenta}{A=B}
\r
13946 \begin_layout Plain Layout
\r
13960 \begin_layout Standard
\r
13961 This formula was created with the command
\r
13962 \begin_inset Newline newline
\r
13970 \begin_inset Formula $\to$
\r
13976 \begin_inset Formula $\to$
\r
13986 \begin_layout Standard
\r
13987 \begin_inset VSpace bigskip
\r
13990 To use other colors than the predefined ones, they have to be defined first.
\r
13993 \begin_layout Standard
\r
13994 One can for example define the color
\r
13995 \begin_inset Quotes eld
\r
14003 \begin_inset Quotes erd
\r
14006 with the LaTeX-preamble line:
\r
14009 \begin_layout Standard
\r
14014 definecolor{darkgreen}{cmyk}{0.5,
\r
14029 \begin_inset Index idx
\r
14032 \begin_layout Plain Layout
\r
14043 \begin_layout Standard
\r
14048 is the color space that denotes the colors
\r
14065 The four comma separated numbers are the portion factor for the corresponding
\r
14066 colors of the color space.
\r
14067 The factors can be in the range of 0
\r
14068 \begin_inset space \thinspace{}
\r
14072 \begin_inset space \thinspace{}
\r
14080 also the color space
\r
14084 can be used for definitions.
\r
14101 , so that there are in this case three portion factors for the corresponding
\r
14103 Furthermore there is the color space
\r
14107 with one portion factor for the gray value.
\r
14110 \begin_layout Standard
\r
14111 As example a framed box with the new defined color
\r
14115 where the characters have been colored
\r
14120 \begin_inset Formula
\r
14122 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}
\r
14130 \begin_layout Standard
\r
14131 Self-defined colors can also be used for text with the help of the command
\r
14139 \begin_inset Index idx
\r
14142 \begin_layout Plain Layout
\r
14151 \begin_layout Standard
\r
14155 \begin_layout Plain Layout
\r
14159 textcolor{darkgreen}{
\r
14164 This sentence is
\r
14165 \begin_inset Quotes eld
\r
14169 \begin_inset Quotes erd
\r
14176 \begin_layout Plain Layout
\r
14186 \begin_layout Standard
\r
14194 \begin_inset Index idx
\r
14197 \begin_layout Plain Layout
\r
14205 is used in the scheme
\r
14209 textcolor{color}{characters to color}
\r
14214 \begin_layout Subsection
\r
14216 \begin_inset CommandInset label
\r
14217 LatexCommand label
\r
14218 name "sub:Paragraph-Boxes"
\r
14223 \begin_inset Index idx
\r
14226 \begin_layout Plain Layout
\r
14227 Boxes ! as paragraph
\r
14235 \begin_layout Standard
\r
14236 A box that can contain several lines and paragraphs, a so-called paragraph
\r
14237 box (parbox), can be created with the menu
\r
14239 Insert\SpecialChar \menuseparator
\r
14242 or the toolbar button
\r
14243 \begin_inset Graphics
\r
14244 filename ../images/box-insert.png
\r
14252 \begin_layout Standard
\r
14253 The following example shows a framed parbox in a line:
\r
14256 \begin_layout Standard
\r
14257 \begin_inset VSpace medskip
\r
14261 \begin_inset Box Boxed
\r
14271 height_special "totalheight"
\r
14274 \begin_layout Plain Layout
\r
14275 This is a paragraph box.
\r
14277 \begin_inset space \thinspace{}
\r
14280 cm long and can also contain formulas:
\r
14281 \begin_inset Formula $\int A\,\mathrm{d}s=C$
\r
14292 \begin_layout Standard
\r
14293 \begin_inset VSpace medskip
\r
14299 \begin_layout Standard
\r
14300 Such a box is created by right-clicking on the gray box inset.
\r
14301 A dialog pops up showing the box properties.
\r
14302 In our case set:
\r
14306 : Rectangular box,
\r
14315 \begin_inset space \thinspace{}
\r
14320 Vertical Box Alignment
\r
14325 \begin_layout Standard
\r
14326 \begin_inset VSpace medskip
\r
14329 In LaTeX a parbox is created with the command
\r
14336 \begin_inset Index idx
\r
14339 \begin_layout Plain Layout
\r
14347 which has the following scheme:
\r
14350 \begin_layout Standard
\r
14355 parbox[position]{width}{box content}
\r
14358 \begin_layout Standard
\r
14373 \begin_inset Quotes eld
\r
14377 \begin_inset Quotes erd
\r
14380 means that the box is aligned within the surrounding text with its last
\r
14387 \begin_inset Quotes eld
\r
14391 \begin_inset Quotes erd
\r
14394 this is done with the first line.
\r
14395 When no position is given, the box will be vertically centered, see section
\r
14403 \begin_inset space ~
\r
14408 manual for examples.
\r
14411 \begin_layout Standard
\r
14412 \begin_inset VSpace bigskip
\r
14415 To frame formulas completely, including the formula number, the formula
\r
14416 must be set into a parbox.
\r
14417 To do this, the command
\r
14431 is inserted in TeX-mode before the formula.
\r
14439 \begin_inset Index idx
\r
14442 \begin_layout Plain Layout
\r
14450 is hereby the line width set for the document.
\r
14451 Because the frame is outside the parbox, 2
\r
14452 \begin_inset space \thinspace{}
\r
14455 times the frame separation and the frame thickness must be subtracted from
\r
14457 As this is not automatically done by LyX due to a bug
\r
14458 \begin_inset Foot
\r
14461 \begin_layout Plain Layout
\r
14462 \begin_inset CommandInset href
\r
14463 LatexCommand href
\r
14464 name "LyX-bug #4483"
\r
14465 target "http://www.lyx.org/trac/ticket/4483"
\r
14474 , TeX-mode has to be used.
\r
14475 To be able to multiply and subtract in arguments, the LaTeX-package
\r
14480 \begin_inset Foot
\r
14483 \begin_layout Plain Layout
\r
14488 is part of every LaTeX standard installation.
\r
14494 \begin_inset Index idx
\r
14497 \begin_layout Plain Layout
\r
14503 must be loaded in the LaTeX-preamble with the line
\r
14506 \begin_layout Standard
\r
14514 \begin_layout Standard
\r
14515 Behind the formula both boxes are closed by entering
\r
14520 Here is an example:
\r
14524 \begin_layout Plain Layout
\r
14538 \begin_layout Standard
\r
14542 \begin_layout Plain Layout
\r
14560 \begin_inset Formula
\r
14562 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}
\r
14571 \begin_layout Plain Layout
\r
14582 \begin_layout Plain Layout
\r
14596 \begin_layout Standard
\r
14597 \begin_inset VSpace medskip
\r
14600 As a parbox is used as the argument of
\r
14606 , there is in this case no difference between
\r
14621 \begin_layout Standard
\r
14622 \begin_inset VSpace bigskip
\r
14625 Paragraph boxes are very useful to comment formulas directly.
\r
14632 is used in combination with the command
\r
14646 \begin_inset CommandInset ref
\r
14648 reference "sub:User-defined-Numbering"
\r
14655 \begin_layout Standard
\r
14656 An example of a formula commented with
\r
14665 \begin_layout Standard
\r
14669 \begin_layout Plain Layout
\r
14682 This is a description.
\r
14683 It is distinctly separated from the formula and multiline.
\r
14687 \begin_layout Plain Layout
\r
14699 \begin_layout Standard
\r
14700 Such a formula must be inserted completely in TeX-mode because LyX does
\r
14701 not yet support the command
\r
14708 The formula is created with the following command sequence:
\r
14711 \begin_layout Standard
\r
14724 is inserted in TeX-mode.
\r
14725 \begin_inset Foot
\r
14728 \begin_layout Plain Layout
\r
14729 When the formula style
\r
14741 can also be replaced by
\r
14748 (formula styles see
\r
14749 \begin_inset CommandInset ref
\r
14751 reference "sec:Formula-Styles"
\r
14760 Then the description follows as normal text and finally
\r
14766 is inserted in TeX-mode.
\r
14779 hereby create a displayed formula.
\r
14782 \begin_layout Standard
\r
14783 The advantages of
\r
14789 can be seen in this example that was
\r
14790 \begin_inset Quotes eld
\r
14794 \begin_inset Quotes erd
\r
14797 using the mathematical textmode:
\r
14798 \begin_inset Formula
\r
14800 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}
\r
14808 \begin_layout Section
\r
14810 \begin_inset Index idx
\r
14813 \begin_layout Plain Layout
\r
14822 \begin_layout Subsection
\r
14824 \begin_inset CommandInset label
\r
14825 LatexCommand label
\r
14826 name "sub:Big-Operators"
\r
14831 \begin_inset Index idx
\r
14834 \begin_layout Plain Layout
\r
14841 \begin_inset Index idx
\r
14844 \begin_layout Plain Layout
\r
14851 \begin_inset Index idx
\r
14854 \begin_layout Plain Layout
\r
14863 \begin_layout Standard
\r
14864 To be able to use all integral operators listed here, the option
\r
14866 Use esint package automatically
\r
14868 must be set in the document settings under
\r
14871 \begin_inset space ~
\r
14879 \begin_layout Standard
\r
14880 \begin_inset space \hfill{}
\r
14884 \begin_inset Tabular
\r
14885 <lyxtabular version="3" rows="11" columns="2">
\r
14886 <features tabularvalignment="middle">
\r
14887 <column alignment="center" valignment="top" width="0pt">
\r
14888 <column alignment="center" valignment="top" width="0pt">
\r
14890 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
14891 \begin_inset Text
\r
14893 \begin_layout Plain Layout
\r
14899 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
14900 \begin_inset Text
\r
14902 \begin_layout Plain Layout
\r
14910 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
14911 \begin_inset Text
\r
14913 \begin_layout Plain Layout
\r
14917 \begin_inset Index idx
\r
14920 \begin_layout Plain Layout
\r
14933 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
14934 \begin_inset Text
\r
14936 \begin_layout Plain Layout
\r
14937 \begin_inset Formula $\int$
\r
14947 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
14948 \begin_inset Text
\r
14950 \begin_layout Plain Layout
\r
14958 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
14959 \begin_inset Text
\r
14961 \begin_layout Plain Layout
\r
14962 \begin_inset Formula $\oint$
\r
14972 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
14973 \begin_inset Text
\r
14975 \begin_layout Plain Layout
\r
14983 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
14984 \begin_inset Text
\r
14986 \begin_layout Plain Layout
\r
14987 \begin_inset Formula $\ointctrclockwise$
\r
14997 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
14998 \begin_inset Text
\r
15000 \begin_layout Plain Layout
\r
15008 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
15009 \begin_inset Text
\r
15011 \begin_layout Plain Layout
\r
15012 \begin_inset Formula $\ointclockwise$
\r
15022 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
15023 \begin_inset Text
\r
15025 \begin_layout Plain Layout
\r
15033 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
15034 \begin_inset Text
\r
15036 \begin_layout Plain Layout
\r
15037 \begin_inset Formula $\sqint$
\r
15047 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
15048 \begin_inset Text
\r
15050 \begin_layout Plain Layout
\r
15058 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
15059 \begin_inset Text
\r
15061 \begin_layout Plain Layout
\r
15063 \begin_inset Formula $\fint$
\r
15073 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
15074 \begin_inset Text
\r
15076 \begin_layout Plain Layout
\r
15084 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
15085 \begin_inset Text
\r
15087 \begin_layout Plain Layout
\r
15089 \begin_inset Formula $\landupint$
\r
15099 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
15100 \begin_inset Text
\r
15102 \begin_layout Plain Layout
\r
15110 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
15111 \begin_inset Text
\r
15113 \begin_layout Plain Layout
\r
15115 \begin_inset Formula $\landdownint$
\r
15125 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
15126 \begin_inset Text
\r
15128 \begin_layout Plain Layout
\r
15136 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
15137 \begin_inset Text
\r
15139 \begin_layout Plain Layout
\r
15140 \begin_inset Formula $\bigcap$
\r
15150 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
15151 \begin_inset Text
\r
15153 \begin_layout Plain Layout
\r
15161 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
15162 \begin_inset Text
\r
15164 \begin_layout Plain Layout
\r
15165 \begin_inset Formula $\bigcup$
\r
15179 \begin_inset space \hfill{}
\r
15183 \begin_inset Tabular
\r
15184 <lyxtabular version="3" rows="11" columns="2">
\r
15185 <features tabularvalignment="middle">
\r
15186 <column alignment="center" valignment="top" width="0pt">
\r
15187 <column alignment="center" valignment="top" width="0pt">
\r
15189 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
15190 \begin_inset Text
\r
15192 \begin_layout Plain Layout
\r
15198 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
15199 \begin_inset Text
\r
15201 \begin_layout Plain Layout
\r
15209 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
15210 \begin_inset Text
\r
15212 \begin_layout Plain Layout
\r
15216 \begin_inset Index idx
\r
15219 \begin_layout Plain Layout
\r
15232 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
15233 \begin_inset Text
\r
15235 \begin_layout Plain Layout
\r
15236 \begin_inset Formula $\sum$
\r
15246 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
15247 \begin_inset Text
\r
15249 \begin_layout Plain Layout
\r
15253 \begin_inset Index idx
\r
15256 \begin_layout Plain Layout
\r
15263 \begin_layout Plain Layout
\r
15282 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
15283 \begin_inset Text
\r
15285 \begin_layout Plain Layout
\r
15286 \begin_inset Formula $\prod$
\r
15296 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
15297 \begin_inset Text
\r
15299 \begin_layout Plain Layout
\r
15307 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
15308 \begin_inset Text
\r
15310 \begin_layout Plain Layout
\r
15311 \begin_inset Formula $\coprod$
\r
15321 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
15322 \begin_inset Text
\r
15324 \begin_layout Plain Layout
\r
15332 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
15333 \begin_inset Text
\r
15335 \begin_layout Plain Layout
\r
15336 \begin_inset Formula $\bigodot$
\r
15346 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
15347 \begin_inset Text
\r
15349 \begin_layout Plain Layout
\r
15357 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
15358 \begin_inset Text
\r
15360 \begin_layout Plain Layout
\r
15361 \begin_inset Formula $\bigotimes$
\r
15371 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
15372 \begin_inset Text
\r
15374 \begin_layout Plain Layout
\r
15382 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
15383 \begin_inset Text
\r
15385 \begin_layout Plain Layout
\r
15386 \begin_inset Formula $\bigoplus$
\r
15396 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
15397 \begin_inset Text
\r
15399 \begin_layout Plain Layout
\r
15407 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
15408 \begin_inset Text
\r
15410 \begin_layout Plain Layout
\r
15411 \begin_inset Formula $\bigwedge$
\r
15421 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
15422 \begin_inset Text
\r
15424 \begin_layout Plain Layout
\r
15432 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
15433 \begin_inset Text
\r
15435 \begin_layout Plain Layout
\r
15436 \begin_inset Formula $\bigvee$
\r
15446 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
15447 \begin_inset Text
\r
15449 \begin_layout Plain Layout
\r
15457 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
15458 \begin_inset Text
\r
15460 \begin_layout Plain Layout
\r
15461 \begin_inset Formula $\bigsqcup$
\r
15471 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
15472 \begin_inset Text
\r
15474 \begin_layout Plain Layout
\r
15482 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
15483 \begin_inset Text
\r
15485 \begin_layout Plain Layout
\r
15486 \begin_inset Formula $\biguplus$
\r
15500 \begin_inset space \hfill{}
\r
15506 \begin_layout Standard
\r
15507 All big operators can also be inserted via the math toolbar button
\r
15508 \begin_inset Graphics
\r
15509 filename ../images/math/intop.png
\r
15517 \begin_layout Standard
\r
15518 The operators are called big because they are bigger than the sometimes
\r
15519 equal looking binary operators.
\r
15520 All big operators can have limits as described in the next subsection.
\r
15523 \begin_layout Standard
\r
15524 For all integral operators there is a second version available, ending in
\r
15542 These operators are different from
\r
15549 \begin_inset space \space{}
\r
15552 in the style the operator limits are displayed, see
\r
15553 \begin_inset CommandInset ref
\r
15555 reference "sub:Operator-Limits"
\r
15563 \begin_layout Subsubsection*
\r
15564 Advice for Integrals
\r
15567 \begin_layout Standard
\r
15572 in an integral is an operator, that therefore has to be set upright.
\r
15573 This is done by highlighting the
\r
15577 and using the keyboard shortcut
\r
15578 \begin_inset Info
\r
15584 \begin_inset Foot
\r
15587 \begin_layout Plain Layout
\r
15593 \begin_inset CommandInset ref
\r
15595 reference "sub:Font-Styles"
\r
15605 Finally the smallest space is inserted before the
\r
15609 , as this is usual for operators.
\r
15613 \begin_layout Standard
\r
15615 \begin_inset Formula $\int A(x)dx$
\r
15619 \begin_inset Newline newline
\r
15623 \begin_inset Phantom HPhantom
\r
15626 \begin_layout Plain Layout
\r
15633 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
\r
15639 \begin_layout Standard
\r
15640 For multiple integrals there are the following commands:
\r
15641 \begin_inset VSpace medskip
\r
15647 \begin_layout Standard
\r
15648 \begin_inset space \hfill{}
\r
15652 \begin_inset Tabular
\r
15653 <lyxtabular version="3" rows="4" columns="2">
\r
15654 <features tabularvalignment="middle">
\r
15655 <column alignment="center" valignment="top" width="0">
\r
15656 <column alignment="center" valignment="top" width="0">
\r
15658 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
15659 \begin_inset Text
\r
15661 \begin_layout Plain Layout
\r
15667 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
15668 \begin_inset Text
\r
15670 \begin_layout Plain Layout
\r
15672 \begin_inset Note Note
\r
15675 \begin_layout Plain Layout
\r
15682 is only used as spacer.
\r
15694 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
15695 \begin_inset Text
\r
15697 \begin_layout Plain Layout
\r
15705 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
15706 \begin_inset Text
\r
15708 \begin_layout Plain Layout
\r
15709 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
\r
15719 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
15720 \begin_inset Text
\r
15722 \begin_layout Plain Layout
\r
15730 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
15731 \begin_inset Text
\r
15733 \begin_layout Plain Layout
\r
15734 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
\r
15744 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
15745 \begin_inset Text
\r
15747 \begin_layout Plain Layout
\r
15755 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
15756 \begin_inset Text
\r
15758 \begin_layout Plain Layout
\r
15759 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
\r
15773 \begin_inset space \hfill{}
\r
15777 \begin_inset Tabular
\r
15778 <lyxtabular version="3" rows="4" columns="2">
\r
15779 <features tabularvalignment="middle">
\r
15780 <column alignment="center" valignment="top" width="0">
\r
15781 <column alignment="center" valignment="top" width="0">
\r
15783 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
15784 \begin_inset Text
\r
15786 \begin_layout Plain Layout
\r
15792 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
15793 \begin_inset Text
\r
15795 \begin_layout Plain Layout
\r
15803 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
15804 \begin_inset Text
\r
15806 \begin_layout Plain Layout
\r
15814 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
15815 \begin_inset Text
\r
15817 \begin_layout Plain Layout
\r
15818 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
\r
15828 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
15829 \begin_inset Text
\r
15831 \begin_layout Plain Layout
\r
15839 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
15840 \begin_inset Text
\r
15842 \begin_layout Plain Layout
\r
15843 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
\r
15853 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
15854 \begin_inset Text
\r
15856 \begin_layout Plain Layout
\r
15864 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
15865 \begin_inset Text
\r
15867 \begin_layout Plain Layout
\r
15868 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
\r
15882 \begin_inset space \hfill{}
\r
15888 \begin_layout Standard
\r
15889 \begin_inset Newpage newpage
\r
15895 \begin_layout Subsection
\r
15897 \begin_inset CommandInset label
\r
15898 LatexCommand label
\r
15899 name "sub:Operator-Limits"
\r
15904 \begin_inset Index idx
\r
15907 \begin_layout Plain Layout
\r
15908 Operators ! Limits
\r
15916 \begin_layout Standard
\r
15917 Limits are created by super- and subscripts:
\r
15920 \begin_layout Standard
\r
15922 \begin_inset Tabular
\r
15923 <lyxtabular version="3" rows="2" columns="2">
\r
15924 <features tabularvalignment="middle">
\r
15925 <column alignment="center" valignment="top" width="0pt">
\r
15926 <column alignment="center" valignment="top" width="0pt">
\r
15928 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
15929 \begin_inset Text
\r
15931 \begin_layout Plain Layout
\r
15937 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
15938 \begin_inset Text
\r
15940 \begin_layout Plain Layout
\r
15942 \begin_inset Note Note
\r
15945 \begin_layout Plain Layout
\r
15952 is only used as spacer.
\r
15964 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
15965 \begin_inset Text
\r
15967 \begin_layout Plain Layout
\r
15976 \begin_layout Plain Layout
\r
15986 \begin_inset Formula $\to$
\r
15990 \begin_inset Formula $\to$
\r
15998 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
15999 \begin_inset Text
\r
16001 \begin_layout Plain Layout
\r
16002 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
\r
16018 \begin_layout Standard
\r
16019 Limits of inline formulas are set right beside the operator.
\r
16020 Limits in displayed formulas are set above or below the operator, except
\r
16021 for integral limits.
\r
16024 \begin_layout Standard
\r
16025 To force that the limits are set beside the operator, the cursor is set
\r
16026 directly behind the operator and the limits type is changed with the menu
\r
16029 Edit\SpecialChar \menuseparator
\r
16030 Math\SpecialChar \menuseparator
\r
16031 Change Limits Type
\r
16040 \begin_inset Info
\r
16042 arg "math-limits"
\r
16049 \begin_layout Standard
\r
16050 The default limits type is this:
\r
16051 \begin_inset Formula
\r
16053 \sum_{x=0}^{\infty}\frac{1}{x^{2}}
\r
16058 This is how it looks when the limits type was changed to
\r
16065 \begin_inset Formula
\r
16067 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}
\r
16072 For integrals, except those ending with
\r
16088 etc., the limits are by default set beside the operator.
\r
16089 But for multiple integrals the limits are often set below the operator.
\r
16090 In the following example the limits type was therefore set to
\r
16094 and so set below the integrals:
\r
16095 \begin_inset Formula
\r
16097 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}
\r
16105 \begin_layout Standard
\r
16106 \begin_inset VSpace medskip
\r
16109 To specify conditions for limits, the commands
\r
16116 \begin_inset Index idx
\r
16119 \begin_layout Plain Layout
\r
16134 \begin_inset Index idx
\r
16137 \begin_layout Plain Layout
\r
16146 To create for example this expression
\r
16147 \begin_inset Formula
\r
16149 \sum_{\begin{subarray}{c}
\r
16152 k\,\in\,\mathbb{N}
\r
16153 \end{subarray}}^{n}k^{-2}\label{eq:substack}
\r
16161 \begin_layout Standard
\r
16162 the following has to be done:
\r
16163 \begin_inset Newline newline
\r
16166 First the command
\r
16178 \begin_layout Plain Layout
\r
16190 One is now in a blue box under the summation operator and insert there
\r
16199 \begin_layout Plain Layout
\r
16211 The blue box is now within a purple box and now several lines can be written
\r
16212 among each other.
\r
16213 A new line is created by inserting a line break (
\r
16214 \begin_inset Info
\r
16216 arg "newline-insert newline"
\r
16221 \begin_inset Newline newline
\r
16226 0<k<1000 Ctrl+Return
\r
16227 \begin_inset Newline newline
\r
16232 is typed in, a new box appears below for the new line.
\r
16235 \begin_layout Standard
\r
16236 The alignment of the lines can be changed to left aligned with the
\r
16246 Edit\SpecialChar \menuseparator
\r
16250 To get right alignment,
\r
16258 \begin_layout Plain Layout
\r
16269 is inserted at the beginning of the line.
\r
16272 \begin_layout Standard
\r
16279 is equivalent to
\r
16285 with the difference that the lines are always centered.
\r
16288 \begin_layout Standard
\r
16289 \begin_inset VSpace bigskip
\r
16293 \begin_inset CommandInset ref
\r
16294 LatexCommand eqref
\r
16295 reference "eq:substack"
\r
16299 there can be too much space beside an operator, because the characters
\r
16300 following the operator are set beside the limits.
\r
16303 \begin_layout Standard
\r
16304 To avoid this, the following macro can be used in the LaTeX-preamble:
\r
16307 \begin_layout Standard
\r
16321 \begin_inset Newline newline
\r
16332 mathclapinternal}
\r
16333 \begin_inset Newline newline
\r
16340 mathclapinternal #1#2{
\r
16344 mathsurround =0pt #1{#2}$}}
\r
16347 \begin_layout Standard
\r
16348 This defines the command
\r
16355 \begin_inset Index idx
\r
16358 \begin_layout Plain Layout
\r
16366 that sets the width of the limit to 0
\r
16367 \begin_inset space \thinspace{}
\r
16371 The command scheme is
\r
16374 \begin_layout Standard
\r
16382 \begin_layout Standard
\r
16383 where the limit can consist of several conditions.
\r
16386 \begin_layout Standard
\r
16387 Applied on formula
\r
16388 \begin_inset CommandInset ref
\r
16389 LatexCommand eqref
\r
16390 reference "eq:substack"
\r
16394 , one uses the command
\r
16397 \begin_layout Standard
\r
16410 \begin_layout Plain Layout
\r
16419 0<k<1000 Ctrl+Return
\r
16422 \begin_layout Standard
\r
16423 to create the lower limit.
\r
16424 The summand is now directly behind the summation operator:
\r
16425 \begin_inset Formula
\r
16427 \sum_{\mathclap{\substack{0<k<1000\\
\r
16429 k\,\in\,\mathbb{N}
\r
16439 \begin_layout Standard
\r
16440 \begin_inset VSpace bigskip
\r
16443 How to use one limit for several operators is described in
\r
16444 \begin_inset CommandInset ref
\r
16446 reference "sub:Self-defined-Operators"
\r
16453 \begin_layout Subsection
\r
16454 Decoration for Operators
\r
16455 \begin_inset Index idx
\r
16458 \begin_layout Plain Layout
\r
16459 Operators ! Decoration
\r
16467 \begin_layout Standard
\r
16468 With the commands
\r
16475 \begin_inset Index idx
\r
16478 \begin_layout Plain Layout
\r
16493 \begin_inset Index idx
\r
16496 \begin_layout Plain Layout
\r
16504 characters can be placed above or below an operator, respectively.
\r
16505 With the command
\r
16512 \begin_inset Index idx
\r
16515 \begin_layout Plain Layout
\r
16523 characters can be set before and behind a big operator.
\r
16524 The command scheme is:
\r
16527 \begin_layout Standard
\r
16532 sideset{character
\r
16536 before}{character
\r
16543 \begin_layout Standard
\r
16550 must always be before the operator.
\r
16551 You can decorate with several characters and even with other operators
\r
16553 To place for example only characters behind a big operator, write nothing
\r
16554 between the first braces but don't omit the braces.
\r
16557 \begin_layout Standard
\r
16558 For example the command
\r
16563 \begin_inset Formula $\to$
\r
16573 \begin_inset Formula $\to$
\r
16582 \begin_layout Plain Layout
\r
16598 \begin_inset Formula
\r
16600 \sideset{}{'}\sum_{k=1}^{n}
\r
16608 \begin_layout Standard
\r
16609 \begin_inset Note Greyedout
\r
16612 \begin_layout Plain Layout
\r
16619 can only be used to decorate big operators, binary operators are not allowed.
\r
16627 \begin_layout Standard
\r
16640 can also be used to decorate symbols and characters.
\r
16641 For example, the command
\r
16649 \begin_layout Plain Layout
\r
16664 \begin_layout Plain Layout
\r
16676 \begin_inset Formula $\uparrow$
\r
16684 \begin_inset Formula
\r
16686 \overset{a}{\maltese}
\r
16694 \begin_layout Subsection
\r
16696 \begin_inset CommandInset label
\r
16697 LatexCommand label
\r
16698 name "sub:Binary-Operators"
\r
16703 \begin_inset Index idx
\r
16706 \begin_layout Plain Layout
\r
16707 Operators ! binary
\r
16715 \begin_layout Standard
\r
16716 Binary operators are surrounded by space when there is a character before
\r
16718 \begin_inset VSpace medskip
\r
16724 \begin_layout Standard
\r
16725 \begin_inset space \hfill{}
\r
16729 \begin_inset Tabular
\r
16730 <lyxtabular version="3" rows="13" columns="2">
\r
16731 <features tabularvalignment="middle">
\r
16732 <column alignment="center" valignment="top" width="0pt">
\r
16733 <column alignment="center" valignment="top" width="0pt">
\r
16735 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
16736 \begin_inset Text
\r
16738 \begin_layout Plain Layout
\r
16740 \begin_inset Note Note
\r
16743 \begin_layout Plain Layout
\r
16750 is only used as spacer.
\r
16760 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
16761 \begin_inset Text
\r
16763 \begin_layout Plain Layout
\r
16771 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
16772 \begin_inset Text
\r
16774 \begin_layout Plain Layout
\r
16780 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
16781 \begin_inset Text
\r
16783 \begin_layout Plain Layout
\r
16784 \begin_inset Formula $+$
\r
16794 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
16795 \begin_inset Text
\r
16797 \begin_layout Plain Layout
\r
16803 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
16804 \begin_inset Text
\r
16806 \begin_layout Plain Layout
\r
16807 \begin_inset Formula $-$
\r
16817 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
16818 \begin_inset Text
\r
16820 \begin_layout Plain Layout
\r
16828 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
16829 \begin_inset Text
\r
16831 \begin_layout Plain Layout
\r
16832 \begin_inset Formula $\pm$
\r
16842 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
16843 \begin_inset Text
\r
16845 \begin_layout Plain Layout
\r
16853 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
16854 \begin_inset Text
\r
16856 \begin_layout Plain Layout
\r
16857 \begin_inset Formula $\mp$
\r
16867 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
16868 \begin_inset Text
\r
16870 \begin_layout Plain Layout
\r
16878 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
16879 \begin_inset Text
\r
16881 \begin_layout Plain Layout
\r
16882 \begin_inset Formula $\cdot$
\r
16892 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
16893 \begin_inset Text
\r
16895 \begin_layout Plain Layout
\r
16903 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
16904 \begin_inset Text
\r
16906 \begin_layout Plain Layout
\r
16907 \begin_inset Formula $\times$
\r
16917 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
16918 \begin_inset Text
\r
16920 \begin_layout Plain Layout
\r
16928 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
16929 \begin_inset Text
\r
16931 \begin_layout Plain Layout
\r
16932 \begin_inset Formula $\div$
\r
16942 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
16943 \begin_inset Text
\r
16945 \begin_layout Plain Layout
\r
16949 \begin_layout Plain Layout
\r
16953 raisebox{-1.2mm}{
\r
16962 \begin_layout Plain Layout
\r
16974 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
16975 \begin_inset Text
\r
16977 \begin_layout Plain Layout
\r
16978 \begin_inset Formula $*$
\r
16988 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
16989 \begin_inset Text
\r
16991 \begin_layout Plain Layout
\r
16999 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
17000 \begin_inset Text
\r
17002 \begin_layout Plain Layout
\r
17003 \begin_inset Formula $\star$
\r
17013 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
17014 \begin_inset Text
\r
17016 \begin_layout Plain Layout
\r
17024 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
17025 \begin_inset Text
\r
17027 \begin_layout Plain Layout
\r
17028 \begin_inset Formula $\circ$
\r
17038 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
17039 \begin_inset Text
\r
17041 \begin_layout Plain Layout
\r
17049 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
17050 \begin_inset Text
\r
17052 \begin_layout Plain Layout
\r
17053 \begin_inset Formula $\diamond$
\r
17063 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
17064 \begin_inset Text
\r
17066 \begin_layout Plain Layout
\r
17074 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
17075 \begin_inset Text
\r
17077 \begin_layout Plain Layout
\r
17078 \begin_inset Formula $\bullet$
\r
17092 \begin_inset space \hfill{}
\r
17096 \begin_inset Tabular
\r
17097 <lyxtabular version="3" rows="13" columns="2">
\r
17098 <features tabularvalignment="middle">
\r
17099 <column alignment="center" valignment="top" width="0pt">
\r
17100 <column alignment="center" valignment="top" width="0pt">
\r
17102 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
17103 \begin_inset Text
\r
17105 \begin_layout Plain Layout
\r
17111 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
17112 \begin_inset Text
\r
17114 \begin_layout Plain Layout
\r
17122 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
17123 \begin_inset Text
\r
17125 \begin_layout Plain Layout
\r
17133 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
17134 \begin_inset Text
\r
17136 \begin_layout Plain Layout
\r
17137 \begin_inset Formula $\nabla$
\r
17147 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
17148 \begin_inset Text
\r
17150 \begin_layout Plain Layout
\r
17158 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
17159 \begin_inset Text
\r
17161 \begin_layout Plain Layout
\r
17162 \begin_inset Formula $\bigtriangledown$
\r
17172 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
17173 \begin_inset Text
\r
17175 \begin_layout Plain Layout
\r
17183 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
17184 \begin_inset Text
\r
17186 \begin_layout Plain Layout
\r
17187 \begin_inset Formula $\bigtriangleup$
\r
17197 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
17198 \begin_inset Text
\r
17200 \begin_layout Plain Layout
\r
17208 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
17209 \begin_inset Text
\r
17211 \begin_layout Plain Layout
\r
17212 \begin_inset Formula $\Box$
\r
17222 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
17223 \begin_inset Text
\r
17225 \begin_layout Plain Layout
\r
17233 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
17234 \begin_inset Text
\r
17236 \begin_layout Plain Layout
\r
17237 \begin_inset Formula $\cap$
\r
17247 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
17248 \begin_inset Text
\r
17250 \begin_layout Plain Layout
\r
17258 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
17259 \begin_inset Text
\r
17261 \begin_layout Plain Layout
\r
17262 \begin_inset Formula $\cup$
\r
17272 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
17273 \begin_inset Text
\r
17275 \begin_layout Plain Layout
\r
17283 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
17284 \begin_inset Text
\r
17286 \begin_layout Plain Layout
\r
17287 \begin_inset Formula $\dagger$
\r
17297 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
17298 \begin_inset Text
\r
17300 \begin_layout Plain Layout
\r
17308 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
17309 \begin_inset Text
\r
17311 \begin_layout Plain Layout
\r
17312 \begin_inset Formula $\ddagger$
\r
17322 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
17323 \begin_inset Text
\r
17325 \begin_layout Plain Layout
\r
17333 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
17334 \begin_inset Text
\r
17336 \begin_layout Plain Layout
\r
17337 \begin_inset Formula $\wr$
\r
17347 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
17348 \begin_inset Text
\r
17350 \begin_layout Plain Layout
\r
17358 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
17359 \begin_inset Text
\r
17361 \begin_layout Plain Layout
\r
17362 \begin_inset Formula $\bigcirc$
\r
17372 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
17373 \begin_inset Text
\r
17375 \begin_layout Plain Layout
\r
17383 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
17384 \begin_inset Text
\r
17386 \begin_layout Plain Layout
\r
17387 \begin_inset Formula $\wedge$
\r
17397 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
17398 \begin_inset Text
\r
17400 \begin_layout Plain Layout
\r
17408 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
17409 \begin_inset Text
\r
17411 \begin_layout Plain Layout
\r
17412 \begin_inset Formula $\vee$
\r
17426 \begin_inset space \hfill{}
\r
17430 \begin_inset Tabular
\r
17431 <lyxtabular version="3" rows="13" columns="2">
\r
17432 <features tabularvalignment="middle">
\r
17433 <column alignment="center" valignment="top" width="0pt">
\r
17434 <column alignment="center" valignment="top" width="0pt">
\r
17436 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
17437 \begin_inset Text
\r
17439 \begin_layout Plain Layout
\r
17445 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
17446 \begin_inset Text
\r
17448 \begin_layout Plain Layout
\r
17456 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
17457 \begin_inset Text
\r
17459 \begin_layout Plain Layout
\r
17467 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
17468 \begin_inset Text
\r
17470 \begin_layout Plain Layout
\r
17471 \begin_inset Formula $\oplus$
\r
17481 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
17482 \begin_inset Text
\r
17484 \begin_layout Plain Layout
\r
17492 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
17493 \begin_inset Text
\r
17495 \begin_layout Plain Layout
\r
17496 \begin_inset Formula $\ominus$
\r
17506 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
17507 \begin_inset Text
\r
17509 \begin_layout Plain Layout
\r
17517 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
17518 \begin_inset Text
\r
17520 \begin_layout Plain Layout
\r
17521 \begin_inset Formula $\otimes$
\r
17531 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
17532 \begin_inset Text
\r
17534 \begin_layout Plain Layout
\r
17542 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
17543 \begin_inset Text
\r
17545 \begin_layout Plain Layout
\r
17546 \begin_inset Formula $\oslash$
\r
17556 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
17557 \begin_inset Text
\r
17559 \begin_layout Plain Layout
\r
17567 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
17568 \begin_inset Text
\r
17570 \begin_layout Plain Layout
\r
17571 \begin_inset Formula $\odot$
\r
17581 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
17582 \begin_inset Text
\r
17584 \begin_layout Plain Layout
\r
17592 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
17593 \begin_inset Text
\r
17595 \begin_layout Plain Layout
\r
17596 \begin_inset Formula $\amalg$
\r
17606 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
17607 \begin_inset Text
\r
17609 \begin_layout Plain Layout
\r
17617 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
17618 \begin_inset Text
\r
17620 \begin_layout Plain Layout
\r
17621 \begin_inset Formula $\uplus$
\r
17631 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
17632 \begin_inset Text
\r
17634 \begin_layout Plain Layout
\r
17642 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
17643 \begin_inset Text
\r
17645 \begin_layout Plain Layout
\r
17646 \begin_inset Formula $\setminus$
\r
17656 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
17657 \begin_inset Text
\r
17659 \begin_layout Plain Layout
\r
17667 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
17668 \begin_inset Text
\r
17670 \begin_layout Plain Layout
\r
17671 \begin_inset Formula $\sqcap$
\r
17681 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
17682 \begin_inset Text
\r
17684 \begin_layout Plain Layout
\r
17692 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
17693 \begin_inset Text
\r
17695 \begin_layout Plain Layout
\r
17696 \begin_inset Formula $\sqcup$
\r
17706 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
17707 \begin_inset Text
\r
17709 \begin_layout Plain Layout
\r
17717 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
17718 \begin_inset Text
\r
17720 \begin_layout Plain Layout
\r
17721 \begin_inset Formula $\triangleleft$
\r
17731 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
17732 \begin_inset Text
\r
17734 \begin_layout Plain Layout
\r
17742 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
17743 \begin_inset Text
\r
17745 \begin_layout Plain Layout
\r
17746 \begin_inset Formula $\triangleright$
\r
17760 \begin_inset space \hfill{}
\r
17766 \begin_layout Standard
\r
17767 All binary operators can also be inserted via the math toolbar button
\r
17768 \begin_inset Graphics
\r
17769 filename ../images/math/pm.png
\r
17777 \begin_layout Standard
\r
17778 To typeset the Laplace operator also
\r
17795 \begin_inset Formula $\nabla^{2}$
\r
17798 ) can be used instead of
\r
17807 \begin_layout Standard
\r
17814 Insert\SpecialChar \menuseparator
\r
17815 Special Character
\r
17826 \begin_layout Subsection
\r
17827 Self-defined Operators
\r
17828 \begin_inset CommandInset label
\r
17829 LatexCommand label
\r
17830 name "sub:Self-defined-Operators"
\r
17835 \begin_inset Index idx
\r
17838 \begin_layout Plain Layout
\r
17839 Operators ! self-defined
\r
17847 \begin_layout Standard
\r
17848 With the help of the command
\r
17852 DeclareMathOperator
\r
17855 \begin_inset Index idx
\r
17858 \begin_layout Plain Layout
\r
17863 DeclareMathOperator
\r
17868 custom operators can be defined in the LaTeX-preamble.
\r
17869 Its command scheme is:
\r
17872 \begin_layout Standard
\r
17877 DeclareMathOperator{new command}{display}
\r
17880 \begin_layout Standard
\r
17881 Display can be characters or symbols that define how the operator looks
\r
17883 To define a big operator a * is set behind the command.
\r
17884 All self-defined big operators can have limits as described in
\r
17885 \begin_inset CommandInset ref
\r
17887 reference "sub:Operator-Limits"
\r
17894 \begin_layout Standard
\r
17895 For example the LaTeX-preamble line
\r
17898 \begin_layout Standard
\r
17903 DeclareMathOperator*{
\r
17910 \begin_layout Standard
\r
17911 defines the command
\r
17917 , that inserts a big operator consisting of the lozenge symbol from
\r
17918 \begin_inset CommandInset ref
\r
17920 reference "sub:Miscellaneous-Symbols"
\r
17925 \begin_inset Formula
\r
17927 \Lozenge_{n=1}^{\infty}
\r
17932 The command for this formula is:
\r
17943 \begin_inset Formula $\to$
\r
17949 \begin_layout Standard
\r
17950 \begin_inset VSpace bigskip
\r
17953 When self-defined operators are not used several times in the document,
\r
17954 they can also be defined with the commands
\r
17961 \begin_inset Index idx
\r
17964 \begin_layout Plain Layout
\r
17979 \begin_inset Index idx
\r
17982 \begin_layout Plain Layout
\r
17990 , which have the following scheme:
\r
17993 \begin_layout Standard
\r
18007 \begin_layout Standard
\r
18014 defines big operators,
\r
18020 binary operators.
\r
18023 \begin_layout Standard
\r
18031 \begin_inset space \thinspace{}
\r
18035 \begin_inset space \space{}
\r
18038 be used to use one limit for several operators:
\r
18041 \begin_layout Standard
\r
18042 \begin_inset Formula
\r
18044 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
\r
18052 \begin_layout Standard
\r
18053 The command for the formula above is:
\r
18054 \begin_inset Newline newline
\r
18073 \begin_layout Plain Layout
\r
18085 \begin_inset Formula $\to$
\r
18094 \begin_layout Plain Layout
\r
18108 \begin_layout Section
\r
18110 \begin_inset Index idx
\r
18113 \begin_layout Plain Layout
\r
18122 \begin_layout Subsection
\r
18124 \begin_inset CommandInset label
\r
18125 LatexCommand label
\r
18126 name "sub:Font-Styles"
\r
18131 \begin_inset Index idx
\r
18134 \begin_layout Plain Layout
\r
18143 \begin_layout Standard
\r
18144 Latin letters in formulas can be set in one of the following font styles:
\r
18145 \begin_inset VSpace -2mm
\r
18151 \begin_layout Standard
\r
18153 \begin_inset Tabular
\r
18154 <lyxtabular version="3" rows="7" columns="3">
\r
18155 <features tabularvalignment="middle">
\r
18156 <column alignment="center" valignment="top" width="0">
\r
18157 <column alignment="center" valignment="top" width="0">
\r
18158 <column alignment="center" valignment="top" width="0">
\r
18160 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
18161 \begin_inset Text
\r
18163 \begin_layout Plain Layout
\r
18169 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
18170 \begin_inset Text
\r
18172 \begin_layout Plain Layout
\r
18178 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
18179 \begin_inset Text
\r
18181 \begin_layout Plain Layout
\r
18189 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
18190 \begin_inset Text
\r
18192 \begin_layout Plain Layout
\r
18201 \begin_layout Plain Layout
\r
18217 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
18218 \begin_inset Text
\r
18220 \begin_layout Plain Layout
\r
18221 \begin_inset Formula $\mathbb{ABC}$
\r
18229 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
18230 \begin_inset Text
\r
18232 \begin_layout Plain Layout
\r
18233 \begin_inset Info
\r
18245 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
18246 \begin_inset Text
\r
18248 \begin_layout Plain Layout
\r
18257 \begin_layout Plain Layout
\r
18273 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
18274 \begin_inset Text
\r
18276 \begin_layout Plain Layout
\r
18277 \begin_inset Formula $\mathbf{AbC}$
\r
18285 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
18286 \begin_inset Text
\r
18288 \begin_layout Plain Layout
\r
18289 \begin_inset Info
\r
18301 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
18302 \begin_inset Text
\r
18304 \begin_layout Plain Layout
\r
18313 \begin_layout Plain Layout
\r
18329 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
18330 \begin_inset Text
\r
18332 \begin_layout Plain Layout
\r
18333 \begin_inset Formula $\boldsymbol{AbC}$
\r
18341 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
18342 \begin_inset Text
\r
18344 \begin_layout Plain Layout
\r
18345 \begin_inset Info
\r
18347 arg "font-boldsymbol"
\r
18357 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
18358 \begin_inset Text
\r
18360 \begin_layout Plain Layout
\r
18369 \begin_layout Plain Layout
\r
18385 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
18386 \begin_inset Text
\r
18388 \begin_layout Plain Layout
\r
18389 \begin_inset Formula $\mathcal{ABC}$
\r
18397 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
18398 \begin_inset Text
\r
18400 \begin_layout Plain Layout
\r
18401 \begin_inset Info
\r
18413 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
18414 \begin_inset Text
\r
18416 \begin_layout Plain Layout
\r
18425 \begin_layout Plain Layout
\r
18441 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
18442 \begin_inset Text
\r
18444 \begin_layout Plain Layout
\r
18445 \begin_inset Formula $\mathfrak{AbC}$
\r
18453 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
18454 \begin_inset Text
\r
18456 \begin_layout Plain Layout
\r
18464 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
18465 \begin_inset Text
\r
18467 \begin_layout Plain Layout
\r
18476 \begin_layout Plain Layout
\r
18492 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
18493 \begin_inset Text
\r
18495 \begin_layout Plain Layout
\r
18496 \begin_inset Formula $\mathscr{AbC}$
\r
18504 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
18505 \begin_inset Text
\r
18507 \begin_layout Plain Layout
\r
18521 \begin_layout Standard
\r
18523 \begin_inset Tabular
\r
18524 <lyxtabular version="3" rows="5" columns="3">
\r
18525 <features tabularvalignment="middle">
\r
18526 <column alignment="center" valignment="top" width="0">
\r
18527 <column alignment="center" valignment="top" width="0">
\r
18528 <column alignment="center" valignment="top" width="0">
\r
18530 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
18531 \begin_inset Text
\r
18533 \begin_layout Plain Layout
\r
18539 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
18540 \begin_inset Text
\r
18542 \begin_layout Plain Layout
\r
18548 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
18549 \begin_inset Text
\r
18551 \begin_layout Plain Layout
\r
18559 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
18560 \begin_inset Text
\r
18562 \begin_layout Plain Layout
\r
18571 \begin_layout Plain Layout
\r
18587 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
18588 \begin_inset Text
\r
18590 \begin_layout Plain Layout
\r
18591 \begin_inset Formula $\mathit{AbC}$
\r
18599 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
18600 \begin_inset Text
\r
18602 \begin_layout Plain Layout
\r
18610 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
18611 \begin_inset Text
\r
18613 \begin_layout Plain Layout
\r
18622 \begin_layout Plain Layout
\r
18638 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
18639 \begin_inset Text
\r
18641 \begin_layout Plain Layout
\r
18642 \begin_inset Formula $\mathrm{AbC}$
\r
18650 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
18651 \begin_inset Text
\r
18653 \begin_layout Plain Layout
\r
18654 \begin_inset Info
\r
18666 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
18667 \begin_inset Text
\r
18669 \begin_layout Plain Layout
\r
18678 \begin_layout Plain Layout
\r
18694 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
18695 \begin_inset Text
\r
18697 \begin_layout Plain Layout
\r
18698 \begin_inset Formula $\mathsf{AbC}$
\r
18706 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
18707 \begin_inset Text
\r
18709 \begin_layout Plain Layout
\r
18710 \begin_inset Info
\r
18722 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
18723 \begin_inset Text
\r
18725 \begin_layout Plain Layout
\r
18734 \begin_layout Plain Layout
\r
18750 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
18751 \begin_inset Text
\r
18753 \begin_layout Plain Layout
\r
18754 \begin_inset Formula $\mathtt{AbC}$
\r
18762 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
18763 \begin_inset Text
\r
18765 \begin_layout Plain Layout
\r
18766 \begin_inset Info
\r
18768 arg "font-typewriter"
\r
18784 \begin_layout Standard
\r
18785 \begin_inset Note Greyedout
\r
18788 \begin_layout Plain Layout
\r
18805 can only be used for big letters.
\r
18813 \begin_layout Standard
\r
18814 Predefined is the style
\r
18823 \begin_layout Standard
\r
18824 The style commands work also for letters in mathematical constructs:
\r
18825 \begin_inset Formula
\r
18827 \mathfrak{A=\frac{b}{C}}
\r
18835 \begin_layout Standard
\r
18836 Characters in mathematical text don't appear in a math font style but in
\r
18837 the text font style
\r
18844 That their style can't be set correctly via the text style dialog is a
\r
18846 \begin_inset Foot
\r
18849 \begin_layout Plain Layout
\r
18850 \begin_inset CommandInset href
\r
18851 LatexCommand href
\r
18852 name "LyX-bug #4629"
\r
18853 target "http://www.lyx.org/trac/ticket/4629"
\r
18865 \begin_layout Standard
\r
18866 Instead of the style commands the dialog
\r
18868 Edit\SpecialChar \menuseparator
\r
18869 Math\SpecialChar \menuseparator
\r
18872 or the toolbar button
\r
18873 \begin_inset Graphics
\r
18874 filename ../images/math/font.png
\r
18882 \begin_layout Subsection
\r
18884 \begin_inset CommandInset label
\r
18885 LatexCommand label
\r
18886 name "sub:Bold-Formulas"
\r
18891 \begin_inset Index idx
\r
18894 \begin_layout Plain Layout
\r
18903 \begin_layout Standard
\r
18904 To make a complete formula bold, the command
\r
18910 from the previous subsection cannot be used, because it doesn't work for
\r
18911 small Greek letters.
\r
18912 Furthermore it prints Latin letters always upright, like in the following
\r
18916 \begin_layout Standard
\r
18917 \begin_inset Formula
\r
18919 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
\r
18927 \begin_layout Standard
\r
18928 To display the formula correctly, the command
\r
18935 \begin_inset Formula
\r
18937 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
\r
18942 It is also possible to set the formula in a
\r
18944 boldmath environment
\r
18947 This environment is created by inserting the command
\r
18954 \begin_inset Index idx
\r
18957 \begin_layout Plain Layout
\r
18966 To end the environment, the command
\r
18973 \begin_inset Index idx
\r
18976 \begin_layout Plain Layout
\r
18984 is inserted in TeX-mode.
\r
18988 \begin_layout Plain Layout
\r
18998 \begin_inset Formula
\r
19000 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
\r
19009 \begin_layout Plain Layout
\r
19021 \begin_layout Subsection
\r
19023 \begin_inset Index idx
\r
19026 \begin_layout Plain Layout
\r
19027 Formula ! colored
\r
19035 \begin_layout Standard
\r
19036 Formulas can be colored like normal text: Highlight a formula or a formula
\r
19037 part and use the
\r
19042 Here is a formula in magenta:
\r
19043 \begin_inset Formula
\r
19045 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
\r
19053 \begin_layout Standard
\r
19054 You can also define your own colors as described in
\r
19055 \begin_inset CommandInset ref
\r
19057 reference "sub:Colored-Boxes"
\r
19062 They can be used with the TeX code command
\r
19069 \begin_inset Index idx
\r
19072 \begin_layout Plain Layout
\r
19083 \begin_layout Standard
\r
19088 textcolor{color}{characters or formula}
\r
19091 \begin_layout Standard
\r
19092 The following example was colored completely dark green and partly red:
\r
19095 \begin_layout Standard
\r
19099 \begin_layout Plain Layout
\r
19103 textcolor{darkgreen}{
\r
19109 \begin_inset Formula
\r
19111 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
\r
19120 \begin_layout Plain Layout
\r
19130 \begin_layout Standard
\r
19131 Due to a bug in LyX only complete formulas can be colored with self-defined
\r
19133 \begin_inset Foot
\r
19136 \begin_layout Plain Layout
\r
19137 \begin_inset CommandInset href
\r
19138 LatexCommand href
\r
19139 name "LyX-bug #5269"
\r
19140 target "http://www.lyx.org/trac/ticket/5269"
\r
19152 \begin_layout Subsection
\r
19154 \begin_inset CommandInset label
\r
19155 LatexCommand label
\r
19156 name "sub:Font-Sizes"
\r
19161 \begin_inset Index idx
\r
19164 \begin_layout Plain Layout
\r
19173 \begin_layout Standard
\r
19174 For characters in formulas there are, analog to characters in text, the
\r
19175 following size commands:
\r
19178 \begin_layout Standard
\r
19222 \begin_inset Newline newline
\r
19244 \begin_layout Standard
\r
19245 The size produced by the commands depends on the document font size, which
\r
19246 corresponds to the command
\r
19253 The other commands produce smaller or larger sizes than
\r
19260 The font size can however not exceed a certain value.
\r
19261 Is for example the document font size 12
\r
19262 \begin_inset space \thinspace{}
\r
19271 switches to the same size as
\r
19281 \begin_layout Standard
\r
19282 A size command is inserted in TeX-mode before the formula and sets the size
\r
19283 for all following formula and text characters.
\r
19284 To switch back to the initial size, the command
\r
19290 is inserted behind the formula in TeX-mode.
\r
19293 \begin_layout Standard
\r
19294 Within a formula the size can be changed using the following size commands:
\r
19297 \begin_layout Standard
\r
19300 \begin_inset Tabular
\r
19301 <lyxtabular version="3" rows="5" columns="2">
\r
19302 <features tabularvalignment="middle">
\r
19303 <column alignment="center" valignment="top" width="0">
\r
19304 <column alignment="center" valignment="top" width="0">
\r
19306 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
19307 \begin_inset Text
\r
19309 \begin_layout Plain Layout
\r
19315 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
19316 \begin_inset Text
\r
19318 \begin_layout Plain Layout
\r
19320 \begin_inset Note Note
\r
19323 \begin_layout Plain Layout
\r
19330 is only used as spacer.
\r
19342 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
19343 \begin_inset Text
\r
19345 \begin_layout Plain Layout
\r
19349 \begin_inset Index idx
\r
19352 \begin_layout Plain Layout
\r
19365 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
19366 \begin_inset Text
\r
19368 \begin_layout Plain Layout
\r
19369 \begin_inset Formula $\raisebox{6.5mm}{}{\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-5.5mm}{}$
\r
19379 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
19380 \begin_inset Text
\r
19382 \begin_layout Plain Layout
\r
19390 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
19391 \begin_inset Text
\r
19393 \begin_layout Plain Layout
\r
19394 \begin_inset Formula $\raisebox{4.5mm}{}{\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-4mm}{}$
\r
19404 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
19405 \begin_inset Text
\r
19407 \begin_layout Plain Layout
\r
19415 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
19416 \begin_inset Text
\r
19418 \begin_layout Plain Layout
\r
19419 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
\r
19429 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
19430 \begin_inset Text
\r
19432 \begin_layout Plain Layout
\r
19435 scriptscriptstyle
\r
19440 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
19441 \begin_inset Text
\r
19443 \begin_layout Plain Layout
\r
19444 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
\r
19460 \begin_layout Standard
\r
19461 After entering these commands, a blue box appears in which the formula parts
\r
19465 \begin_layout Standard
\r
19466 There is a further method to change the font size, that though only works
\r
19467 for symbols or letters in mathematical text.
\r
19468 To use it, one of the above text size commands is inserted in mathematical
\r
19470 All following characters until the end of the mathematical text or until
\r
19471 another size command will have the selected size.
\r
19473 \begin_inset VSpace -2mm
\r
19479 \begin_layout Standard
\r
19483 \begin_layout Plain Layout
\r
19493 \begin_inset Formula
\r
19495 A=\frac{B}{c}\cdot\maltese
\r
19501 \begin_inset Formula
\r
19503 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
\r
19512 \begin_layout Plain Layout
\r
19524 \begin_layout Standard
\r
19525 \begin_inset VSpace medskip
\r
19528 Before both formulas the command
\r
19535 The command for the second formula is:
\r
19536 \begin_inset Newline newline
\r
19547 \begin_layout Plain Layout
\r
19562 \begin_layout Plain Layout
\r
19577 \begin_layout Plain Layout
\r
19592 \begin_layout Plain Layout
\r
19602 \begin_inset Formula $\to$
\r
19606 \begin_inset Formula $\to$
\r
19610 \begin_inset Newline newline
\r
19614 \begin_inset space \hspace*{}
\r
19628 \begin_layout Plain Layout
\r
19643 \begin_layout Plain Layout
\r
19658 \begin_layout Plain Layout
\r
19670 \begin_layout Standard
\r
19671 If a symbol cannot be displayed in different sizes, it will always be displayed
\r
19672 in the default size.
\r
19675 \begin_layout Section
\r
19677 \begin_inset Index idx
\r
19680 \begin_layout Plain Layout
\r
19689 \begin_layout Standard
\r
19690 Greek letters can also be inserted via the toolbar button
\r
19691 \begin_inset Graphics
\r
19692 filename ../images/math/alpha.png
\r
19698 All international typesetting norms purport that Greek letters in math
\r
19699 have to be typeset italic/slanted.
\r
19700 In some languages, like French or Russian, they are nevertheless sometimes
\r
19704 \begin_layout Subsection
\r
19706 \begin_inset Index idx
\r
19709 \begin_layout Plain Layout
\r
19710 Greek letters ! small
\r
19718 \begin_layout Standard
\r
19719 \begin_inset space \hfill{}
\r
19723 \begin_inset Tabular
\r
19724 <lyxtabular version="3" rows="11" columns="2">
\r
19725 <features tabularvalignment="middle">
\r
19726 <column alignment="center" valignment="top" width="0pt">
\r
19727 <column alignment="center" valignment="top" width="0pt">
\r
19729 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
19730 \begin_inset Text
\r
19732 \begin_layout Plain Layout
\r
19738 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
19739 \begin_inset Text
\r
19741 \begin_layout Plain Layout
\r
19749 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
19750 \begin_inset Text
\r
19752 \begin_layout Plain Layout
\r
19760 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
19761 \begin_inset Text
\r
19763 \begin_layout Plain Layout
\r
19764 \begin_inset Formula $\alpha$
\r
19774 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
19775 \begin_inset Text
\r
19777 \begin_layout Plain Layout
\r
19785 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
19786 \begin_inset Text
\r
19788 \begin_layout Plain Layout
\r
19789 \begin_inset Formula $\beta$
\r
19799 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
19800 \begin_inset Text
\r
19802 \begin_layout Plain Layout
\r
19810 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
19811 \begin_inset Text
\r
19813 \begin_layout Plain Layout
\r
19814 \begin_inset Formula $\gamma$
\r
19824 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
19825 \begin_inset Text
\r
19827 \begin_layout Plain Layout
\r
19835 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
19836 \begin_inset Text
\r
19838 \begin_layout Plain Layout
\r
19839 \begin_inset Formula $\delta$
\r
19849 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
19850 \begin_inset Text
\r
19852 \begin_layout Plain Layout
\r
19860 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
19861 \begin_inset Text
\r
19863 \begin_layout Plain Layout
\r
19864 \begin_inset Formula $\epsilon$
\r
19874 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
19875 \begin_inset Text
\r
19877 \begin_layout Plain Layout
\r
19885 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
19886 \begin_inset Text
\r
19888 \begin_layout Plain Layout
\r
19889 \begin_inset Formula $\varepsilon$
\r
19899 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
19900 \begin_inset Text
\r
19902 \begin_layout Plain Layout
\r
19910 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
19911 \begin_inset Text
\r
19913 \begin_layout Plain Layout
\r
19914 \begin_inset Formula $\zeta$
\r
19924 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
19925 \begin_inset Text
\r
19927 \begin_layout Plain Layout
\r
19935 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
19936 \begin_inset Text
\r
19938 \begin_layout Plain Layout
\r
19939 \begin_inset Formula $\eta$
\r
19949 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
19950 \begin_inset Text
\r
19952 \begin_layout Plain Layout
\r
19960 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
19961 \begin_inset Text
\r
19963 \begin_layout Plain Layout
\r
19964 \begin_inset Formula $\theta$
\r
19974 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
19975 \begin_inset Text
\r
19977 \begin_layout Plain Layout
\r
19985 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
19986 \begin_inset Text
\r
19988 \begin_layout Plain Layout
\r
19989 \begin_inset Formula $\vartheta$
\r
20003 \begin_inset space \hfill{}
\r
20007 \begin_inset Tabular
\r
20008 <lyxtabular version="3" rows="12" columns="2">
\r
20009 <features tabularvalignment="middle">
\r
20010 <column alignment="center" valignment="top" width="0pt">
\r
20011 <column alignment="center" valignment="top" width="0pt">
\r
20013 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
20014 \begin_inset Text
\r
20016 \begin_layout Plain Layout
\r
20022 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
20023 \begin_inset Text
\r
20025 \begin_layout Plain Layout
\r
20033 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
20034 \begin_inset Text
\r
20036 \begin_layout Plain Layout
\r
20044 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
20045 \begin_inset Text
\r
20047 \begin_layout Plain Layout
\r
20048 \begin_inset Formula $\iota$
\r
20058 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
20059 \begin_inset Text
\r
20061 \begin_layout Plain Layout
\r
20069 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
20070 \begin_inset Text
\r
20072 \begin_layout Plain Layout
\r
20073 \begin_inset Formula $\kappa$
\r
20083 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
20084 \begin_inset Text
\r
20086 \begin_layout Plain Layout
\r
20094 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
20095 \begin_inset Text
\r
20097 \begin_layout Plain Layout
\r
20098 \begin_inset Formula $\varkappa$
\r
20108 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
20109 \begin_inset Text
\r
20111 \begin_layout Plain Layout
\r
20119 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
20120 \begin_inset Text
\r
20122 \begin_layout Plain Layout
\r
20123 \begin_inset Formula $\lambda$
\r
20133 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
20134 \begin_inset Text
\r
20136 \begin_layout Plain Layout
\r
20144 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
20145 \begin_inset Text
\r
20147 \begin_layout Plain Layout
\r
20148 \begin_inset Formula $\mu$
\r
20158 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
20159 \begin_inset Text
\r
20161 \begin_layout Plain Layout
\r
20169 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
20170 \begin_inset Text
\r
20172 \begin_layout Plain Layout
\r
20173 \begin_inset Formula $\nu$
\r
20183 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
20184 \begin_inset Text
\r
20186 \begin_layout Plain Layout
\r
20194 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
20195 \begin_inset Text
\r
20197 \begin_layout Plain Layout
\r
20198 \begin_inset Formula $\xi$
\r
20208 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
20209 \begin_inset Text
\r
20211 \begin_layout Plain Layout
\r
20217 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
20218 \begin_inset Text
\r
20220 \begin_layout Plain Layout
\r
20221 \begin_inset Formula $o$
\r
20231 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
20232 \begin_inset Text
\r
20234 \begin_layout Plain Layout
\r
20242 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
20243 \begin_inset Text
\r
20245 \begin_layout Plain Layout
\r
20246 \begin_inset Formula $\pi$
\r
20256 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
20257 \begin_inset Text
\r
20259 \begin_layout Plain Layout
\r
20267 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
20268 \begin_inset Text
\r
20270 \begin_layout Plain Layout
\r
20271 \begin_inset Formula $\varpi$
\r
20281 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
20282 \begin_inset Text
\r
20284 \begin_layout Plain Layout
\r
20292 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
20293 \begin_inset Text
\r
20295 \begin_layout Plain Layout
\r
20296 \begin_inset Formula $\rho$
\r
20310 \begin_inset space \hfill{}
\r
20314 \begin_inset Tabular
\r
20315 <lyxtabular version="3" rows="11" columns="2">
\r
20316 <features tabularvalignment="middle">
\r
20317 <column alignment="center" valignment="top" width="0pt">
\r
20318 <column alignment="center" valignment="top" width="0pt">
\r
20320 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
20321 \begin_inset Text
\r
20323 \begin_layout Plain Layout
\r
20329 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
20330 \begin_inset Text
\r
20332 \begin_layout Plain Layout
\r
20340 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
20341 \begin_inset Text
\r
20343 \begin_layout Plain Layout
\r
20351 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
20352 \begin_inset Text
\r
20354 \begin_layout Plain Layout
\r
20355 \begin_inset Formula $\varrho$
\r
20365 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
20366 \begin_inset Text
\r
20368 \begin_layout Plain Layout
\r
20376 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
20377 \begin_inset Text
\r
20379 \begin_layout Plain Layout
\r
20380 \begin_inset Formula $\sigma$
\r
20390 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
20391 \begin_inset Text
\r
20393 \begin_layout Plain Layout
\r
20401 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
20402 \begin_inset Text
\r
20404 \begin_layout Plain Layout
\r
20405 \begin_inset Formula $\varsigma$
\r
20415 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
20416 \begin_inset Text
\r
20418 \begin_layout Plain Layout
\r
20426 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
20427 \begin_inset Text
\r
20429 \begin_layout Plain Layout
\r
20430 \begin_inset Formula $\tau$
\r
20440 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
20441 \begin_inset Text
\r
20443 \begin_layout Plain Layout
\r
20451 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
20452 \begin_inset Text
\r
20454 \begin_layout Plain Layout
\r
20455 \begin_inset Formula $\upsilon$
\r
20465 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
20466 \begin_inset Text
\r
20468 \begin_layout Plain Layout
\r
20476 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
20477 \begin_inset Text
\r
20479 \begin_layout Plain Layout
\r
20480 \begin_inset Formula $\phi$
\r
20490 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
20491 \begin_inset Text
\r
20493 \begin_layout Plain Layout
\r
20501 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
20502 \begin_inset Text
\r
20504 \begin_layout Plain Layout
\r
20505 \begin_inset Formula $\varphi$
\r
20515 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
20516 \begin_inset Text
\r
20518 \begin_layout Plain Layout
\r
20526 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
20527 \begin_inset Text
\r
20529 \begin_layout Plain Layout
\r
20530 \begin_inset Formula $\chi$
\r
20540 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
20541 \begin_inset Text
\r
20543 \begin_layout Plain Layout
\r
20551 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
20552 \begin_inset Text
\r
20554 \begin_layout Plain Layout
\r
20555 \begin_inset Formula $\psi$
\r
20565 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
20566 \begin_inset Text
\r
20568 \begin_layout Plain Layout
\r
20576 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
20577 \begin_inset Text
\r
20579 \begin_layout Plain Layout
\r
20580 \begin_inset Formula $\omega$
\r
20594 \begin_inset space \hfill{}
\r
20600 \begin_layout Standard
\r
20601 \begin_inset VSpace medskip
\r
20607 \begin_layout Standard
\r
20608 How to create special upright Greek letters is explained in
\r
20609 \begin_inset CommandInset ref
\r
20611 reference "sub:Upright-small-Greek"
\r
20618 \begin_layout Subsection
\r
20620 \begin_inset Index idx
\r
20623 \begin_layout Plain Layout
\r
20624 Greek letters ! big
\r
20632 \begin_layout Standard
\r
20633 \begin_inset space \hfill{}
\r
20637 \begin_inset Tabular
\r
20638 <lyxtabular version="3" rows="7" columns="2">
\r
20639 <features tabularvalignment="middle">
\r
20640 <column alignment="center" valignment="top" width="0pt">
\r
20641 <column alignment="center" valignment="top" width="0pt">
\r
20643 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
20644 \begin_inset Text
\r
20646 \begin_layout Plain Layout
\r
20652 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
20653 \begin_inset Text
\r
20655 \begin_layout Plain Layout
\r
20663 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
20664 \begin_inset Text
\r
20666 \begin_layout Plain Layout
\r
20674 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
20675 \begin_inset Text
\r
20677 \begin_layout Plain Layout
\r
20678 \begin_inset Formula $\Gamma$
\r
20688 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
20689 \begin_inset Text
\r
20691 \begin_layout Plain Layout
\r
20699 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
20700 \begin_inset Text
\r
20702 \begin_layout Plain Layout
\r
20703 \begin_inset Formula $\Delta$
\r
20713 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
20714 \begin_inset Text
\r
20716 \begin_layout Plain Layout
\r
20724 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
20725 \begin_inset Text
\r
20727 \begin_layout Plain Layout
\r
20728 \begin_inset Formula $\Theta$
\r
20738 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
20739 \begin_inset Text
\r
20741 \begin_layout Plain Layout
\r
20749 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
20750 \begin_inset Text
\r
20752 \begin_layout Plain Layout
\r
20753 \begin_inset Formula $\Lambda$
\r
20763 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
20764 \begin_inset Text
\r
20766 \begin_layout Plain Layout
\r
20774 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
20775 \begin_inset Text
\r
20777 \begin_layout Plain Layout
\r
20778 \begin_inset Formula $\Xi$
\r
20788 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
20789 \begin_inset Text
\r
20791 \begin_layout Plain Layout
\r
20799 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
20800 \begin_inset Text
\r
20802 \begin_layout Plain Layout
\r
20803 \begin_inset Formula $\Pi$
\r
20817 \begin_inset space \hfill{}
\r
20821 \begin_inset Tabular
\r
20822 <lyxtabular version="3" rows="6" columns="2">
\r
20823 <features tabularvalignment="middle">
\r
20824 <column alignment="center" valignment="top" width="0pt">
\r
20825 <column alignment="center" valignment="top" width="0pt">
\r
20827 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
20828 \begin_inset Text
\r
20830 \begin_layout Plain Layout
\r
20836 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
20837 \begin_inset Text
\r
20839 \begin_layout Plain Layout
\r
20847 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
20848 \begin_inset Text
\r
20850 \begin_layout Plain Layout
\r
20858 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
20859 \begin_inset Text
\r
20861 \begin_layout Plain Layout
\r
20862 \begin_inset Formula $\Sigma$
\r
20872 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
20873 \begin_inset Text
\r
20875 \begin_layout Plain Layout
\r
20883 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
20884 \begin_inset Text
\r
20886 \begin_layout Plain Layout
\r
20887 \begin_inset Formula $\Upsilon$
\r
20897 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
20898 \begin_inset Text
\r
20900 \begin_layout Plain Layout
\r
20908 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
20909 \begin_inset Text
\r
20911 \begin_layout Plain Layout
\r
20912 \begin_inset Formula $\Phi$
\r
20922 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
20923 \begin_inset Text
\r
20925 \begin_layout Plain Layout
\r
20933 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
20934 \begin_inset Text
\r
20936 \begin_layout Plain Layout
\r
20937 \begin_inset Formula $\Psi$
\r
20947 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
20948 \begin_inset Text
\r
20950 \begin_layout Plain Layout
\r
20958 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
20959 \begin_inset Text
\r
20961 \begin_layout Plain Layout
\r
20962 \begin_inset Formula $\Omega$
\r
20976 \begin_inset space \hfill{}
\r
20982 \begin_layout Standard
\r
20983 \begin_inset VSpace medskip
\r
20986 That the big Greek letters appear upright is caused by a design bug when
\r
20987 TeX was developed.
\r
20988 To get correct italic big letters, begin every command with
\r
20993 For example the command
\r
21000 \begin_inset Formula $\varGamma$
\r
21004 Another way is to load the package
\r
21009 \begin_inset Foot
\r
21012 \begin_layout Plain Layout
\r
21017 is part of the LaTeX-package
\r
21022 \begin_inset Index idx
\r
21025 \begin_layout Plain Layout
\r
21030 \begin_layout Plain Layout
\r
21050 \begin_inset Index idx
\r
21053 \begin_layout Plain Layout
\r
21054 Packages ! fixmath
\r
21059 with the LaTeX-preamble line
\r
21062 \begin_layout Standard
\r
21067 usepackage{fixmath}
\r
21070 \begin_layout Standard
\r
21071 Then all big Greek letters in a document will automatically be typeset italic.
\r
21074 \begin_layout Subsection
\r
21076 \begin_inset Index idx
\r
21079 \begin_layout Plain Layout
\r
21080 Greek letters ! bold
\r
21088 \begin_layout Standard
\r
21089 Greek letters cannot be set with different font styles like Latin letters.
\r
21090 They can only be made bold with the command
\r
21097 \begin_inset Index idx
\r
21100 \begin_layout Plain Layout
\r
21111 \begin_layout Standard
\r
21113 \begin_inset Tabular
\r
21114 <lyxtabular version="3" rows="3" columns="2">
\r
21115 <features tabularvalignment="middle">
\r
21116 <column alignment="center" valignment="top" width="0">
\r
21117 <column alignment="center" valignment="top" width="0">
\r
21119 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
21120 \begin_inset Text
\r
21122 \begin_layout Plain Layout
\r
21128 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
21129 \begin_inset Text
\r
21131 \begin_layout Plain Layout
\r
21139 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
21140 \begin_inset Text
\r
21142 \begin_layout Plain Layout
\r
21154 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
21155 \begin_inset Text
\r
21157 \begin_layout Plain Layout
\r
21158 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
\r
21168 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
21169 \begin_inset Text
\r
21171 \begin_layout Plain Layout
\r
21183 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
21184 \begin_inset Text
\r
21186 \begin_layout Plain Layout
\r
21187 \begin_inset Formula $\theta\boldsymbol{\theta}$
\r
21203 \begin_layout Section
\r
21208 \begin_layout Plain Layout
\r
21218 \begin_inset Foot
\r
21221 \begin_layout Plain Layout
\r
21222 A list with all symbols of most of the LaTeX-packages can be found in
\r
21223 \begin_inset CommandInset citation
\r
21224 LatexCommand cite
\r
21238 \begin_layout Plain Layout
\r
21246 \begin_inset Note Note
\r
21249 \begin_layout Plain Layout
\r
21252 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
\r
21255 \begin_layout Plain Layout
\r
21258 texorpdfstring is in section
\r
21259 \begin_inset CommandInset ref
\r
21261 reference "sub:Formulas-in-Section"
\r
21271 \begin_inset Index idx
\r
21274 \begin_layout Plain Layout
\r
21283 \begin_layout Standard
\r
21284 Many of the symbols listed in this section can also be inserted via the
\r
21286 \begin_inset Graphics
\r
21287 filename ../images/math/nabla.png
\r
21293 \begin_inset Graphics
\r
21294 filename ../images/math/digamma.png
\r
21302 \begin_layout Subsection
\r
21303 Mathematical Symbols
\r
21304 \begin_inset CommandInset label
\r
21305 LatexCommand label
\r
21306 name "sub:Mathematical-Symbols"
\r
21311 \begin_inset Index idx
\r
21314 \begin_layout Plain Layout
\r
21315 Symbols ! mathematical
\r
21323 \begin_layout Standard
\r
21324 \begin_inset space \hfill{}
\r
21328 \begin_inset Tabular
\r
21329 <lyxtabular version="3" rows="10" columns="2">
\r
21330 <features tabularvalignment="middle">
\r
21331 <column alignment="center" valignment="top" width="0pt">
\r
21332 <column alignment="center" valignment="top" width="0pt">
\r
21334 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
21335 \begin_inset Text
\r
21337 \begin_layout Plain Layout
\r
21343 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
21344 \begin_inset Text
\r
21346 \begin_layout Plain Layout
\r
21354 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
21355 \begin_inset Text
\r
21357 \begin_layout Plain Layout
\r
21365 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
21366 \begin_inset Text
\r
21368 \begin_layout Plain Layout
\r
21369 \begin_inset Formula $\neg$
\r
21379 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
21380 \begin_inset Text
\r
21382 \begin_layout Plain Layout
\r
21390 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
21391 \begin_inset Text
\r
21393 \begin_layout Plain Layout
\r
21394 \begin_inset Formula $\Im$
\r
21404 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
21405 \begin_inset Text
\r
21407 \begin_layout Plain Layout
\r
21415 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
21416 \begin_inset Text
\r
21418 \begin_layout Plain Layout
\r
21419 \begin_inset Formula $\Re$
\r
21429 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
21430 \begin_inset Text
\r
21432 \begin_layout Plain Layout
\r
21440 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
21441 \begin_inset Text
\r
21443 \begin_layout Plain Layout
\r
21444 \begin_inset Formula $\aleph$
\r
21454 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
21455 \begin_inset Text
\r
21457 \begin_layout Plain Layout
\r
21465 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
21466 \begin_inset Text
\r
21468 \begin_layout Plain Layout
\r
21469 \begin_inset Formula $\partial$
\r
21479 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
21480 \begin_inset Text
\r
21482 \begin_layout Plain Layout
\r
21490 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
21491 \begin_inset Text
\r
21493 \begin_layout Plain Layout
\r
21494 \begin_inset Formula $\infty$
\r
21504 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
21505 \begin_inset Text
\r
21507 \begin_layout Plain Layout
\r
21515 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
21516 \begin_inset Text
\r
21518 \begin_layout Plain Layout
\r
21519 \begin_inset Formula $\wp$
\r
21529 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
21530 \begin_inset Text
\r
21532 \begin_layout Plain Layout
\r
21540 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
21541 \begin_inset Text
\r
21543 \begin_layout Plain Layout
\r
21544 \begin_inset Formula $\imath$
\r
21554 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
21555 \begin_inset Text
\r
21557 \begin_layout Plain Layout
\r
21565 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
21566 \begin_inset Text
\r
21568 \begin_layout Plain Layout
\r
21569 \begin_inset Formula $\jmath$
\r
21583 \begin_inset space \hfill{}
\r
21587 \begin_inset Tabular
\r
21588 <lyxtabular version="3" rows="10" columns="2">
\r
21589 <features tabularvalignment="middle">
\r
21590 <column alignment="center" valignment="top" width="0pt">
\r
21591 <column alignment="center" valignment="top" width="0pt">
\r
21593 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
21594 \begin_inset Text
\r
21596 \begin_layout Plain Layout
\r
21602 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
21603 \begin_inset Text
\r
21605 \begin_layout Plain Layout
\r
21607 \begin_inset Note Note
\r
21610 \begin_layout Plain Layout
\r
21617 is only used as spacer.
\r
21629 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
21630 \begin_inset Text
\r
21632 \begin_layout Plain Layout
\r
21640 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
21641 \begin_inset Text
\r
21643 \begin_layout Plain Layout
\r
21644 \begin_inset Formula $\forall$
\r
21654 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
21655 \begin_inset Text
\r
21657 \begin_layout Plain Layout
\r
21665 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
21666 \begin_inset Text
\r
21668 \begin_layout Plain Layout
\r
21669 \begin_inset Formula $\exists$
\r
21679 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
21680 \begin_inset Text
\r
21682 \begin_layout Plain Layout
\r
21690 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
21691 \begin_inset Text
\r
21693 \begin_layout Plain Layout
\r
21694 \begin_inset Formula $\nexists$
\r
21704 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
21705 \begin_inset Text
\r
21707 \begin_layout Plain Layout
\r
21715 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
21716 \begin_inset Text
\r
21718 \begin_layout Plain Layout
\r
21719 \begin_inset Formula $\emptyset$
\r
21729 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
21730 \begin_inset Text
\r
21732 \begin_layout Plain Layout
\r
21740 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
21741 \begin_inset Text
\r
21743 \begin_layout Plain Layout
\r
21744 \begin_inset Formula $\varnothing$
\r
21754 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
21755 \begin_inset Text
\r
21757 \begin_layout Plain Layout
\r
21765 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
21766 \begin_inset Text
\r
21768 \begin_layout Plain Layout
\r
21769 \begin_inset Formula $\dag$
\r
21779 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
21780 \begin_inset Text
\r
21782 \begin_layout Plain Layout
\r
21790 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
21791 \begin_inset Text
\r
21793 \begin_layout Plain Layout
\r
21794 \begin_inset Formula $\ddag$
\r
21804 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
21805 \begin_inset Text
\r
21807 \begin_layout Plain Layout
\r
21815 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
21816 \begin_inset Text
\r
21818 \begin_layout Plain Layout
\r
21822 \begin_layout Plain Layout
\r
21826 raisebox{-0.8mm}{
\r
21832 \begin_inset Formula $\complement$
\r
21839 \begin_layout Plain Layout
\r
21853 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
21854 \begin_inset Text
\r
21856 \begin_layout Plain Layout
\r
21864 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
21865 \begin_inset Text
\r
21867 \begin_layout Plain Layout
\r
21868 \begin_inset Formula $\Bbbk$
\r
21882 \begin_inset space \hfill{}
\r
21886 \begin_inset Tabular
\r
21887 <lyxtabular version="3" rows="10" columns="2">
\r
21888 <features tabularvalignment="middle">
\r
21889 <column alignment="center" valignment="top" width="0pt">
\r
21890 <column alignment="center" valignment="top" width="0pt">
\r
21892 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
21893 \begin_inset Text
\r
21895 \begin_layout Plain Layout
\r
21901 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
21902 \begin_inset Text
\r
21904 \begin_layout Plain Layout
\r
21912 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
21913 \begin_inset Text
\r
21915 \begin_layout Plain Layout
\r
21923 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
21924 \begin_inset Text
\r
21926 \begin_layout Plain Layout
\r
21927 \begin_inset Formula $\prime$
\r
21937 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
21938 \begin_inset Text
\r
21940 \begin_layout Plain Layout
\r
21948 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
21949 \begin_inset Text
\r
21951 \begin_layout Plain Layout
\r
21952 \begin_inset Formula $\backprime$
\r
21962 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
21963 \begin_inset Text
\r
21965 \begin_layout Plain Layout
\r
21973 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
21974 \begin_inset Text
\r
21976 \begin_layout Plain Layout
\r
21977 \begin_inset Formula $\mho$
\r
21987 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
21988 \begin_inset Text
\r
21990 \begin_layout Plain Layout
\r
21998 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
21999 \begin_inset Text
\r
22001 \begin_layout Plain Layout
\r
22002 \begin_inset Formula $\triangle$
\r
22012 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
22013 \begin_inset Text
\r
22015 \begin_layout Plain Layout
\r
22023 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
22024 \begin_inset Text
\r
22026 \begin_layout Plain Layout
\r
22027 \begin_inset Formula $\angle$
\r
22037 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
22038 \begin_inset Text
\r
22040 \begin_layout Plain Layout
\r
22048 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
22049 \begin_inset Text
\r
22051 \begin_layout Plain Layout
\r
22052 \begin_inset Formula $\measuredangle$
\r
22062 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
22063 \begin_inset Text
\r
22065 \begin_layout Plain Layout
\r
22073 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
22074 \begin_inset Text
\r
22076 \begin_layout Plain Layout
\r
22077 \begin_inset Formula $\sphericalangle$
\r
22087 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
22088 \begin_inset Text
\r
22090 \begin_layout Plain Layout
\r
22098 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
22099 \begin_inset Text
\r
22101 \begin_layout Plain Layout
\r
22102 \begin_inset Formula $\top$
\r
22112 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
22113 \begin_inset Text
\r
22115 \begin_layout Plain Layout
\r
22123 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
22124 \begin_inset Text
\r
22126 \begin_layout Plain Layout
\r
22127 \begin_inset Formula $\bot$
\r
22141 \begin_inset space \hfill{}
\r
22147 \begin_layout Subsection
\r
22148 Miscellaneous Symbols
\r
22149 \begin_inset CommandInset label
\r
22150 LatexCommand label
\r
22151 name "sub:Miscellaneous-Symbols"
\r
22156 \begin_inset Index idx
\r
22159 \begin_layout Plain Layout
\r
22160 Symbols ! miscellaneous
\r
22168 \begin_layout Standard
\r
22171 \begin_inset Tabular
\r
22172 <lyxtabular version="3" rows="10" columns="2">
\r
22173 <features tabularvalignment="middle">
\r
22174 <column alignment="center" valignment="top" width="0pt">
\r
22175 <column alignment="center" valignment="top" width="0pt">
\r
22177 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
22178 \begin_inset Text
\r
22180 \begin_layout Plain Layout
\r
22186 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
22187 \begin_inset Text
\r
22189 \begin_layout Plain Layout
\r
22197 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
22198 \begin_inset Text
\r
22200 \begin_layout Plain Layout
\r
22208 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
22209 \begin_inset Text
\r
22211 \begin_layout Plain Layout
\r
22212 \begin_inset Formula $\flat$
\r
22222 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
22223 \begin_inset Text
\r
22225 \begin_layout Plain Layout
\r
22233 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
22234 \begin_inset Text
\r
22236 \begin_layout Plain Layout
\r
22237 \begin_inset Formula $\natural$
\r
22247 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
22248 \begin_inset Text
\r
22250 \begin_layout Plain Layout
\r
22258 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
22259 \begin_inset Text
\r
22261 \begin_layout Plain Layout
\r
22262 \begin_inset Formula $\sharp$
\r
22272 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
22273 \begin_inset Text
\r
22275 \begin_layout Plain Layout
\r
22283 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
22284 \begin_inset Text
\r
22286 \begin_layout Plain Layout
\r
22287 \begin_inset Formula $\surd$
\r
22297 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
22298 \begin_inset Text
\r
22300 \begin_layout Plain Layout
\r
22308 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
22309 \begin_inset Text
\r
22311 \begin_layout Plain Layout
\r
22312 \begin_inset Formula $\checkmark$
\r
22322 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
22323 \begin_inset Text
\r
22325 \begin_layout Plain Layout
\r
22333 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
22334 \begin_inset Text
\r
22336 \begin_layout Plain Layout
\r
22337 \begin_inset Formula $\yen$
\r
22347 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
22348 \begin_inset Text
\r
22350 \begin_layout Plain Layout
\r
22358 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
22359 \begin_inset Text
\r
22361 \begin_layout Plain Layout
\r
22362 \begin_inset Formula $\pounds$
\r
22372 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
22373 \begin_inset Text
\r
22375 \begin_layout Plain Layout
\r
22381 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
22382 \begin_inset Text
\r
22384 \begin_layout Plain Layout
\r
22385 \begin_inset Formula $\$$
\r
22395 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
22396 \begin_inset Text
\r
22398 \begin_layout Plain Layout
\r
22404 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
22405 \begin_inset Text
\r
22407 \begin_layout Plain Layout
\r
22408 \begin_inset Formula $§$
\r
22422 \begin_inset Tabular
\r
22423 <lyxtabular version="3" rows="10" columns="2">
\r
22424 <features tabularvalignment="middle">
\r
22425 <column alignment="center" valignment="top" width="0">
\r
22426 <column alignment="center" valignment="top" width="0">
\r
22428 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
22429 \begin_inset Text
\r
22431 \begin_layout Plain Layout
\r
22437 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
22438 \begin_inset Text
\r
22440 \begin_layout Plain Layout
\r
22448 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
22449 \begin_inset Text
\r
22451 \begin_layout Plain Layout
\r
22459 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
22460 \begin_inset Text
\r
22462 \begin_layout Plain Layout
\r
22463 \begin_inset Formula $\hbar$
\r
22473 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
22474 \begin_inset Text
\r
22476 \begin_layout Plain Layout
\r
22484 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
22485 \begin_inset Text
\r
22487 \begin_layout Plain Layout
\r
22488 \begin_inset Formula $\hslash$
\r
22498 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
22499 \begin_inset Text
\r
22501 \begin_layout Plain Layout
\r
22509 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
22510 \begin_inset Text
\r
22512 \begin_layout Plain Layout
\r
22513 \begin_inset Formula $\clubsuit$
\r
22523 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
22524 \begin_inset Text
\r
22526 \begin_layout Plain Layout
\r
22534 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
22535 \begin_inset Text
\r
22537 \begin_layout Plain Layout
\r
22538 \begin_inset Formula $\spadesuit$
\r
22548 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
22549 \begin_inset Text
\r
22551 \begin_layout Plain Layout
\r
22559 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
22560 \begin_inset Text
\r
22562 \begin_layout Plain Layout
\r
22563 \begin_inset Formula $\bigstar$
\r
22573 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
22574 \begin_inset Text
\r
22576 \begin_layout Plain Layout
\r
22584 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
22585 \begin_inset Text
\r
22587 \begin_layout Plain Layout
\r
22588 \begin_inset Formula $\blacklozenge$
\r
22598 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
22599 \begin_inset Text
\r
22601 \begin_layout Plain Layout
\r
22609 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
22610 \begin_inset Text
\r
22612 \begin_layout Plain Layout
\r
22613 \begin_inset Formula $\blacktriangle$
\r
22623 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
22624 \begin_inset Text
\r
22626 \begin_layout Plain Layout
\r
22634 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
22635 \begin_inset Text
\r
22637 \begin_layout Plain Layout
\r
22638 \begin_inset Formula $\blacktriangledown$
\r
22648 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
22649 \begin_inset Text
\r
22651 \begin_layout Plain Layout
\r
22659 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
22660 \begin_inset Text
\r
22662 \begin_layout Plain Layout
\r
22663 \begin_inset Formula $\bullet$
\r
22677 \begin_inset Tabular
\r
22678 <lyxtabular version="3" rows="10" columns="2">
\r
22679 <features tabularvalignment="middle">
\r
22680 <column alignment="center" valignment="top" width="0pt">
\r
22681 <column alignment="center" valignment="top" width="0pt">
\r
22683 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
22684 \begin_inset Text
\r
22686 \begin_layout Plain Layout
\r
22692 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
22693 \begin_inset Text
\r
22695 \begin_layout Plain Layout
\r
22703 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
22704 \begin_inset Text
\r
22706 \begin_layout Plain Layout
\r
22714 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
22715 \begin_inset Text
\r
22717 \begin_layout Plain Layout
\r
22718 \begin_inset Formula $\diamondsuit$
\r
22728 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
22729 \begin_inset Text
\r
22731 \begin_layout Plain Layout
\r
22739 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
22740 \begin_inset Text
\r
22742 \begin_layout Plain Layout
\r
22743 \begin_inset Formula $\Diamond$
\r
22753 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
22754 \begin_inset Text
\r
22756 \begin_layout Plain Layout
\r
22764 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
22765 \begin_inset Text
\r
22767 \begin_layout Plain Layout
\r
22768 \begin_inset Formula $\heartsuit$
\r
22778 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
22779 \begin_inset Text
\r
22781 \begin_layout Plain Layout
\r
22789 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
22790 \begin_inset Text
\r
22792 \begin_layout Plain Layout
\r
22793 \begin_inset Formula $\P$
\r
22803 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
22804 \begin_inset Text
\r
22806 \begin_layout Plain Layout
\r
22814 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
22815 \begin_inset Text
\r
22817 \begin_layout Plain Layout
\r
22818 \begin_inset Formula $\copyright$
\r
22828 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
22829 \begin_inset Text
\r
22831 \begin_layout Plain Layout
\r
22839 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
22840 \begin_inset Text
\r
22842 \begin_layout Plain Layout
\r
22843 \begin_inset Formula $\circledR$
\r
22853 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
22854 \begin_inset Text
\r
22856 \begin_layout Plain Layout
\r
22864 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
22865 \begin_inset Text
\r
22867 \begin_layout Plain Layout
\r
22868 \begin_inset Formula $\maltese$
\r
22878 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
22879 \begin_inset Text
\r
22881 \begin_layout Plain Layout
\r
22889 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
22890 \begin_inset Text
\r
22892 \begin_layout Plain Layout
\r
22893 \begin_inset Formula $\diagup$
\r
22903 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
22904 \begin_inset Text
\r
22906 \begin_layout Plain Layout
\r
22914 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
22915 \begin_inset Text
\r
22917 \begin_layout Plain Layout
\r
22918 \begin_inset Formula $\diagdown$
\r
22934 \begin_layout Standard
\r
22935 \begin_inset VSpace medskip
\r
22938 More symbols are listed in
\r
22939 \begin_inset CommandInset ref
\r
22941 reference "sub:Miscellaneous-special-Characters"
\r
22948 \begin_layout Standard
\r
22949 Some symbols can be displayed in different sizes, see
\r
22950 \begin_inset CommandInset ref
\r
22952 reference "sub:Font-Sizes"
\r
22959 \begin_layout Subsection
\r
22960 The Euro-Symbol €
\r
22961 \begin_inset Index idx
\r
22964 \begin_layout Plain Layout
\r
22965 Symbols ! Euro-symbol
\r
22971 \begin_inset Index idx
\r
22974 \begin_layout Plain Layout
\r
22981 \begin_layout Plain Layout
\r
22998 \begin_layout Standard
\r
22999 To use the Euro symbol in formulas, the LaTeX-package
\r
23004 \begin_inset Index idx
\r
23007 \begin_layout Plain Layout
\r
23008 Packages ! eurosym
\r
23013 must be installed and loaded with the LaTeX-preamble line
\r
23016 \begin_layout Standard
\r
23021 usepackage[gennarrow]{eurosym}
\r
23024 \begin_layout Standard
\r
23025 The Euro symbol can now be inserted with the command
\r
23032 \begin_inset Index idx
\r
23035 \begin_layout Plain Layout
\r
23046 \begin_layout Standard
\r
23047 The Euro symbol can directly be inserted with the € key in mathematical
\r
23048 text, without having
\r
23063 can also be inserted in TeX-mode.
\r
23064 The official currency symbol can then be inserted with the command
\r
23071 \begin_inset Index idx
\r
23074 \begin_layout Plain Layout
\r
23082 , that is only available in TeX-mode.
\r
23085 \begin_layout Standard
\r
23089 \begin_layout Plain Layout
\r
23099 \begin_inset Note Note
\r
23102 \begin_layout Plain Layout
\r
23103 The following table will only be displayed when the LaTeX-package
\r
23115 \begin_layout Standard
\r
23116 An overview about the different Euro symbols:
\r
23119 \begin_layout Standard
\r
23121 \begin_inset Tabular
\r
23122 <lyxtabular version="3" rows="4" columns="3">
\r
23123 <features tabularvalignment="middle">
\r
23124 <column alignment="center" valignment="top" width="0pt">
\r
23125 <column alignment="center" valignment="top" width="0pt">
\r
23126 <column alignment="center" valignment="top" width="0pt">
\r
23128 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
\r
23129 \begin_inset Text
\r
23131 \begin_layout Plain Layout
\r
23137 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
23138 \begin_inset Text
\r
23140 \begin_layout Plain Layout
\r
23146 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
23147 \begin_inset Text
\r
23149 \begin_layout Plain Layout
\r
23157 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
23158 \begin_inset Text
\r
23160 \begin_layout Plain Layout
\r
23166 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
23167 \begin_inset Text
\r
23169 \begin_layout Plain Layout
\r
23177 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
23178 \begin_inset Text
\r
23180 \begin_layout Plain Layout
\r
23181 \begin_inset Formula $\euro$
\r
23191 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
23192 \begin_inset Text
\r
23194 \begin_layout Plain Layout
\r
23195 mathematical text
\r
23200 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
23201 \begin_inset Text
\r
23203 \begin_layout Plain Layout
\r
23209 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
23210 \begin_inset Text
\r
23212 \begin_layout Plain Layout
\r
23213 \begin_inset Formula $\mbox{€}$
\r
23223 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
23224 \begin_inset Text
\r
23226 \begin_layout Plain Layout
\r
23232 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
23233 \begin_inset Text
\r
23235 \begin_layout Plain Layout
\r
23243 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
23244 \begin_inset Text
\r
23246 \begin_layout Plain Layout
\r
23250 \begin_layout Plain Layout
\r
23272 \begin_layout Standard
\r
23276 \begin_layout Plain Layout
\r
23286 \begin_inset Note Note
\r
23289 \begin_layout Plain Layout
\r
23290 The following will be displayed when the LaTeX-package
\r
23294 is not installed:
\r
23302 \begin_layout Standard
\r
23303 You need to install the LaTeX-package
\r
23307 to see the rest of this subsection in the output.
\r
23310 \begin_layout Standard
\r
23314 \begin_layout Plain Layout
\r
23326 \begin_layout Section
\r
23328 \begin_inset CommandInset label
\r
23329 LatexCommand label
\r
23330 name "sec:Relations"
\r
23335 \begin_inset Index idx
\r
23338 \begin_layout Plain Layout
\r
23345 \begin_inset Index idx
\r
23348 \begin_layout Plain Layout
\r
23353 \begin_layout Plain Layout
\r
23364 \begin_layout Plain Layout
\r
23379 \begin_layout Standard
\r
23380 All relations can also be inserted via the toolbar button
\r
23381 \begin_inset Graphics
\r
23382 filename ../images/math/leq.png
\r
23390 \begin_layout Standard
\r
23391 \begin_inset space \hfill{}
\r
23395 \begin_inset Tabular
\r
23396 <lyxtabular version="3" rows="17" columns="2">
\r
23397 <features tabularvalignment="middle">
\r
23398 <column alignment="center" valignment="top" width="0pt">
\r
23399 <column alignment="center" valignment="top" width="0pt">
\r
23401 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
23402 \begin_inset Text
\r
23404 \begin_layout Plain Layout
\r
23410 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
23411 \begin_inset Text
\r
23413 \begin_layout Plain Layout
\r
23421 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
23422 \begin_inset Text
\r
23424 \begin_layout Plain Layout
\r
23430 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
23431 \begin_inset Text
\r
23433 \begin_layout Plain Layout
\r
23434 \begin_inset Formula $<$
\r
23444 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
23445 \begin_inset Text
\r
23447 \begin_layout Plain Layout
\r
23455 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
23456 \begin_inset Text
\r
23458 \begin_layout Plain Layout
\r
23459 \begin_inset Formula $\le$
\r
23469 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
23470 \begin_inset Text
\r
23472 \begin_layout Plain Layout
\r
23480 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
23481 \begin_inset Text
\r
23483 \begin_layout Plain Layout
\r
23484 \begin_inset Formula $\ll$
\r
23494 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
23495 \begin_inset Text
\r
23497 \begin_layout Plain Layout
\r
23505 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
23506 \begin_inset Text
\r
23508 \begin_layout Plain Layout
\r
23509 \begin_inset Formula $\prec$
\r
23519 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
23520 \begin_inset Text
\r
23522 \begin_layout Plain Layout
\r
23530 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
23531 \begin_inset Text
\r
23533 \begin_layout Plain Layout
\r
23534 \begin_inset Formula $\preceq$
\r
23544 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
23545 \begin_inset Text
\r
23547 \begin_layout Plain Layout
\r
23555 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
23556 \begin_inset Text
\r
23558 \begin_layout Plain Layout
\r
23559 \begin_inset Formula $\subset$
\r
23569 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
23570 \begin_inset Text
\r
23572 \begin_layout Plain Layout
\r
23580 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
23581 \begin_inset Text
\r
23583 \begin_layout Plain Layout
\r
23584 \begin_inset Formula $\subseteq$
\r
23594 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
23595 \begin_inset Text
\r
23597 \begin_layout Plain Layout
\r
23605 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
23606 \begin_inset Text
\r
23608 \begin_layout Plain Layout
\r
23609 \begin_inset Formula $\sqsubseteq$
\r
23619 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
23620 \begin_inset Text
\r
23622 \begin_layout Plain Layout
\r
23630 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
23631 \begin_inset Text
\r
23633 \begin_layout Plain Layout
\r
23634 \begin_inset Formula $\in$
\r
23644 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
23645 \begin_inset Text
\r
23647 \begin_layout Plain Layout
\r
23655 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
23656 \begin_inset Text
\r
23658 \begin_layout Plain Layout
\r
23659 \begin_inset Formula $\vdash$
\r
23669 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
23670 \begin_inset Text
\r
23672 \begin_layout Plain Layout
\r
23680 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
23681 \begin_inset Text
\r
23683 \begin_layout Plain Layout
\r
23684 \begin_inset Formula $\smile$
\r
23694 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
23695 \begin_inset Text
\r
23697 \begin_layout Plain Layout
\r
23705 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
23706 \begin_inset Text
\r
23708 \begin_layout Plain Layout
\r
23709 \begin_inset Formula $\lhd$
\r
23719 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
23720 \begin_inset Text
\r
23722 \begin_layout Plain Layout
\r
23730 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
23731 \begin_inset Text
\r
23733 \begin_layout Plain Layout
\r
23734 \begin_inset Formula $\unlhd$
\r
23744 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
23745 \begin_inset Text
\r
23747 \begin_layout Plain Layout
\r
23755 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
23756 \begin_inset Text
\r
23758 \begin_layout Plain Layout
\r
23759 \begin_inset Formula $\gtrless$
\r
23769 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
23770 \begin_inset Text
\r
23772 \begin_layout Plain Layout
\r
23780 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
23781 \begin_inset Text
\r
23783 \begin_layout Plain Layout
\r
23784 \begin_inset Formula $\mid$
\r
23794 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
23795 \begin_inset Text
\r
23797 \begin_layout Plain Layout
\r
23805 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
23806 \begin_inset Text
\r
23808 \begin_layout Plain Layout
\r
23809 \begin_inset Formula $\nmid$
\r
23823 \begin_inset space \hfill{}
\r
23827 \begin_inset Tabular
\r
23828 <lyxtabular version="3" rows="17" columns="2">
\r
23829 <features tabularvalignment="middle">
\r
23830 <column alignment="center" valignment="top" width="0pt">
\r
23831 <column alignment="center" valignment="top" width="0pt">
\r
23833 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
23834 \begin_inset Text
\r
23836 \begin_layout Plain Layout
\r
23842 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
23843 \begin_inset Text
\r
23845 \begin_layout Plain Layout
\r
23853 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
23854 \begin_inset Text
\r
23856 \begin_layout Plain Layout
\r
23862 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
23863 \begin_inset Text
\r
23865 \begin_layout Plain Layout
\r
23866 \begin_inset Formula $=$
\r
23876 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
23877 \begin_inset Text
\r
23879 \begin_layout Plain Layout
\r
23887 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
23888 \begin_inset Text
\r
23890 \begin_layout Plain Layout
\r
23891 \begin_inset Formula $\not=$
\r
23901 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
23902 \begin_inset Text
\r
23904 \begin_layout Plain Layout
\r
23912 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
23913 \begin_inset Text
\r
23915 \begin_layout Plain Layout
\r
23916 \begin_inset Formula $\equiv$
\r
23926 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
23927 \begin_inset Text
\r
23929 \begin_layout Plain Layout
\r
23937 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
23938 \begin_inset Text
\r
23940 \begin_layout Plain Layout
\r
23941 \begin_inset Formula $\sim$
\r
23951 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
23952 \begin_inset Text
\r
23954 \begin_layout Plain Layout
\r
23962 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
23963 \begin_inset Text
\r
23965 \begin_layout Plain Layout
\r
23966 \begin_inset Formula $\simeq$
\r
23976 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
23977 \begin_inset Text
\r
23979 \begin_layout Plain Layout
\r
23987 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
23988 \begin_inset Text
\r
23990 \begin_layout Plain Layout
\r
23991 \begin_inset Formula $\approx$
\r
24001 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
24002 \begin_inset Text
\r
24004 \begin_layout Plain Layout
\r
24012 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
24013 \begin_inset Text
\r
24015 \begin_layout Plain Layout
\r
24016 \begin_inset Formula $\cong$
\r
24026 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
24027 \begin_inset Text
\r
24029 \begin_layout Plain Layout
\r
24037 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
24038 \begin_inset Text
\r
24040 \begin_layout Plain Layout
\r
24041 \begin_inset Formula $\bowtie$
\r
24051 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
24052 \begin_inset Text
\r
24054 \begin_layout Plain Layout
\r
24062 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
24063 \begin_inset Text
\r
24065 \begin_layout Plain Layout
\r
24066 \begin_inset Formula $\notin$
\r
24076 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
24077 \begin_inset Text
\r
24079 \begin_layout Plain Layout
\r
24087 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
24088 \begin_inset Text
\r
24090 \begin_layout Plain Layout
\r
24091 \begin_inset Formula $\perp$
\r
24101 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
24102 \begin_inset Text
\r
24104 \begin_layout Plain Layout
\r
24112 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
24113 \begin_inset Text
\r
24115 \begin_layout Plain Layout
\r
24116 \begin_inset Formula $\propto$
\r
24126 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
24127 \begin_inset Text
\r
24129 \begin_layout Plain Layout
\r
24137 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
24138 \begin_inset Text
\r
24140 \begin_layout Plain Layout
\r
24141 \begin_inset Formula $\asymp$
\r
24151 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
24152 \begin_inset Text
\r
24154 \begin_layout Plain Layout
\r
24162 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
24163 \begin_inset Text
\r
24165 \begin_layout Plain Layout
\r
24166 \begin_inset Formula $\doteq$
\r
24176 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
24177 \begin_inset Text
\r
24179 \begin_layout Plain Layout
\r
24187 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
24188 \begin_inset Text
\r
24190 \begin_layout Plain Layout
\r
24191 \begin_inset Formula $\circeq$
\r
24201 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
24202 \begin_inset Text
\r
24204 \begin_layout Plain Layout
\r
24212 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
24213 \begin_inset Text
\r
24215 \begin_layout Plain Layout
\r
24216 \begin_inset Formula $\models$
\r
24226 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
24227 \begin_inset Text
\r
24229 \begin_layout Plain Layout
\r
24237 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
24238 \begin_inset Text
\r
24240 \begin_layout Plain Layout
\r
24241 \begin_inset Formula $\widehat{=}$
\r
24255 \begin_inset space \hfill{}
\r
24259 \begin_inset Tabular
\r
24260 <lyxtabular version="3" rows="17" columns="2">
\r
24261 <features tabularvalignment="middle">
\r
24262 <column alignment="center" valignment="top" width="0pt">
\r
24263 <column alignment="center" valignment="top" width="0pt">
\r
24265 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
24266 \begin_inset Text
\r
24268 \begin_layout Plain Layout
\r
24274 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
24275 \begin_inset Text
\r
24277 \begin_layout Plain Layout
\r
24285 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
24286 \begin_inset Text
\r
24288 \begin_layout Plain Layout
\r
24294 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
24295 \begin_inset Text
\r
24297 \begin_layout Plain Layout
\r
24298 \begin_inset Formula $>$
\r
24308 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
24309 \begin_inset Text
\r
24311 \begin_layout Plain Layout
\r
24319 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
24320 \begin_inset Text
\r
24322 \begin_layout Plain Layout
\r
24323 \begin_inset Formula $\ge$
\r
24333 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
24334 \begin_inset Text
\r
24336 \begin_layout Plain Layout
\r
24344 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
24345 \begin_inset Text
\r
24347 \begin_layout Plain Layout
\r
24348 \begin_inset Formula $\gg$
\r
24358 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
24359 \begin_inset Text
\r
24361 \begin_layout Plain Layout
\r
24369 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
24370 \begin_inset Text
\r
24372 \begin_layout Plain Layout
\r
24373 \begin_inset Formula $\succ$
\r
24383 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
24384 \begin_inset Text
\r
24386 \begin_layout Plain Layout
\r
24394 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
24395 \begin_inset Text
\r
24397 \begin_layout Plain Layout
\r
24398 \begin_inset Formula $\succeq$
\r
24408 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
24409 \begin_inset Text
\r
24411 \begin_layout Plain Layout
\r
24419 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
24420 \begin_inset Text
\r
24422 \begin_layout Plain Layout
\r
24423 \begin_inset Formula $\supset$
\r
24433 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
24434 \begin_inset Text
\r
24436 \begin_layout Plain Layout
\r
24444 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
24445 \begin_inset Text
\r
24447 \begin_layout Plain Layout
\r
24448 \begin_inset Formula $\supseteq$
\r
24458 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
24459 \begin_inset Text
\r
24461 \begin_layout Plain Layout
\r
24469 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
24470 \begin_inset Text
\r
24472 \begin_layout Plain Layout
\r
24473 \begin_inset Formula $\sqsupseteq$
\r
24483 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
24484 \begin_inset Text
\r
24486 \begin_layout Plain Layout
\r
24494 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
24495 \begin_inset Text
\r
24497 \begin_layout Plain Layout
\r
24498 \begin_inset Formula $\ni$
\r
24508 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
24509 \begin_inset Text
\r
24511 \begin_layout Plain Layout
\r
24519 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
24520 \begin_inset Text
\r
24522 \begin_layout Plain Layout
\r
24523 \begin_inset Formula $\dashv$
\r
24533 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
24534 \begin_inset Text
\r
24536 \begin_layout Plain Layout
\r
24544 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
24545 \begin_inset Text
\r
24547 \begin_layout Plain Layout
\r
24548 \begin_inset Formula $\frown$
\r
24558 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
24559 \begin_inset Text
\r
24561 \begin_layout Plain Layout
\r
24569 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
24570 \begin_inset Text
\r
24572 \begin_layout Plain Layout
\r
24573 \begin_inset Formula $\rhd$
\r
24583 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
24584 \begin_inset Text
\r
24586 \begin_layout Plain Layout
\r
24594 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
24595 \begin_inset Text
\r
24597 \begin_layout Plain Layout
\r
24598 \begin_inset Formula $\unrhd$
\r
24608 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
24609 \begin_inset Text
\r
24611 \begin_layout Plain Layout
\r
24619 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
24620 \begin_inset Text
\r
24622 \begin_layout Plain Layout
\r
24623 \begin_inset Formula $\lessgtr$
\r
24633 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
24634 \begin_inset Text
\r
24636 \begin_layout Plain Layout
\r
24644 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
24645 \begin_inset Text
\r
24647 \begin_layout Plain Layout
\r
24648 \begin_inset Formula $\parallel$
\r
24658 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
24659 \begin_inset Text
\r
24661 \begin_layout Plain Layout
\r
24669 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
24670 \begin_inset Text
\r
24672 \begin_layout Plain Layout
\r
24673 \begin_inset Formula $\nparallel$
\r
24687 \begin_inset space \hfill{}
\r
24693 \begin_layout Standard
\r
24694 \begin_inset VSpace medskip
\r
24709 are bigger than the equal looking operators
\r
24724 \begin_layout Standard
\r
24725 Relations are, in contrary to symbols, always surrounded by space.
\r
24728 \begin_layout Standard
\r
24729 Relations with labels can be created with the command
\r
24736 \begin_inset Index idx
\r
24739 \begin_layout Plain Layout
\r
24750 \begin_layout Standard
\r
24752 \begin_inset Tabular
\r
24753 <lyxtabular version="3" rows="2" columns="2">
\r
24754 <features tabularvalignment="middle">
\r
24755 <column alignment="center" valignment="top" width="0">
\r
24756 <column alignment="center" valignment="top" width="0">
\r
24758 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
24759 \begin_inset Text
\r
24761 \begin_layout Plain Layout
\r
24767 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
24768 \begin_inset Text
\r
24770 \begin_layout Plain Layout
\r
24772 \begin_inset Note Note
\r
24775 \begin_layout Plain Layout
\r
24782 is only used as spacer.
\r
24794 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
24795 \begin_inset Text
\r
24797 \begin_layout Plain Layout
\r
24804 \begin_layout Plain Layout
\r
24821 \begin_layout Plain Layout
\r
24831 \begin_inset Formula $\downarrow$
\r
24840 \begin_layout Plain Layout
\r
24853 \begin_layout Plain Layout
\r
24867 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
24868 \begin_inset Text
\r
24870 \begin_layout Plain Layout
\r
24871 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
\r
24887 \begin_layout Section
\r
24891 \begin_layout Subsection
\r
24892 Predefined Functions
\r
24893 \begin_inset CommandInset label
\r
24894 LatexCommand label
\r
24895 name "sub:Predefined-Functions"
\r
24900 \begin_inset Index idx
\r
24903 \begin_layout Plain Layout
\r
24904 Functions ! predefined
\r
24912 \begin_layout Standard
\r
24913 In general, variables are set
\r
24917 in mathematical expressions, but not function names, because
\r
24918 \begin_inset Formula $sin$
\r
24921 could be misunderstood as
\r
24922 \begin_inset Formula $s\cdot i\cdot n$
\r
24926 Therefore there are predefined functionswhich are additionally a bit separated
\r
24928 They are inserted as commands starting with a backslash before their name.
\r
24931 \begin_layout Standard
\r
24933 \begin_inset Tabular
\r
24934 <lyxtabular version="3" rows="2" columns="4">
\r
24935 <features tabularvalignment="middle">
\r
24936 <column alignment="center" valignment="top" width="0pt">
\r
24937 <column alignment="center" valignment="top" width="0pt">
\r
24938 <column alignment="center" valignment="top" width="0pt">
\r
24939 <column alignment="center" valignment="top" width="0pt">
\r
24941 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
24942 \begin_inset Text
\r
24944 \begin_layout Plain Layout
\r
24950 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
24951 \begin_inset Text
\r
24953 \begin_layout Plain Layout
\r
24959 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
24960 \begin_inset Text
\r
24962 \begin_layout Plain Layout
\r
24968 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
24969 \begin_inset Text
\r
24971 \begin_layout Plain Layout
\r
24979 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
24980 \begin_inset Text
\r
24982 \begin_layout Plain Layout
\r
24988 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
24989 \begin_inset Text
\r
24991 \begin_layout Plain Layout
\r
24992 \begin_inset Formula $Asin(x)+B$
\r
25000 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
25001 \begin_inset Text
\r
25003 \begin_layout Plain Layout
\r
25011 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
25012 \begin_inset Text
\r
25014 \begin_layout Plain Layout
\r
25015 \begin_inset Formula $A\sin(x)+B$
\r
25031 \begin_layout Standard
\r
25032 The following functions are predefined:
\r
25035 \begin_layout Standard
\r
25036 \begin_inset VSpace -2mm
\r
25042 \begin_layout Standard
\r
25044 \begin_inset Tabular
\r
25045 <lyxtabular version="3" rows="9" columns="4">
\r
25046 <features tabularvalignment="middle">
\r
25047 <column alignment="center" valignment="top" width="0pt">
\r
25048 <column alignment="center" valignment="top" width="0pt">
\r
25049 <column alignment="center" valignment="top" width="0pt">
\r
25050 <column alignment="center" valignment="top" width="0pt">
\r
25052 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
25053 \begin_inset Text
\r
25055 \begin_layout Plain Layout
\r
25061 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
25062 \begin_inset Text
\r
25064 \begin_layout Plain Layout
\r
25070 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
25071 \begin_inset Text
\r
25073 \begin_layout Plain Layout
\r
25079 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
25080 \begin_inset Text
\r
25082 \begin_layout Plain Layout
\r
25090 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
25091 \begin_inset Text
\r
25093 \begin_layout Plain Layout
\r
25101 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
25102 \begin_inset Text
\r
25104 \begin_layout Plain Layout
\r
25112 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
25113 \begin_inset Text
\r
25115 \begin_layout Plain Layout
\r
25123 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
25124 \begin_inset Text
\r
25126 \begin_layout Plain Layout
\r
25136 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
25137 \begin_inset Text
\r
25139 \begin_layout Plain Layout
\r
25147 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
25148 \begin_inset Text
\r
25150 \begin_layout Plain Layout
\r
25158 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
25159 \begin_inset Text
\r
25161 \begin_layout Plain Layout
\r
25169 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
25170 \begin_inset Text
\r
25172 \begin_layout Plain Layout
\r
25182 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
25183 \begin_inset Text
\r
25185 \begin_layout Plain Layout
\r
25193 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
25194 \begin_inset Text
\r
25196 \begin_layout Plain Layout
\r
25204 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
25205 \begin_inset Text
\r
25207 \begin_layout Plain Layout
\r
25215 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
25216 \begin_inset Text
\r
25218 \begin_layout Plain Layout
\r
25228 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
25229 \begin_inset Text
\r
25231 \begin_layout Plain Layout
\r
25239 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
25240 \begin_inset Text
\r
25242 \begin_layout Plain Layout
\r
25250 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
25251 \begin_inset Text
\r
25253 \begin_layout Plain Layout
\r
25261 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
25262 \begin_inset Text
\r
25264 \begin_layout Plain Layout
\r
25274 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
25275 \begin_inset Text
\r
25277 \begin_layout Plain Layout
\r
25285 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
25286 \begin_inset Text
\r
25288 \begin_layout Plain Layout
\r
25296 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
25297 \begin_inset Text
\r
25299 \begin_layout Plain Layout
\r
25307 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
25308 \begin_inset Text
\r
25310 \begin_layout Plain Layout
\r
25320 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
25321 \begin_inset Text
\r
25323 \begin_layout Plain Layout
\r
25331 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
25332 \begin_inset Text
\r
25334 \begin_layout Plain Layout
\r
25342 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
25343 \begin_inset Text
\r
25345 \begin_layout Plain Layout
\r
25353 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
25354 \begin_inset Text
\r
25356 \begin_layout Plain Layout
\r
25366 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
25367 \begin_inset Text
\r
25369 \begin_layout Plain Layout
\r
25377 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
25378 \begin_inset Text
\r
25380 \begin_layout Plain Layout
\r
25388 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
25389 \begin_inset Text
\r
25391 \begin_layout Plain Layout
\r
25399 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
25400 \begin_inset Text
\r
25402 \begin_layout Plain Layout
\r
25412 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
25413 \begin_inset Text
\r
25415 \begin_layout Plain Layout
\r
25423 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
25424 \begin_inset Text
\r
25426 \begin_layout Plain Layout
\r
25434 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
25435 \begin_inset Text
\r
25437 \begin_layout Plain Layout
\r
25445 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
25446 \begin_inset Text
\r
25448 \begin_layout Plain Layout
\r
25464 \begin_layout Standard
\r
25465 They can also be inserted with the math toolbar button
\r
25466 \begin_inset Graphics
\r
25467 filename ../images/math/functions.png
\r
25475 \begin_layout Subsection
\r
25476 Self-defined Functions
\r
25477 \begin_inset Index idx
\r
25480 \begin_layout Plain Layout
\r
25481 Functions ! self-defined
\r
25489 \begin_layout Standard
\r
25490 To use a function that is not predefined, like for example the sign function
\r
25491 sgn(x), there are two possibilities:
\r
25494 \begin_layout Itemize
\r
25495 Define the function by inserting the following line to the LaTeX-preamble
\r
25496 \begin_inset Foot
\r
25499 \begin_layout Plain Layout
\r
25504 DeclareMathOperator
\r
25507 \begin_inset CommandInset ref
\r
25509 reference "sub:Self-defined-Operators"
\r
25519 \begin_inset Newline newline
\r
25523 \begin_inset VSpace -3mm
\r
25527 \begin_inset Newline newline
\r
25534 DeclareMathOperator{
\r
25539 \begin_inset Index idx
\r
25542 \begin_layout Plain Layout
\r
25547 DeclareMathOperator
\r
25553 \begin_inset Newline newline
\r
25557 \begin_inset VSpace -2mm
\r
25561 \begin_inset Newline newline
\r
25564 Now the new defined function can be called with the command
\r
25573 \begin_layout Itemize
\r
25574 Write the formula as usual, mark the formula name, in our example the letters
\r
25579 , and change it to mathematical text.
\r
25580 Finally, a space is inserted between prefactor and function.
\r
25583 \begin_layout Standard
\r
25584 The result is the same with both methods as with a predefined function
\r
25585 \begin_inset Foot
\r
25588 \begin_layout Plain Layout
\r
25589 In LyX self-defined functions are displayed red, predefined ones black.
\r
25597 \begin_layout Standard
\r
25599 \begin_inset Tabular
\r
25600 <lyxtabular version="3" rows="3" columns="2">
\r
25601 <features tabularvalignment="middle">
\r
25602 <column alignment="center" valignment="top" width="0pt">
\r
25603 <column alignment="center" valignment="top" width="0pt">
\r
25605 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
25606 \begin_inset Text
\r
25608 \begin_layout Plain Layout
\r
25614 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
25615 \begin_inset Text
\r
25617 \begin_layout Plain Layout
\r
25625 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
25626 \begin_inset Text
\r
25628 \begin_layout Plain Layout
\r
25636 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
25637 \begin_inset Text
\r
25639 \begin_layout Plain Layout
\r
25640 \begin_inset Formula $A\sgn(x)+B$
\r
25650 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
25651 \begin_inset Text
\r
25653 \begin_layout Plain Layout
\r
25657 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
\r
25665 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
25666 \begin_inset Text
\r
25668 \begin_layout Plain Layout
\r
25669 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
\r
25685 \begin_layout Standard
\r
25686 The first method is more suitable when the self-defined function should
\r
25687 be used several times.
\r
25690 \begin_layout Subsection
\r
25692 \begin_inset Index idx
\r
25695 \begin_layout Plain Layout
\r
25704 \begin_layout Standard
\r
25705 For limits, in addition to the commands
\r
25712 \begin_inset Index idx
\r
25715 \begin_layout Plain Layout
\r
25735 the following functions are defined:
\r
25738 \begin_layout Standard
\r
25740 \begin_inset Tabular
\r
25741 <lyxtabular version="3" rows="5" columns="2">
\r
25742 <features tabularvalignment="middle">
\r
25743 <column alignment="center" valignment="top" width="0">
\r
25744 <column alignment="center" valignment="top" width="0">
\r
25746 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
25747 \begin_inset Text
\r
25749 \begin_layout Plain Layout
\r
25755 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
25756 \begin_inset Text
\r
25758 \begin_layout Plain Layout
\r
25760 \begin_inset Note Note
\r
25763 \begin_layout Plain Layout
\r
25770 is only used as spacer.
\r
25782 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
25783 \begin_inset Text
\r
25785 \begin_layout Plain Layout
\r
25793 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
25794 \begin_inset Text
\r
25796 \begin_layout Plain Layout
\r
25797 \begin_inset Formula $\varliminf$
\r
25807 <cell alignment="center" valignment="top" leftline="true" usebox="none">
\r
25808 \begin_inset Text
\r
25810 \begin_layout Plain Layout
\r
25818 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
\r
25819 \begin_inset Text
\r
25821 \begin_layout Plain Layout
\r
25822 \begin_inset Formula $\varlimsup$
\r
25832 <cell alignment="center" valignment="top" leftline="true" usebox="none">
\r
25833 \begin_inset Text
\r
25835 \begin_layout Plain Layout
\r
25843 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
\r
25844 \begin_inset Text
\r
25846 \begin_layout Plain Layout
\r
25847 \begin_inset Formula $\varprojlim$
\r
25857 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
25858 \begin_inset Text
\r
25860 \begin_layout Plain Layout
\r
25868 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
25869 \begin_inset Text
\r
25871 \begin_layout Plain Layout
\r
25872 \begin_inset Formula $\varinjlim$
\r
25876 \begin_inset Formula $\raisebox{-2.5mm}{}$
\r
25892 \begin_layout Standard
\r
25893 \begin_inset VSpace medskip
\r
25896 The limit is created by inserting a subscript.
\r
25897 It is set right beside the function in an inline formula:
\r
25900 \begin_layout Standard
\r
25902 \begin_inset Tabular
\r
25903 <lyxtabular version="3" rows="2" columns="2">
\r
25904 <features tabularvalignment="middle">
\r
25905 <column alignment="center" valignment="top" width="0pt">
\r
25906 <column alignment="center" valignment="top" width="0pt">
\r
25908 <cell alignment="center" valignment="top" usebox="none">
\r
25909 \begin_inset Text
\r
25911 \begin_layout Plain Layout
\r
25917 <cell alignment="center" valignment="top" usebox="none">
\r
25918 \begin_inset Text
\r
25920 \begin_layout Plain Layout
\r
25921 \begin_inset space \hspace{}
\r
25926 \begin_inset Note Note
\r
25929 \begin_layout Plain Layout
\r
25936 are used here as spacer.
\r
25948 <cell alignment="center" valignment="top" usebox="none">
\r
25949 \begin_inset Text
\r
25951 \begin_layout Plain Layout
\r
25960 \begin_layout Plain Layout
\r
25973 \begin_layout Plain Layout
\r
25987 <cell alignment="center" valignment="top" usebox="none">
\r
25988 \begin_inset Text
\r
25990 \begin_layout Plain Layout
\r
25991 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
\r
26007 \begin_layout Standard
\r
26008 In a displayed formula the limit is set below the formula, as usual:
\r
26009 \begin_inset Formula
\r
26019 \begin_layout Subsection
\r
26021 \begin_inset Index idx
\r
26024 \begin_layout Plain Layout
\r
26025 Functions ! modulo-
\r
26033 \begin_layout Standard
\r
26034 The modulo-function is special, because it exists in four variants.
\r
26035 The variants in a displayed formula are:
\r
26036 \begin_inset Formula
\r
26038 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
\r
26039 \mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
\r
26040 \mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
\r
26041 \mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
\r
26042 \mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b
\r
26050 \begin_layout Standard
\r
26051 In an inline formula less space is set before the function names for all
\r
26053 By default the modulo-functions take only the first following character
\r
26055 To use more than one character, one has to put them into TeX-braces:
\r
26056 \begin_inset Formula
\r
26058 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
\r
26059 \mathrm{a\backslash pod\textrm{\spce}bcd} & & a\pod bcd\\
\r
26060 \mathrm{a\backslash pod\backslash\{bc\to d} & & a\pod{bc}d
\r
26068 \begin_layout Section
\r
26069 Special Characters
\r
26070 \begin_inset Index idx
\r
26073 \begin_layout Plain Layout
\r
26074 Special characters
\r
26082 \begin_layout Subsection
\r
26083 Special Characters in Mathematical Text
\r
26086 \begin_layout Standard
\r
26087 The following commands can only be used in mathematical text or in TeX-mode:
\r
26090 \begin_layout Standard
\r
26091 \begin_inset space \hfill{}
\r
26095 \begin_inset Tabular
\r
26096 <lyxtabular version="3" rows="8" columns="2">
\r
26097 <features tabularvalignment="middle">
\r
26098 <column alignment="block" valignment="top" width="0">
\r
26099 <column alignment="block" valignment="top" width="0">
\r
26101 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
26102 \begin_inset Text
\r
26104 \begin_layout Plain Layout
\r
26110 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
26111 \begin_inset Text
\r
26113 \begin_layout Plain Layout
\r
26121 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
26122 \begin_inset Text
\r
26124 \begin_layout Plain Layout
\r
26132 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
26133 \begin_inset Text
\r
26135 \begin_layout Plain Layout
\r
26136 \begin_inset Formula $\textrm{œ}$
\r
26146 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
26147 \begin_inset Text
\r
26149 \begin_layout Plain Layout
\r
26157 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
26158 \begin_inset Text
\r
26160 \begin_layout Plain Layout
\r
26161 \begin_inset Formula $\textrm{Œ}$
\r
26171 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
26172 \begin_inset Text
\r
26174 \begin_layout Plain Layout
\r
26182 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
26183 \begin_inset Text
\r
26185 \begin_layout Plain Layout
\r
26186 \begin_inset Formula $\textrm{æ}$
\r
26196 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
26197 \begin_inset Text
\r
26199 \begin_layout Plain Layout
\r
26207 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
26208 \begin_inset Text
\r
26210 \begin_layout Plain Layout
\r
26211 \begin_inset Formula $\textrm{Æ}$
\r
26221 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
26222 \begin_inset Text
\r
26224 \begin_layout Plain Layout
\r
26232 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
26233 \begin_inset Text
\r
26235 \begin_layout Plain Layout
\r
26236 \begin_inset Formula $\textrm{\aa}$
\r
26246 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
26247 \begin_inset Text
\r
26249 \begin_layout Plain Layout
\r
26253 \begin_inset Index idx
\r
26256 \begin_layout Plain Layout
\r
26263 \begin_layout Plain Layout
\r
26284 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
26285 \begin_inset Text
\r
26287 \begin_layout Plain Layout
\r
26288 \begin_inset Formula $\textrm{Å}$
\r
26298 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
26299 \begin_inset Text
\r
26301 \begin_layout Plain Layout
\r
26309 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
26310 \begin_inset Text
\r
26312 \begin_layout Plain Layout
\r
26313 \begin_inset Formula $\textrm{ı}$
\r
26327 \begin_inset space \hfill{}
\r
26331 \begin_inset Tabular
\r
26332 <lyxtabular version="3" rows="8" columns="2">
\r
26333 <features tabularvalignment="middle">
\r
26334 <column alignment="block" valignment="top" width="0">
\r
26335 <column alignment="center" valignment="top" width="0">
\r
26337 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
26338 \begin_inset Text
\r
26340 \begin_layout Plain Layout
\r
26342 \begin_inset Note Note
\r
26345 \begin_layout Plain Layout
\r
26347 \begin_inset space \thinspace{}
\r
26350 mm is used for separation, because otherwise the output will be ¡ and ¿
\r
26361 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
26362 \begin_inset Text
\r
26364 \begin_layout Plain Layout
\r
26372 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
26373 \begin_inset Text
\r
26375 \begin_layout Plain Layout
\r
26383 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
26384 \begin_inset Text
\r
26386 \begin_layout Plain Layout
\r
26387 \begin_inset Formula $\textrm{ø}$
\r
26397 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
26398 \begin_inset Text
\r
26400 \begin_layout Plain Layout
\r
26408 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
26409 \begin_inset Text
\r
26411 \begin_layout Plain Layout
\r
26412 \begin_inset Formula $\textrm{Ø}$
\r
26422 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
26423 \begin_inset Text
\r
26425 \begin_layout Plain Layout
\r
26433 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
26434 \begin_inset Text
\r
26436 \begin_layout Plain Layout
\r
26437 \begin_inset Formula $\textrm{ł}$
\r
26447 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
26448 \begin_inset Text
\r
26450 \begin_layout Plain Layout
\r
26458 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
26459 \begin_inset Text
\r
26461 \begin_layout Plain Layout
\r
26462 \begin_inset Formula $\textrm{Ł}$
\r
26472 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
26473 \begin_inset Text
\r
26475 \begin_layout Plain Layout
\r
26477 \begin_inset space \hspace{}
\r
26485 \begin_layout Plain Layout
\r
26499 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
26500 \begin_inset Text
\r
26502 \begin_layout Plain Layout
\r
26503 \begin_inset Formula $\textrm{!`}$
\r
26513 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
26514 \begin_inset Text
\r
26516 \begin_layout Plain Layout
\r
26518 \begin_inset space \hspace{}
\r
26526 \begin_layout Plain Layout
\r
26540 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
26541 \begin_inset Text
\r
26543 \begin_layout Plain Layout
\r
26544 \begin_inset Formula $\textrm{?`}$
\r
26554 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
26555 \begin_inset Text
\r
26557 \begin_layout Plain Layout
\r
26565 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
26566 \begin_inset Text
\r
26568 \begin_layout Plain Layout
\r
26569 \begin_inset Formula $\textrm{ȷ}$
\r
26583 \begin_inset space \hfill{}
\r
26589 \begin_layout Standard
\r
26591 \begin_inset Formula $\textrm{\textrm{Å}}$
\r
26595 \begin_inset Formula $\textrm{\textrm{Ø}}$
\r
26598 can also be inserted via the math toolbar button
\r
26599 \begin_inset Graphics
\r
26600 filename ../images/math/digamma.png
\r
26608 \begin_layout Standard
\r
26609 An exception are the commands
\r
26612 \begin_inset space \hspace{}
\r
26621 \begin_inset space \hspace{}
\r
26627 , because they can be inserted in LyX directly to text.
\r
26630 \begin_layout Subsection
\r
26632 \begin_inset CommandInset label
\r
26633 LatexCommand label
\r
26634 name "sub:Accents-in-Text"
\r
26639 \begin_inset Index idx
\r
26642 \begin_layout Plain Layout
\r
26643 Accents ! in text
\r
26651 \begin_layout Standard
\r
26652 With the following commands all letters can be accented.
\r
26653 The commands must be inserted in TeX-mode.
\r
26656 \begin_layout Standard
\r
26657 \begin_inset space \hfill{}
\r
26661 \begin_inset Tabular
\r
26662 <lyxtabular version="3" rows="8" columns="2">
\r
26663 <features tabularvalignment="middle">
\r
26664 <column alignment="block" valignment="top" width="0">
\r
26665 <column alignment="block" valignment="top" width="0">
\r
26667 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
26668 \begin_inset Text
\r
26670 \begin_layout Plain Layout
\r
26676 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
26677 \begin_inset Text
\r
26679 \begin_layout Plain Layout
\r
26687 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
26688 \begin_inset Text
\r
26690 \begin_layout Plain Layout
\r
26694 \begin_inset Quotes grd
\r
26702 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
26703 \begin_inset Text
\r
26705 \begin_layout Plain Layout
\r
26709 \begin_layout Plain Layout
\r
26725 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
26726 \begin_inset Text
\r
26728 \begin_layout Plain Layout
\r
26736 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
26737 \begin_inset Text
\r
26739 \begin_layout Plain Layout
\r
26743 \begin_layout Plain Layout
\r
26759 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
26760 \begin_inset Text
\r
26762 \begin_layout Plain Layout
\r
26769 \begin_layout Plain Layout
\r
26783 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
26784 \begin_inset Text
\r
26786 \begin_layout Plain Layout
\r
26790 \begin_layout Plain Layout
\r
26806 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
26807 \begin_inset Text
\r
26809 \begin_layout Plain Layout
\r
26817 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
26818 \begin_inset Text
\r
26820 \begin_layout Plain Layout
\r
26824 \begin_layout Plain Layout
\r
26840 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
26841 \begin_inset Text
\r
26843 \begin_layout Plain Layout
\r
26850 \begin_layout Plain Layout
\r
26864 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
26865 \begin_inset Text
\r
26867 \begin_layout Plain Layout
\r
26871 \begin_layout Plain Layout
\r
26887 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
26888 \begin_inset Text
\r
26890 \begin_layout Plain Layout
\r
26897 \begin_layout Plain Layout
\r
26911 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
26912 \begin_inset Text
\r
26914 \begin_layout Plain Layout
\r
26918 \begin_layout Plain Layout
\r
26934 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
26935 \begin_inset Text
\r
26937 \begin_layout Plain Layout
\r
26944 \begin_layout Plain Layout
\r
26958 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
26959 \begin_inset Text
\r
26961 \begin_layout Plain Layout
\r
26965 \begin_layout Plain Layout
\r
26985 \begin_inset space \hfill{}
\r
26989 \begin_inset Tabular
\r
26990 <lyxtabular version="3" rows="8" columns="2">
\r
26991 <features tabularvalignment="middle">
\r
26992 <column alignment="block" valignment="top" width="0">
\r
26993 <column alignment="center" valignment="top" width="0">
\r
26995 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
26996 \begin_inset Text
\r
26998 \begin_layout Plain Layout
\r
27004 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
27005 \begin_inset Text
\r
27007 \begin_layout Plain Layout
\r
27015 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
27016 \begin_inset Text
\r
27018 \begin_layout Plain Layout
\r
27025 \begin_layout Plain Layout
\r
27039 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
27040 \begin_inset Text
\r
27042 \begin_layout Plain Layout
\r
27046 \begin_layout Plain Layout
\r
27062 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
27063 \begin_inset Text
\r
27065 \begin_layout Plain Layout
\r
27073 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
27074 \begin_inset Text
\r
27076 \begin_layout Plain Layout
\r
27080 \begin_layout Plain Layout
\r
27096 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
27097 \begin_inset Text
\r
27099 \begin_layout Plain Layout
\r
27103 \begin_inset Index idx
\r
27106 \begin_layout Plain Layout
\r
27117 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
27118 \begin_inset Text
\r
27120 \begin_layout Plain Layout
\r
27124 \begin_layout Plain Layout
\r
27140 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
27141 \begin_inset Text
\r
27143 \begin_layout Plain Layout
\r
27151 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
27152 \begin_inset Text
\r
27154 \begin_layout Plain Layout
\r
27158 \begin_layout Plain Layout
\r
27174 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
27175 \begin_inset Text
\r
27177 \begin_layout Plain Layout
\r
27184 \begin_layout Plain Layout
\r
27198 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
27199 \begin_inset Text
\r
27201 \begin_layout Plain Layout
\r
27205 \begin_layout Plain Layout
\r
27221 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
27222 \begin_inset Text
\r
27224 \begin_layout Plain Layout
\r
27231 \begin_layout Plain Layout
\r
27245 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
27246 \begin_inset Text
\r
27248 \begin_layout Plain Layout
\r
27252 \begin_layout Plain Layout
\r
27268 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
27269 \begin_inset Text
\r
27271 \begin_layout Plain Layout
\r
27278 \begin_layout Plain Layout
\r
27292 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
27293 \begin_inset Text
\r
27295 \begin_layout Plain Layout
\r
27299 \begin_layout Plain Layout
\r
27319 \begin_inset space \hfill{}
\r
27325 \begin_layout Standard
\r
27326 \begin_inset VSpace medskip
\r
27329 With the command
\r
27335 also two different characters can be accented.
\r
27344 \begin_layout Plain Layout
\r
27359 \begin_layout Plain Layout
\r
27371 \begin_layout Standard
\r
27384 can in combination with vowels directly be inserted with the keyboard without
\r
27386 The same applies for the tilde
\r
27387 \begin_inset Foot
\r
27390 \begin_layout Plain Layout
\r
27391 This only applies for keyboards where the tilde is defined as accent.
\r
27400 in combination with
\r
27415 \begin_layout Standard
\r
27458 and accents that are inserted directly with the keyboard are also available
\r
27459 in mathematical text.
\r
27460 For the other accents there are special math commands to be used in formulas,
\r
27462 \begin_inset CommandInset ref
\r
27464 reference "sub:Accents-for-one"
\r
27471 \begin_layout Standard
\r
27472 \begin_inset VSpace bigskip
\r
27475 Furthermore, with the command
\r
27482 \begin_inset Index idx
\r
27485 \begin_layout Plain Layout
\r
27493 all numbers and letters can be set into a circle, quasi accented with a
\r
27494 circle, similar to the copyright symbol.
\r
27497 \begin_layout Standard
\r
27499 \begin_inset Tabular
\r
27500 <lyxtabular version="3" rows="3" columns="2">
\r
27501 <features tabularvalignment="middle">
\r
27502 <column alignment="center" valignment="top" width="0">
\r
27503 <column alignment="center" valignment="top" width="0">
\r
27505 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
27506 \begin_inset Text
\r
27508 \begin_layout Plain Layout
\r
27514 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
27515 \begin_inset Text
\r
27517 \begin_layout Plain Layout
\r
27519 \begin_inset Note Note
\r
27522 \begin_layout Plain Layout
\r
27529 is only used as spacer.
\r
27541 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
27542 \begin_inset Text
\r
27544 \begin_layout Plain Layout
\r
27552 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
27553 \begin_inset Text
\r
27555 \begin_layout Plain Layout
\r
27559 \begin_layout Plain Layout
\r
27575 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
27576 \begin_inset Text
\r
27578 \begin_layout Plain Layout
\r
27589 raisebox{-1.5pt}{W}}
\r
27594 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
27595 \begin_inset Text
\r
27597 \begin_layout Plain Layout
\r
27598 \begin_inset Formula $\raisebox{4.5mm}{}$
\r
27605 \begin_layout Plain Layout
\r
27617 raisebox{-1.5pt}W}
\r
27623 \begin_inset Formula $\raisebox{-2mm}{}$
\r
27639 \begin_layout Standard
\r
27640 One has to take care that the character fits in the circle.
\r
27648 \begin_inset Foot
\r
27651 \begin_layout Plain Layout
\r
27653 \begin_inset CommandInset ref
\r
27655 reference "sub:Font-Sizes"
\r
27664 specifies thereby the size of the circle.
\r
27665 With the help of
\r
27672 \begin_inset Foot
\r
27675 \begin_layout Plain Layout
\r
27677 \begin_inset CommandInset ref
\r
27679 reference "sub:Boxes-without-Frame"
\r
27688 the character can be centered.
\r
27691 \begin_layout Subsection
\r
27692 Old-style Figures
\r
27693 \begin_inset Index idx
\r
27696 \begin_layout Plain Layout
\r
27697 Old-style Figures
\r
27705 \begin_layout Standard
\r
27706 Old-style figures (also known as old-style numerals) are created with the
\r
27714 \begin_inset Index idx
\r
27717 \begin_layout Plain Layout
\r
27726 The command can be used in formulas and in TeX-mode.
\r
27727 The command scheme is:
\r
27730 \begin_layout Standard
\r
27735 oldstylenums{number}
\r
27738 \begin_layout Standard
\r
27743 oldstylenums{0123456789
\r
27746 \begin_inset Formula $\oldstylenums{0123456789}$
\r
27752 \begin_layout Subsection
\r
27753 Miscellaneous special Characters
\r
27754 \begin_inset CommandInset label
\r
27755 LatexCommand label
\r
27756 name "sub:Miscellaneous-special-Characters"
\r
27761 \begin_inset Index idx
\r
27764 \begin_layout Plain Layout
\r
27765 Special characters ! miscellaneous
\r
27773 \begin_layout Standard
\r
27774 The following characters can only be inserted to formulas by using commands:
\r
27777 \begin_layout Standard
\r
27779 \begin_inset Tabular
\r
27780 <lyxtabular version="3" rows="4" columns="2">
\r
27781 <features tabularvalignment="middle">
\r
27782 <column alignment="center" valignment="top" width="0">
\r
27783 <column alignment="center" valignment="top" width="0">
\r
27785 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
27786 \begin_inset Text
\r
27788 \begin_layout Plain Layout
\r
27794 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
27795 \begin_inset Text
\r
27797 \begin_layout Plain Layout
\r
27805 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
27806 \begin_inset Text
\r
27808 \begin_layout Plain Layout
\r
27815 \begin_layout Plain Layout
\r
27829 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
27830 \begin_inset Text
\r
27832 \begin_layout Plain Layout
\r
27833 \begin_inset Formula $\mathcircumflex$
\r
27843 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
27844 \begin_inset Text
\r
27846 \begin_layout Plain Layout
\r
27854 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
27855 \begin_inset Text
\r
27857 \begin_layout Plain Layout
\r
27858 \begin_inset Formula $\_$
\r
27868 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
27869 \begin_inset Text
\r
27871 \begin_layout Plain Layout
\r
27876 \begin_layout Plain Layout
\r
27888 \begin_inset Index idx
\r
27891 \begin_layout Plain Layout
\r
27904 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
27905 \begin_inset Text
\r
27907 \begin_layout Plain Layout
\r
27908 \begin_inset Formula $^{\circ}$
\r
27924 \begin_layout Standard
\r
27925 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
\r
27926 contains the following line
\r
27927 \begin_inset Foot
\r
27930 \begin_layout Plain Layout
\r
27931 More about this is described in
\r
27932 \begin_inset CommandInset ref
\r
27934 reference "sub:Text-Characters-in"
\r
27946 \begin_layout Standard
\r
27951 DeclareInputtext{176}{
\r
27964 \begin_layout Section
\r
27966 \begin_inset CommandInset label
\r
27967 LatexCommand label
\r
27968 name "sec:Formula-Styles"
\r
27973 \begin_inset Index idx
\r
27976 \begin_layout Plain Layout
\r
27985 \begin_layout Itemize
\r
27986 There are two different alignment styles:
\r
27990 \begin_layout Description
\r
27991 Centered is the predefined standard
\r
27994 \begin_layout Description
\r
27995 Indented for this the option
\r
27999 must be inserted in the menu
\r
28001 Document\SpecialChar \menuseparator
\r
28007 \begin_inset space ~
\r
28013 \begin_layout Standard
\r
28018 is used, the indentation can be adjusted with the length
\r
28025 \begin_inset Index idx
\r
28028 \begin_layout Plain Layout
\r
28037 Should the distance be 15
\r
28038 \begin_inset space \thinspace{}
\r
28041 mm, the following command line is inserted in the LaTeX-preamble
\r
28044 \begin_layout Standard
\r
28051 mathindent}{15mm}
\r
28054 \begin_layout Standard
\r
28055 When no length is specified, the predefined value of 30
\r
28056 \begin_inset space \thinspace{}
\r
28063 \begin_layout Itemize
\r
28064 And two different numbering styles:
\r
28068 \begin_layout Description
\r
28069 Right is the predefined standard
\r
28072 \begin_layout Description
\r
28073 Left for this the option
\r
28077 must be inserted in the menu
\r
28079 Document\SpecialChar \menuseparator
\r
28085 \begin_inset space ~
\r
28092 \begin_layout Standard
\r
28101 can also be used together.
\r
28102 In this case both options are inserted, separated by a comma.
\r
28105 \begin_layout Standard
\r
28106 The chosen styles are used for all displayed formulas of the document.
\r
28107 When both, centered and indented formulas should be created in a document,
\r
28113 The indented formulas are then set in a flalign environment, see
\r
28114 \begin_inset CommandInset ref
\r
28116 reference "sub:Flalign-Environment"
\r
28123 \begin_layout Section
\r
28124 Multiline Formulas
\r
28125 \begin_inset CommandInset label
\r
28126 LatexCommand label
\r
28127 name "sec:Multiline-Formulas"
\r
28132 \begin_inset Index idx
\r
28135 \begin_layout Plain Layout
\r
28136 Formula ! multiline
\r
28144 \begin_layout Subsection
\r
28148 \begin_layout Standard
\r
28149 In LyX multiline formulas are created by pressing
\r
28152 \begin_inset Info
\r
28154 arg "newline-insert newline"
\r
28159 inside a formula.
\r
28160 This creates either an
\r
28162 eqnarray environment
\r
28164 that is described in
\r
28165 \begin_inset CommandInset ref
\r
28167 reference "sub:Eqnarray-Environment"
\r
28171 or, when the option
\r
28173 Use AMS math package
\r
28175 in the document settings is selected, an
\r
28177 align environment
\r
28179 that is described in
\r
28180 \begin_inset CommandInset ref
\r
28182 reference "sub:Standard-align-Environment"
\r
28187 The align environment is recommended because it provides in any case a
\r
28188 typographically correct output.
\r
28191 \begin_layout Standard
\r
28192 There are other multiline formula environments that can be created via the
\r
28195 Insert\SpecialChar \menuseparator
\r
28199 These environments are described in the following sections.
\r
28202 \begin_layout Standard
\r
28203 In all multiline formula environments a new line is created by pressing
\r
28205 \begin_inset Info
\r
28207 arg "newline-insert newline"
\r
28211 To add or delete lines, the math toolbar buttons
\r
28212 \begin_inset Graphics
\r
28213 filename ../images/tabular-feature_append-row.png
\r
28219 \begin_inset Graphics
\r
28220 filename ../images/tabular-feature_delete-row.png
\r
28225 , respectively, or the menu
\r
28227 Edit\SpecialChar \menuseparator
\r
28233 \begin_layout Subsubsection
\r
28235 \begin_inset CommandInset label
\r
28236 LatexCommand label
\r
28237 name "sub:Line-Separation"
\r
28242 \begin_inset Index idx
\r
28245 \begin_layout Plain Layout
\r
28246 Formula ! multiline ! Line separation
\r
28254 \begin_layout Standard
\r
28255 There is sometimes not enough space in multiline formulas between the lines:
\r
28256 \begin_inset Formula
\r
28257 \begin{eqnarray*}
\r
28258 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}\\
\r
28259 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
\r
28267 \begin_layout Standard
\r
28268 In LaTeX additional line space is specified as optional argument of the
\r
28269 new line command.
\r
28270 This is not yet possible in LyX
\r
28271 \begin_inset Foot
\r
28274 \begin_layout Plain Layout
\r
28276 \begin_inset CommandInset href
\r
28277 LatexCommand href
\r
28278 name "LyX-bug #1505"
\r
28279 target "http://www.lyx.org/trac/ticket/1505"
\r
28288 , therefore the whole formula must be inserted in TeX-mode.
\r
28289 To add in our example space, the command
\r
28297 is inserted at the end of the first line.
\r
28302 \begin_layout Plain Layout
\r
28309 \begin_layout Plain Layout
\r
28311 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
\r
28314 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
\r
28321 \begin_layout Plain Layout
\r
28325 left(B^{2}+x_{0}^{2}
\r
28333 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
\r
28338 \begin_layout Plain Layout
\r
28350 \begin_layout Standard
\r
28351 \begin_inset VSpace bigskip
\r
28354 To set the line separation for all lines in a formula, the length
\r
28361 \begin_inset Index idx
\r
28364 \begin_layout Plain Layout
\r
28373 The definition is:
\r
28374 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
\r
28385 \begin_inset space \thinspace{}
\r
28390 \begin_inset space \thinspace{}
\r
28393 mm additional line separation as in the previous example, the command
\r
28396 \begin_layout Standard
\r
28406 \begin_layout Standard
\r
28407 is inserted in TeX-mode before the formula.
\r
28408 This requires that the LaTeX-package
\r
28413 \begin_inset Foot
\r
28416 \begin_layout Plain Layout
\r
28421 is part of every LaTeX standard installation.
\r
28427 \begin_inset Index idx
\r
28430 \begin_layout Plain Layout
\r
28436 was loaded in LaTeX-preamble with the line
\r
28439 \begin_layout Standard
\r
28447 \begin_layout Standard
\r
28452 \begin_layout Plain Layout
\r
28464 \begin_inset Formula
\r
28465 \begin{eqnarray*}
\r
28466 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}\\
\r
28467 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
\r
28475 \begin_layout Standard
\r
28479 \begin_layout Plain Layout
\r
28490 To get back to the predefined distance,
\r
28496 is set to the value 3
\r
28497 \begin_inset space \thinspace{}
\r
28503 \begin_layout Subsubsection
\r
28504 Column Separation
\r
28505 \begin_inset CommandInset label
\r
28506 LatexCommand label
\r
28507 name "sub:Column-Separation"
\r
28512 \begin_inset Index idx
\r
28515 \begin_layout Plain Layout
\r
28516 Formula ! multiline ! Column separation
\r
28524 \begin_layout Standard
\r
28525 Multiline formulas form a matrix.
\r
28526 A formula in the eqnarray environment is for example a matrix with three
\r
28528 By changing the column separation in this environment, the space beside
\r
28529 the relation sign can be changed.
\r
28532 \begin_layout Standard
\r
28533 The column separation is specified with the length
\r
28540 \begin_inset Index idx
\r
28543 \begin_layout Plain Layout
\r
28552 \begin_inset Newline newline
\r
28555 column separation = 2
\r
28556 \begin_inset space \thinspace{}
\r
28566 \begin_inset Newline newline
\r
28569 Thus, the command
\r
28572 \begin_layout Standard
\r
28579 arraycolsep}{1cm}
\r
28582 \begin_layout Standard
\r
28583 inserted in TeX-mode, sets for all following formulas a column separation
\r
28585 \begin_inset space \thinspace{}
\r
28589 To get back to the predefined distance,
\r
28596 \begin_inset space \thinspace{}
\r
28602 \begin_layout Standard
\r
28604 \begin_inset space \thinspace{}
\r
28607 cm column separation:
\r
28611 \begin_layout Plain Layout
\r
28617 arraycolsep}{1cm}
\r
28623 \begin_inset Formula
\r
28624 \begin{eqnarray*}
\r
28631 A formula with the predefined column separation for matrices of 10
\r
28632 \begin_inset space \thinspace{}
\r
28639 \begin_layout Plain Layout
\r
28645 arraycolsep}{5pt}
\r
28651 \begin_inset Formula
\r
28652 \begin{eqnarray*}
\r
28662 \begin_layout Subsubsection
\r
28664 \begin_inset Index idx
\r
28667 \begin_layout Plain Layout
\r
28676 \begin_layout Standard
\r
28677 Long formulas can be typeset using these methods:
\r
28680 \begin_layout Itemize
\r
28681 When one side of the equation is much shorter than the line width, this
\r
28682 one is chosen for the left side and the right side is typeset over two
\r
28684 \begin_inset Formula
\r
28686 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 \\
\r
28687 & & -\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}
\r
28692 The minus sign at the beginning of the second line does normally not appear
\r
28693 as an operator because it is the first character of the line.
\r
28694 Thus it would not be surrounded by space and could not be distinguished
\r
28695 from the fraction bar.
\r
28697 \begin_inset space \thinspace{}
\r
28700 pt space was inserted behind the minus sign with the command
\r
28707 \begin_inset Foot
\r
28710 \begin_layout Plain Layout
\r
28718 \begin_inset CommandInset ref
\r
28720 reference "sub:Variable-Space"
\r
28730 \begin_inset Index idx
\r
28733 \begin_layout Plain Layout
\r
28744 \begin_layout Itemize
\r
28745 When both sides of the equation are too long, the command
\r
28752 \begin_inset Index idx
\r
28755 \begin_layout Plain Layout
\r
28764 It is inserted in the first column of the first line and causes all further
\r
28765 insertions to overwrite the following columns:
\r
28766 \begin_inset Formula
\r
28768 \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 \\
\r
28769 & & -\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 \\
\r
28770 & & =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}
\r
28775 After the insertion of
\r
28781 , the cursor is in a purple box that is a bit shifted to the left from the
\r
28783 In this the formula is inserted.
\r
28784 \begin_inset Newline newline
\r
28787 The content of the further lines is inserted to the second or another formula
\r
28789 The greater the column number where it was inserted, the larger the indentation.
\r
28790 \begin_inset VSpace medskip
\r
28794 \begin_inset Newline newline
\r
28798 \begin_inset Note Greyedout
\r
28801 \begin_layout Plain Layout
\r
28802 Note the following when using
\r
28811 \begin_layout Itemize
\r
28812 The formula doesn't use the full page width.
\r
28814 \begin_inset space \thinspace{}
\r
28818 \begin_inset space \space{}
\r
28822 \begin_inset Formula $-B^{2}$
\r
28825 is added to the first line in the above example, it would have been outside
\r
28827 To better use the width, negative space can be inserted at the beginning
\r
28828 of the first line.
\r
28831 \begin_layout Itemize
\r
28832 Due to a bug in LyX the cursor cannot be set with the mouse into the first
\r
28834 \begin_inset Foot
\r
28837 \begin_layout Plain Layout
\r
28838 \begin_inset CommandInset href
\r
28839 LatexCommand href
\r
28840 name "LyX-bug #1429"
\r
28841 target "http://www.lyx.org/trac/ticket/1429"
\r
28850 One can only set the cursor at the beginning of the line and move it with
\r
28859 \begin_layout Itemize
\r
28860 Other methods to set long formulas are offered by the environments described
\r
28862 \begin_inset CommandInset ref
\r
28864 reference "sub:Multline-Environment"
\r
28869 \begin_inset CommandInset ref
\r
28871 reference "sub:Multiline-Formula-Parts"
\r
28878 \begin_layout Subsubsection
\r
28879 Multiline Brackets
\r
28880 \begin_inset CommandInset label
\r
28881 LatexCommand label
\r
28882 name "sub:Multiline-Brackets"
\r
28887 \begin_inset Index idx
\r
28890 \begin_layout Plain Layout
\r
28891 Brackets ! for multiline expressions
\r
28899 \begin_layout Standard
\r
28900 For brackets spanning multiple lines the following problem occurs:
\r
28901 \begin_inset Formula
\r
28902 \begin{eqnarray*}
\r
28903 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
\r
28904 & & \left.\cdots+B-D\right]
\r
28912 \begin_layout Standard
\r
28913 The closing bracket is smaller than the opening bracket because brackets
\r
28914 with variable size may not span multiple lines.
\r
28917 \begin_layout Standard
\r
28918 To set the bracket size for the second line correctly, the first line is
\r
28926 \begin_inset Index idx
\r
28929 \begin_layout Plain Layout
\r
28937 and the second line with
\r
28942 \begin_inset Foot
\r
28945 \begin_layout Plain Layout
\r
28959 \begin_inset CommandInset ref
\r
28961 reference "sub:Automatic-Bracket-Size"
\r
28973 \begin_inset Index idx
\r
28976 \begin_layout Plain Layout
\r
29002 \begin_layout Plain Layout
\r
29021 \begin_layout Plain Layout
\r
29040 \begin_layout Plain Layout
\r
29052 \begin_inset Formula $\downarrow$
\r
29058 \begin_inset Index idx
\r
29061 \begin_layout Plain Layout
\r
29069 is inserted, because the multiplication operator with its limits is the
\r
29070 largest symbol in the first line and this should be the size for the bracket
\r
29071 in the second line.
\r
29074 \begin_layout Standard
\r
29075 The result is this:
\r
29076 \begin_inset Formula
\r
29077 \begin{eqnarray*}
\r
29078 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
\r
29079 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
\r
29087 \begin_layout Subsection
\r
29088 Align Environments
\r
29091 \begin_layout Standard
\r
29092 Align environments can be used for every kind of multiline formulas.
\r
29093 They are especially useful to set several formulas side by side.
\r
29096 \begin_layout Standard
\r
29097 Align environments consist of columns.
\r
29098 The odd columns are right aligned, the even ones left aligned.
\r
29099 Every line in an Align environment can be numbered.
\r
29102 \begin_layout Standard
\r
29103 Align environments are created via the menu
\r
29105 Insert\SpecialChar \menuseparator
\r
29111 Edit\SpecialChar \menuseparator
\r
29112 Math\SpecialChar \menuseparator
\r
29113 Change Formula Type
\r
29115 already existing formulas can be converted to Align environments.
\r
29118 \begin_layout Standard
\r
29119 To add or delete columns, the math toolbar buttons
\r
29120 \begin_inset Graphics
\r
29121 filename ../images/tabular-feature_append-column.png
\r
29127 \begin_inset Graphics
\r
29128 filename ../images/tabular-feature_delete-column.png
\r
29133 , respectively, or the menu
\r
29135 Edit\SpecialChar \menuseparator
\r
29141 \begin_layout Subsubsection
\r
29142 Standard align Environment
\r
29143 \begin_inset CommandInset label
\r
29144 LatexCommand label
\r
29145 name "sub:Standard-align-Environment"
\r
29150 \begin_inset Index idx
\r
29153 \begin_layout Plain Layout
\r
29154 Formula ! multiline ! align environment
\r
29162 \begin_layout Standard
\r
29163 This Align environment is created by pressing
\r
29164 \begin_inset Info
\r
29166 arg "newline-insert newline"
\r
29169 in a formula or by the menu
\r
29171 Insert\SpecialChar \menuseparator
\r
29172 Math\SpecialChar \menuseparator
\r
29173 AMS align Environment
\r
29178 \begin_layout Standard
\r
29179 An example for two formulas set side by side, that are created with a four
\r
29180 column align environment:
\r
29181 \begin_inset Formula
\r
29183 A & =\sin(B) & C & =D\\
\r
29184 C & \ne A & B & \ne D
\r
29189 As it can be seen, the formulas in this environment are placed so as if
\r
29190 there would be a
\r
29195 \begin_inset Foot
\r
29198 \begin_layout Plain Layout
\r
29206 \begin_inset CommandInset ref
\r
29208 reference "sub:Variable-Space"
\r
29219 before the first and after every even column.
\r
29220 When the formula style
\r
29223 \begin_inset Foot
\r
29226 \begin_layout Plain Layout
\r
29227 formula styles see
\r
29228 \begin_inset CommandInset ref
\r
29230 reference "sec:Formula-Styles"
\r
29241 is used, the formula is set without the
\r
29247 before the first column.
\r
29250 \begin_layout Subsubsection
\r
29251 Alignat Environment
\r
29252 \begin_inset Index idx
\r
29255 \begin_layout Plain Layout
\r
29256 Formula ! multiline ! alignat environment
\r
29264 \begin_layout Standard
\r
29265 The alignat environment has no predefined column separation.
\r
29266 It can be inserted manually with the spaces that are described
\r
29267 \begin_inset CommandInset ref
\r
29269 reference "sub:Space"
\r
29276 \begin_layout Standard
\r
29277 The above example in the alignat environment where 1
\r
29278 \begin_inset space \thinspace{}
\r
29281 cm space was inserted at the beginning of the second formula:
\r
29282 \begin_inset Formula
\r
29283 \begin{alignat*}{2}
\r
29284 A & =\sin(B) & \hspace{1cm}C & =D\\
\r
29285 C & \ne A & B & \ne D
\r
29290 Because the column separation can be set separately for every column, this
\r
29291 environment is especially suitable to set three and more formulas side
\r
29295 \begin_layout Subsubsection
\r
29296 Flalign Environment
\r
29297 \begin_inset CommandInset label
\r
29298 LatexCommand label
\r
29299 name "sub:Flalign-Environment"
\r
29304 \begin_inset Index idx
\r
29307 \begin_layout Plain Layout
\r
29308 Formula ! multiline ! flalign environment
\r
29316 \begin_layout Standard
\r
29317 In this environment the first two columns are always set as much as possible
\r
29318 to the left and the last two ones to the right.
\r
29320 \begin_inset Formula
\r
29322 A & =1 & B & =2 & C & =3\\
\r
29323 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
\r
29331 \begin_layout Standard
\r
29332 By creating a flalign environment with an odd number of columns where an
\r
29333 empty TeX-brace is inserted to the last column, several formulas in a document
\r
29334 can be set to the left, although the formula style
\r
29339 As example the indented formula
\r
29340 \begin_inset CommandInset ref
\r
29341 LatexCommand eqref
\r
29342 reference "eq:VolInt"
\r
29347 \begin_inset Formula
\r
29349 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}
\r
29354 The first two columns contain the formula.
\r
29355 To indent it as with the formula style
\r
29360 \begin_inset space \thinspace{}
\r
29363 pt space was inserted at the beginning of the first column.
\r
29366 \begin_layout Subsection
\r
29367 Eqnarray Environment
\r
29368 \begin_inset CommandInset label
\r
29369 LatexCommand label
\r
29370 name "sub:Eqnarray-Environment"
\r
29375 \begin_inset Index idx
\r
29378 \begin_layout Plain Layout
\r
29379 Formula ! multiline ! eqnarray environment
\r
29387 \begin_layout Standard
\r
29388 When this environment has been created, three blue boxes appear.
\r
29389 The content of the first box is right aligned, the content of the last
\r
29390 one left aligned.
\r
29391 The content of the middle box appears centered and a bit smaller, because
\r
29392 it is designed to insert there only relation characters.
\r
29393 \begin_inset Formula
\r
29394 \begin{eqnarray*}
\r
29395 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
\r
29405 \begin_layout Subsection
\r
29406 Gather Environment
\r
29407 \begin_inset Index idx
\r
29410 \begin_layout Plain Layout
\r
29411 Formula ! multiline ! gather environment
\r
29419 \begin_layout Standard
\r
29420 This environment consists of only one centered column.
\r
29421 Every line can be numbered.
\r
29422 \begin_inset Formula
\r
29433 \begin_layout Subsection
\r
29434 Multline Environment
\r
29435 \begin_inset CommandInset label
\r
29436 LatexCommand label
\r
29437 name "sub:Multline-Environment"
\r
29442 \begin_inset Index idx
\r
29445 \begin_layout Plain Layout
\r
29446 Formula ! multiline ! multline environment
\r
29454 \begin_layout Standard
\r
29455 The multline environment consists, like the gather environment, of only
\r
29457 But the first line is left aligned, the last one right aligned.
\r
29458 All other lines are centered.
\r
29459 Therefore this environment is suitable for long formulas.
\r
29460 As example formula
\r
29461 \begin_inset CommandInset ref
\r
29462 LatexCommand eqref
\r
29463 reference "eq:lefteqn"
\r
29467 in the multline environment:
\r
29468 \begin_inset Formula
\r
29470 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}\\
\r
29471 -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}\\
\r
29472 =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}}
\r
29480 \begin_layout Standard
\r
29481 In the output only the last (first) line of a multline environment appears
\r
29482 numbered when the document numbering is right (left).
\r
29483 \begin_inset Foot
\r
29486 \begin_layout Plain Layout
\r
29487 numbering styles see
\r
29488 \begin_inset CommandInset ref
\r
29490 reference "sec:Formula-Styles"
\r
29502 \begin_layout Standard
\r
29503 With the commands
\r
29510 \begin_inset Index idx
\r
29513 \begin_layout Plain Layout
\r
29528 \begin_inset Index idx
\r
29531 \begin_layout Plain Layout
\r
29539 a centered line can be right or left aligned, respectively.
\r
29540 The commands are used as follows:
\r
29543 \begin_layout Standard
\r
29548 shoveright{line content}
\r
29554 shoveleft{line content}
\r
29557 \begin_layout Standard
\r
29558 \begin_inset VSpace medskip
\r
29568 \begin_inset Index idx
\r
29571 \begin_layout Plain Layout
\r
29579 specifies the distance of the first line from the left page margin.
\r
29580 Predefined is the length 0
\r
29581 \begin_inset space \thinspace{}
\r
29587 \begin_layout Standard
\r
29588 As example the above formula where the command
\r
29591 \begin_layout Standard
\r
29598 multlinegap}{2cm}
\r
29601 \begin_layout Standard
\r
29602 was inserted in TeX-mode before:
\r
29606 \begin_layout Plain Layout
\r
29612 multlinegap}{2cm}
\r
29618 \begin_inset Formula
\r
29620 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}\\
\r
29621 \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}}\\
\r
29622 =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}}
\r
29631 \begin_layout Plain Layout
\r
29637 multlinegap}{0pt}
\r
29642 The second line was left aligned using
\r
29651 \begin_layout Subsection
\r
29652 Multiline Formula Parts
\r
29653 \begin_inset CommandInset label
\r
29654 LatexCommand label
\r
29655 name "sub:Multiline-Formula-Parts"
\r
29660 \begin_inset Index idx
\r
29663 \begin_layout Plain Layout
\r
29664 Formula ! multiline ! formula parts
\r
29672 \begin_layout Standard
\r
29673 To display only parts of a formula with multiple lines, one of the following
\r
29674 environments is used:
\r
29691 They can be inserted via the menu
\r
29693 Insert\SpecialChar \menuseparator
\r
29696 or by using the commands described in this section.
\r
29699 \begin_layout Standard
\r
29700 The first three have the same properties as the corresponding multiline
\r
29701 formula environments, but it is possible to set further formula parts beside
\r
29704 \begin_inset Formula
\r
29706 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
\r
29707 \Delta E\Delta t & \ge\frac{\hbar}{2}
\r
29709 \right\} \textrm{Uncertainty relations}
\r
29717 \begin_layout Standard
\r
29718 To get this formula, a displayed formula is created where the command
\r
29725 \begin_inset Index idx
\r
29728 \begin_layout Plain Layout
\r
29737 A purple box appears around the blue formula box where now columns and
\r
29738 lines can be added.
\r
29739 Outside the multiline environment other formula parts can be set, like
\r
29743 \begin_layout Standard
\r
29744 The aligned environment is also suitable for long formulas whose lines are
\r
29745 horizontally aligned.
\r
29746 Using aligned in a displayed formula has the advantage that the formula
\r
29747 number is vertically centered behind the lines.
\r
29748 As example formula
\r
29749 \begin_inset CommandInset ref
\r
29750 LatexCommand eqref
\r
29751 reference "eq:shortlong"
\r
29755 in the aligned environment:
\r
29756 \begin_inset Formula
\r
29758 \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}|}\\
\r
29759 & -\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}|}
\r
29768 \begin_layout Standard
\r
29769 To use the environments
\r
29788 \begin_inset Index idx
\r
29791 \begin_layout Plain Layout
\r
29806 \begin_inset Index idx
\r
29809 \begin_layout Plain Layout
\r
29824 \begin_inset Index idx
\r
29827 \begin_layout Plain Layout
\r
29835 are inserted, respectively.
\r
29836 The split environment has the same properties as the aligned environment
\r
29837 but it can only have two columns.
\r
29840 \begin_layout Subsection
\r
29841 Text in multiline Formulas
\r
29842 \begin_inset CommandInset label
\r
29843 LatexCommand label
\r
29844 name "sub:Text-in-multiline"
\r
29849 \begin_inset Index idx
\r
29852 \begin_layout Plain Layout
\r
29853 Text ! in formulas
\r
29859 \begin_inset Index idx
\r
29862 \begin_layout Plain Layout
\r
29863 Formula ! multiline ! text
\r
29871 \begin_layout Standard
\r
29872 In the Align environments, and the multline and gather environment, text
\r
29873 can be inserted that will appear in a separate line and doesn't affect
\r
29874 the column alignment.
\r
29875 To do this, the command
\r
29882 \begin_inset Index idx
\r
29885 \begin_layout Plain Layout
\r
29893 is used in the following scheme:
\r
29896 \begin_layout Standard
\r
29904 \begin_layout Standard
\r
29905 The text should not be longer than a line because it cannot be hyphenated.
\r
29906 As LyX doesn't yet support
\r
29912 directly, the text is written as mathematical text.
\r
29919 must hereby be at the beginning of a line and appears in the output above
\r
29921 An example where the text was inserted at the beginning of the second line:
\r
29922 \begin_inset Formula
\r
29924 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
\r
29925 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
\r
29933 \begin_layout Section
\r
29934 Formula Numbering
\r
29935 \begin_inset Index idx
\r
29938 \begin_layout Plain Layout
\r
29939 Formula numbering
\r
29945 \begin_inset Index idx
\r
29948 \begin_layout Plain Layout
\r
29949 Formula ! numbering|see
\r
29953 \begin_layout Plain Layout
\r
29960 Formula numbering
\r
29964 \begin_layout Plain Layout
\r
29979 \begin_layout Subsection
\r
29983 \begin_layout Standard
\r
29984 Numbered formulas can be created with the menu
\r
29986 Insert\SpecialChar \menuseparator
\r
29987 Math\SpecialChar \menuseparator
\r
29989 \begin_inset space ~
\r
29997 \begin_inset space ~
\r
30003 Existing formulas can be numbered with the menu
\r
30005 Edit\SpecialChar \menuseparator
\r
30006 Math\SpecialChar \menuseparator
\r
30008 \begin_inset space ~
\r
30014 \begin_inset Info
\r
30016 arg "math-number-toggle"
\r
30020 The formula number is displayed in LyX behind the formula as a number sign
\r
30022 The number sign is replaced in the output by the formula number.
\r
30025 \begin_layout Standard
\r
30026 When numbering is turned on in multiline formulas, all lines will be numbered.
\r
30027 But the numbering can be controlled with the menu
\r
30029 Edit\SpecialChar \menuseparator
\r
30030 Math\SpecialChar \menuseparator
\r
30032 \begin_inset space ~
\r
30036 \begin_inset space ~
\r
30040 \begin_inset space ~
\r
30046 \begin_inset Info
\r
30048 arg "math-number-line-toggle"
\r
30051 ) for every line.
\r
30054 \begin_layout Standard
\r
30055 Except for inline formulas, all formulas can be numbered with two different
\r
30057 \begin_inset CommandInset ref
\r
30059 reference "sec:Formula-Styles"
\r
30066 \begin_layout Subsection
\r
30068 \begin_inset Index idx
\r
30071 \begin_layout Plain Layout
\r
30072 Cross-references ! to formulas
\r
30080 \begin_layout Standard
\r
30081 All labeled formulas can be cross-referenced.
\r
30082 A label is added by the menu
\r
30084 Insert\SpecialChar \menuseparator
\r
30087 or the toolbar button
\r
30088 \begin_inset Graphics
\r
30089 filename ../images/label-insert.png
\r
30095 The cursor must hereby be inside a displayed formula.
\r
30096 Alternatively you can right-click on the formula and choose
\r
30101 A dialog pops up displaying the prefix
\r
30106 The label is inserted there behind the prefix.
\r
30107 The predefined prefix means
\r
30108 \begin_inset Quotes eld
\r
30112 \begin_inset Quotes erd
\r
30115 and makes it easier to find labels in large documents because it marks
\r
30116 it as formula label to divide it from e.
\r
30117 \begin_inset space \thinspace{}
\r
30121 \begin_inset space \space{}
\r
30125 To change a label, the menu
\r
30127 Insert\SpecialChar \menuseparator
\r
30130 is used again or you right-click on a formula and then on
\r
30137 \begin_layout Standard
\r
30138 The name of the label is displayed in LyX within two parentheses behind
\r
30140 A formula with a label is always numbered.
\r
30143 \begin_layout Standard
\r
30144 Cross-references are inserted via the menu
\r
30146 Insert\SpecialChar \menuseparator
\r
30149 or with the toolbar button
\r
30150 \begin_inset Graphics
\r
30151 filename ../images/dialog-show-new-inset_ref.png
\r
30157 A formula cross-reference appears in the output as formula number.
\r
30158 When in the cross-reference dialog window the format
\r
30162 is chosen, the cross-reference appears in the output as formula number
\r
30164 \begin_inset Newline newline
\r
30167 By right-clicking on a cross-reference in LyX, one jumps to the formula
\r
30168 that is referenced.
\r
30171 \begin_layout Standard
\r
30172 Here are as examples cross-references to formulas of the following subsections:
\r
30173 \begin_inset Note Note
\r
30176 \begin_layout Plain Layout
\r
30177 Note the different cross-reference types.
\r
30185 \begin_layout Standard
\r
30187 \begin_inset CommandInset ref
\r
30188 LatexCommand eqref
\r
30189 reference "eq:tag"
\r
30194 \begin_inset CommandInset ref
\r
30195 LatexCommand eqref
\r
30202 \begin_inset CommandInset ref
\r
30204 reference "eq:Lat"
\r
30208 ) big Latin letters are used for the numbering in contrary to (
\r
30209 \begin_inset CommandInset ref
\r
30211 reference "eq:Rom"
\r
30218 \begin_layout Standard
\r
30219 \begin_inset VSpace medskip
\r
30222 When the argument of
\r
30227 \begin_inset Foot
\r
30230 \begin_layout Plain Layout
\r
30238 \begin_inset CommandInset ref
\r
30240 reference "sub:User-defined-Numbering"
\r
30251 contains a box like in
\r
30252 \begin_inset CommandInset ref
\r
30254 reference "sub:Paragraph-Boxes"
\r
30258 , the formula cannot be referenced.
\r
30261 \begin_layout Subsection
\r
30263 \begin_inset Index idx
\r
30266 \begin_layout Plain Layout
\r
30267 Formula numbering ! subnumbering
\r
30275 \begin_layout Standard
\r
30276 With the help of the commands
\r
30280 begin{subequations}
\r
30286 end{subequations}
\r
30288 formulas can be subnumbered.
\r
30289 Both commands are inserted in TeX-mode.
\r
30292 \begin_layout Standard
\r
30294 \begin_inset Formula
\r
30296 A=C-B\label{eq:a}
\r
30305 \begin_layout Plain Layout
\r
30309 addtocounter{equation}{-1}
\r
30318 \begin_layout Plain Layout
\r
30322 begin{subequations}
\r
30328 \begin_inset VSpace -5mm
\r
30332 \begin_inset Formula
\r
30334 B=C-A\label{eq:b}
\r
30340 \begin_inset Formula
\r
30342 C=A+B\label{eq:c}
\r
30350 \begin_layout Standard
\r
30354 \begin_layout Plain Layout
\r
30358 end{subequations}
\r
30366 \begin_layout Standard
\r
30367 To create the example, the following is done:
\r
30370 \begin_layout Enumerate
\r
30371 first formula is inserted
\r
30374 \begin_layout Enumerate
\r
30379 addtocounter{equation}{-1}
\r
30381 begin{subequations}
\r
30382 \begin_inset Index idx
\r
30385 \begin_layout Plain Layout
\r
30394 \begin_inset Newline newline
\r
30399 is inserted after the first formula
\r
30402 \begin_layout Enumerate
\r
30403 second formula is inserted
\r
30406 \begin_layout Enumerate
\r
30407 third formula is inserted
\r
30410 \begin_layout Enumerate
\r
30415 end{subequations}
\r
30417 is inserted after the third formula
\r
30420 \begin_layout Standard
\r
30421 Every formula between the commands
\r
30433 is subnumbered as a, b,
\r
30434 \begin_inset Newline linebreak
\r
30437 c, \SpecialChar \ldots{}
\r
30438 For multiline formulas every line will be subnumbered.
\r
30439 All subnumbered formulas are treated as
\r
30443 numbered formula.
\r
30444 But as every numbered formula increases the counter
\r
30448 by one, the command
\r
30454 is needed to decrease it.
\r
30455 Otherwise the formulas
\r
30456 \begin_inset CommandInset ref
\r
30457 LatexCommand eqref
\r
30463 \begin_inset CommandInset ref
\r
30464 LatexCommand eqref
\r
30470 \begin_inset CommandInset ref
\r
30471 LatexCommand eqref
\r
30476 would be numbered as
\r
30477 \begin_inset CommandInset ref
\r
30478 LatexCommand eqref
\r
30484 \begin_inset CommandInset ref
\r
30485 LatexCommand eqref
\r
30491 \begin_inset CommandInset ref
\r
30492 LatexCommand eqref
\r
30500 \begin_layout Standard
\r
30501 By inserting the commands in TeX-mode, a space is created between the first
\r
30503 To revert this -5
\r
30504 \begin_inset space \thinspace{}
\r
30507 mm vertical space is inserted after the command
\r
30511 begin{subequations}
\r
30514 When the formula style
\r
30517 \begin_inset Foot
\r
30520 \begin_layout Plain Layout
\r
30521 formula styles see
\r
30522 \begin_inset CommandInset ref
\r
30524 reference "sec:Formula-Styles"
\r
30536 \begin_inset space \thinspace{}
\r
30539 mm space is inserted instead.
\r
30542 \begin_layout Standard
\r
30543 Here is an example for a multiline formula where the numbering was turned
\r
30544 off for the second line:
\r
30548 \begin_layout Plain Layout
\r
30552 begin{subequations}
\r
30558 \begin_inset Formula
\r
30560 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
\r
30561 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
\r
30562 & = & B^{2}-2BZ+Z^{2}\label{eq:f}
\r
30571 \begin_layout Plain Layout
\r
30575 end{subequations}
\r
30583 \begin_layout Subsection
\r
30584 User-defined Numbering
\r
30585 \begin_inset CommandInset label
\r
30586 LatexCommand label
\r
30587 name "sub:User-defined-Numbering"
\r
30592 \begin_inset Index idx
\r
30595 \begin_layout Plain Layout
\r
30596 Formula numbering ! user-defined
\r
30604 \begin_layout Standard
\r
30605 \begin_inset Index idx
\r
30608 \begin_layout Plain Layout
\r
30609 Formula numbering ! self-defined delimiters
\r
30614 With the standard numbering parentheses are set around the formula number.
\r
30615 To replace the parentheses for example by vertical bars, the following
\r
30616 line is added to the LaTeX-preamble:
\r
30619 \begin_layout Standard
\r
30628 maketag@@@{|#1|}}
\r
30631 \begin_inset Note Note
\r
30634 \begin_layout Plain Layout
\r
30635 This macro is already declared in the LaTeX-preamble for testing.
\r
30636 To activate it, remove the percent sign at the beginning.
\r
30644 \begin_layout Standard
\r
30645 To use other characters, the vertical bars besides the
\r
30649 are replaced by one ore more characters.
\r
30650 To get only the formula number the vertical bars are omitted.
\r
30653 \begin_layout Standard
\r
30654 \begin_inset VSpace bigskip
\r
30657 When there should be an expression of your choice instead of the consecutive
\r
30658 formula number in parentheses behind the formula, the command
\r
30665 \begin_inset Index idx
\r
30668 \begin_layout Plain Layout
\r
30677 \begin_inset Formula
\r
30679 A+B=C\tag{something}\label{eq:tag}
\r
30684 In this example the command
\r
30692 \begin_layout Plain Layout
\r
30703 was inserted in the formula.
\r
30706 \begin_layout Standard
\r
30707 When the command
\r
30715 \begin_layout Plain Layout
\r
30726 is inserted instead, the star prevents the parentheses around the expression:
\r
30727 \begin_inset Formula
\r
30729 A+B=C\tag*{something}
\r
30737 \begin_layout Standard
\r
30738 \begin_inset VSpace bigskip
\r
30741 To restart the formula numbering with new document parts or sections, the
\r
30742 following command is used:
\r
30745 \begin_layout Standard
\r
30750 @addtoreset{equation}{part}
\r
30753 \begin_inset Index idx
\r
30756 \begin_layout Plain Layout
\r
30761 \begin_layout Plain Layout
\r
30772 \begin_layout Plain Layout
\r
30785 \begin_layout Plain Layout
\r
30796 \begin_layout Plain Layout
\r
30809 \begin_inset Newline newline
\r
30813 \begin_inset Newline newline
\r
30820 @addtoreset{equation}{section}
\r
30823 \begin_layout Standard
\r
30824 To be able to use these commands in TeX-mode, the
\r
30825 \begin_inset Quotes eld
\r
30829 \begin_inset Quotes erd
\r
30832 character has to be made
\r
30833 \begin_inset Quotes eld
\r
30837 \begin_inset Quotes erd
\r
30840 for LaTeX using the command
\r
30854 So the command sequence in TeX-mode is:
\r
30857 \begin_layout Standard
\r
30863 \begin_inset Newline newline
\r
30868 @addtoreset{equation}{section}
\r
30869 \begin_inset Newline newline
\r
30877 \begin_layout Standard
\r
30878 In the LaTeX-preamble
\r
30890 can be omitted as they are automatically internally inserted by LyX.
\r
30893 \begin_layout Standard
\r
30905 \begin_inset Foot
\r
30908 \begin_layout Plain Layout
\r
30913 is part of the LaTeX-package
\r
30918 \begin_inset Index idx
\r
30921 \begin_layout Plain Layout
\r
30922 Packages ! carlisle
\r
30927 that is part of every LaTeX standard installation.
\r
30933 \begin_inset Index idx
\r
30936 \begin_layout Plain Layout
\r
30937 Packages ! remreset
\r
30942 has to be loaded in the LaTeX-preamble with the line
\r
30945 \begin_layout Standard
\r
30950 usepackage{remreset}
\r
30953 \begin_layout Standard
\r
30954 Then the command
\r
30961 \begin_inset Index idx
\r
30964 \begin_layout Plain Layout
\r
30969 \begin_layout Plain Layout
\r
30980 \begin_layout Plain Layout
\r
30993 \begin_layout Plain Layout
\r
31004 \begin_layout Plain Layout
\r
31016 can be used with the same scheme as
\r
31025 \begin_layout Standard
\r
31026 \begin_inset VSpace bigskip
\r
31029 Sometimes formulas should be numbered in the following form:
\r
31032 \begin_layout Standard
\r
31034 \family typewriter
\r
31035 (section number.formula number)
\r
31038 \begin_layout Standard
\r
31039 The formula number should start with every section with
\r
31040 \begin_inset Quotes eld
\r
31044 \begin_inset Quotes erd
\r
31050 \begin_layout Standard
\r
31051 For this case there is the command
\r
31058 \begin_inset Index idx
\r
31061 \begin_layout Plain Layout
\r
31069 , which is used with the following scheme:
\r
31072 \begin_layout Standard
\r
31077 numberwithin{counter}{sectioning}
\r
31080 \begin_layout Standard
\r
31081 Counter denotes what kind of numbering is affected, sectioning denotes what
\r
31082 number is before the dot.
\r
31085 \begin_layout Standard
\r
31086 Thus in our case the following LaTeX-preamble or TeX code line is used:
\r
31089 \begin_layout Standard
\r
31094 numberwithin{equation}{section}
\r
31097 \begin_layout Standard
\r
31098 This is the result:
\r
31102 \begin_layout Plain Layout
\r
31106 numberwithin{equation}{section}
\r
31112 \begin_inset Formula
\r
31122 \begin_layout Standard
\r
31124 \begin_inset space \thinspace{}
\r
31128 \begin_inset space \space{}
\r
31131 tables so that the number of the part is the sectioning,
\r
31132 \begin_inset Newline newline
\r
31139 numberwithin{table}{part}
\r
31144 \begin_layout Standard
\r
31145 To go back to the standard numbering or to prevent this kind of numbering
\r
31146 when it is defined by the document class, the following command is inserted
\r
31147 as TeX code or to the LaTeX-preamble:
\r
31150 \begin_layout Standard
\r
31159 arabic{equation}}
\r
31160 \begin_inset Index idx
\r
31163 \begin_layout Plain Layout
\r
31177 \begin_layout Plain Layout
\r
31185 arabic{equation}}
\r
31193 \begin_inset Newline newline
\r
31201 \begin_inset Newline newline
\r
31213 \begin_layout Standard
\r
31220 uses internally the command
\r
31226 , described above, that also needs to be reverted.
\r
31230 \begin_layout Plain Layout
\r
31237 \begin_layout Plain Layout
\r
31241 @removefromreset{equation}{section}
\r
31244 \begin_layout Plain Layout
\r
31256 \begin_layout Subsection
\r
31257 Numbering with Roman Numbers and Letters
\r
31258 \begin_inset Index idx
\r
31261 \begin_layout Plain Layout
\r
31262 Formula numbering ! with letters
\r
31268 \begin_inset Index idx
\r
31271 \begin_layout Plain Layout
\r
31272 Formula numbering ! with Roman numbers
\r
31280 \begin_layout Standard
\r
31281 Formulas can also be numbered with Roman numbers and Latin letters.
\r
31282 To number for example with small Roman numbers, the command
\r
31285 \begin_layout Standard
\r
31297 \begin_layout Standard
\r
31298 is inserted before the formula in TeX-mode.
\r
31306 \begin_inset Index idx
\r
31309 \begin_layout Plain Layout
\r
31317 redefines the predefined command
\r
31330 \begin_inset Foot
\r
31333 \begin_layout Plain Layout
\r
31340 has the same scheme like the command
\r
31346 that is described in
\r
31347 \begin_inset CommandInset ref
\r
31349 reference "sub:The-Command-newcommand"
\r
31362 is the formula counter.
\r
31363 When the command
\r
31369 is used as prefix for a counter, the value of the counter is output as
\r
31371 When a formula is numbered, LaTeX sets internally the command
\r
31377 behind the formula.
\r
31383 \begin_inset Index idx
\r
31386 \begin_layout Plain Layout
\r
31396 outputs the counter as small Roman number.
\r
31399 \begin_layout Standard
\r
31400 All formulas behind the command
\r
31410 are now numbered Roman.
\r
31411 To switch to numbering with big Roman numbers, the command is inserted
\r
31425 \begin_inset Index idx
\r
31428 \begin_layout Plain Layout
\r
31440 \begin_inset Quotes eld
\r
31444 \begin_inset Quotes erd
\r
31447 with small Latin letters there is the command
\r
31454 \begin_inset Index idx
\r
31457 \begin_layout Plain Layout
\r
31465 , for big ones there is the command
\r
31472 \begin_inset Index idx
\r
31475 \begin_layout Plain Layout
\r
31488 \begin_layout Standard
\r
31489 \begin_inset Note Greyedout
\r
31492 \begin_layout Plain Layout
\r
31499 \begin_inset space ~
\r
31502 formulas can be numbered with Latin letters in one document.
\r
31510 \begin_layout Standard
\r
31514 \begin_layout Plain Layout
\r
31530 \begin_layout Standard
\r
31531 \begin_inset Formula
\r
31533 A=\textrm{small roman}
\r
31542 \begin_layout Plain Layout
\r
31556 \begin_inset Formula
\r
31558 B=\textrm{big Roman}\label{eq:Rom}
\r
31567 \begin_layout Plain Layout
\r
31581 \begin_inset Formula
\r
31583 C=\textrm{small Latin}
\r
31592 \begin_layout Plain Layout
\r
31606 \begin_inset Formula
\r
31608 D=\textrm{big Latin}\label{eq:Lat}
\r
31616 \begin_layout Standard
\r
31617 To switch back to the default numbering, insert the command:
\r
31620 \begin_layout Standard
\r
31629 arabic{equation}}
\r
31630 \begin_inset Index idx
\r
31633 \begin_layout Plain Layout
\r
31644 \begin_layout Standard
\r
31648 \begin_layout Plain Layout
\r
31656 arabic{equation}}
\r
31662 \begin_inset Formula
\r
31664 E=\textrm{Arabic}
\r
31672 \begin_layout Standard
\r
31673 \begin_inset VSpace medskip
\r
31676 As you see, formulas are numbered serially independent from the numbering
\r
31678 When then numbering should start with
\r
31679 \begin_inset Quotes eld
\r
31683 \begin_inset Quotes erd
\r
31686 when the style is changed, new equation counters have to be defined.
\r
31687 A description about this can be found in the file
\r
31688 \begin_inset CommandInset href
\r
31689 LatexCommand href
\r
31690 name "Formula-numbering.lyx"
\r
31691 target "run:Formula-numbering.lyx"
\r
31698 \begin_layout Standard
\r
31699 \begin_inset Newpage newpage
\r
31705 \begin_layout Section
\r
31706 Chemical Symbols and Equations
\r
31707 \begin_inset CommandInset label
\r
31708 LatexCommand label
\r
31709 name "sub:Chemical-Symbols-and"
\r
31714 \begin_inset Index idx
\r
31717 \begin_layout Plain Layout
\r
31718 Chemical characters ! Symbols
\r
31724 \begin_inset Index idx
\r
31727 \begin_layout Plain Layout
\r
31728 Chemical equations
\r
31734 \begin_inset Index idx
\r
31737 \begin_layout Plain Layout
\r
31738 Symbols ! chemical
\r
31746 \begin_layout Standard
\r
31747 An example text from chemistry:
\r
31750 \begin_layout Quote
\r
31752 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
\r
31755 -ion reacts with two
\r
31756 \begin_inset Formula $\mathrm{Na^{+}}$
\r
31759 -ions to sodium sulfate
\r
31760 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
\r
31764 The chemical equation for this is:
\r
31765 \begin_inset Formula
\r
31767 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
\r
31775 \begin_layout Standard
\r
31776 This chemical equation can directly be created as formula.
\r
31777 To avoid that the symbols appear italic, everything is highlighted and
\r
31778 changed by the shortcut
\r
31779 \begin_inset Info
\r
31784 to the upright font style.
\r
31785 \begin_inset Foot
\r
31788 \begin_layout Plain Layout
\r
31794 \begin_inset CommandInset ref
\r
31796 reference "sub:Font-Styles"
\r
31808 \begin_layout Standard
\r
31809 A more convenient way to typeset chemical formulas is to use the command
\r
31817 \begin_inset Index idx
\r
31820 \begin_layout Plain Layout
\r
31828 that is available when the LaTeX-package
\r
31833 \begin_inset Index idx
\r
31836 \begin_layout Plain Layout
\r
31837 Packages ! mhchem
\r
31849 to a formula a new blue box appears where chemical formulas can be inserted
\r
31850 in an intuitive way.
\r
31853 \begin_layout Standard
\r
31855 \begin_inset Tabular
\r
31856 <lyxtabular version="3" rows="9" columns="2">
\r
31857 <features tabularvalignment="middle">
\r
31858 <column alignment="center" valignment="top" width="0">
\r
31859 <column alignment="center" valignment="top" width="0">
\r
31861 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
31862 \begin_inset Text
\r
31864 \begin_layout Plain Layout
\r
31870 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
31871 \begin_inset Text
\r
31873 \begin_layout Plain Layout
\r
31875 \begin_inset Note Note
\r
31878 \begin_layout Plain Layout
\r
31885 is only used as spacer.
\r
31897 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
31898 \begin_inset Text
\r
31900 \begin_layout Plain Layout
\r
31907 \begin_layout Plain Layout
\r
31921 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
31922 \begin_inset Text
\r
31924 \begin_layout Plain Layout
\r
31925 \begin_inset Formula $\raisebox{4.5mm}{}\ce{H2CO3}\raisebox{-2mm}{}$
\r
31935 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
31936 \begin_inset Text
\r
31938 \begin_layout Plain Layout
\r
31945 \begin_layout Plain Layout
\r
31959 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
31960 \begin_inset Text
\r
31962 \begin_layout Plain Layout
\r
31963 \begin_inset Formula $\raisebox{5mm}{}\ce{SO4^{2-}}\raisebox{-2mm}{}$
\r
31973 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
31974 \begin_inset Text
\r
31976 \begin_layout Plain Layout
\r
31983 \begin_layout Plain Layout
\r
31997 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
31998 \begin_inset Text
\r
32000 \begin_layout Plain Layout
\r
32001 \begin_inset Formula $\raisebox{4.5mm}{}\ce{(NH4)2S}\raisebox{-2mm}{}$
\r
32011 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
32012 \begin_inset Text
\r
32014 \begin_layout Plain Layout
\r
32021 \begin_layout Plain Layout
\r
32035 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
32036 \begin_inset Text
\r
32038 \begin_layout Plain Layout
\r
32039 \begin_inset Formula $\raisebox{4.5mm}{}\ce{KCr(SO4)2.12H2O}\raisebox{-2mm}{}$
\r
32049 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
32050 \begin_inset Text
\r
32052 \begin_layout Plain Layout
\r
32059 \begin_layout Plain Layout
\r
32074 \begin_layout Plain Layout
\r
32089 \begin_layout Plain Layout
\r
32103 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
32104 \begin_inset Text
\r
32106 \begin_layout Plain Layout
\r
32107 \begin_inset Formula $\raisebox{4.5mm}{}\ce{A-B\dbond C\tbond D}\raisebox{-2mm}{}$
\r
32117 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
32118 \begin_inset Text
\r
32120 \begin_layout Plain Layout
\r
32127 \begin_layout Plain Layout
\r
32137 \begin_inset Formula $\downarrow$
\r
32141 \begin_inset Formula $\to$
\r
32149 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
32150 \begin_inset Text
\r
32152 \begin_layout Plain Layout
\r
32153 \begin_inset Formula $\raisebox{5mm}{}\ce{_{90}^{227}Th+}\raisebox{-2mm}{}$
\r
32163 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
32164 \begin_inset Text
\r
32166 \begin_layout Plain Layout
\r
32173 \begin_layout Plain Layout
\r
32186 \begin_layout Plain Layout
\r
32199 \begin_layout Plain Layout
\r
32212 \begin_layout Plain Layout
\r
32225 \begin_layout Plain Layout
\r
32239 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
32240 \begin_inset Text
\r
32242 \begin_layout Plain Layout
\r
32243 \begin_inset Formula $\raisebox{4.5mm}{}\ce{CO2 + C <=> 2CO}\raisebox{-2mm}{}$
\r
32253 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
32254 \begin_inset Text
\r
32256 \begin_layout Plain Layout
\r
32263 \begin_layout Plain Layout
\r
32276 \begin_layout Plain Layout
\r
32289 \begin_layout Plain Layout
\r
32302 \begin_layout Plain Layout
\r
32319 \begin_layout Plain Layout
\r
32333 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
32334 \begin_inset Text
\r
32336 \begin_layout Plain Layout
\r
32337 \begin_inset Formula $\raisebox{5mm}{}\ce{CO2 + C ->[\alpha][\beta] 2CO}\raisebox{-4mm}{}$
\r
32353 \begin_layout Standard
\r
32354 \begin_inset Note Greyedout
\r
32357 \begin_layout Plain Layout
\r
32363 Inserting a formula to a
\r
32369 box will lead to LaTeX errors due to a LyX bug.
\r
32372 \begin_inset Foot
\r
32375 \begin_layout Plain Layout
\r
32376 \begin_inset CommandInset href
\r
32377 LatexCommand href
\r
32378 name "LyX-bug #8566"
\r
32379 target "http://www.lyx.org/trac/ticket/8566"
\r
32390 In this case TeX code has to be used like for
\r
32404 \begin_layout Plain Layout
\r
32425 \begin_layout Standard
\r
32426 \begin_inset Note Greyedout
\r
32429 \begin_layout Plain Layout
\r
32435 It is not possible in LyX to use the character ^ to get an up-arrow as
\r
32436 described in the
\r
32441 One instead uses a negative thin space followed by the command
\r
32448 \begin_inset Formula $\ce{Fe + 2H+ -> Fe^{2+} + H2\negthinspace\uparrow}$
\r
32459 \begin_layout Standard
\r
32466 the command for equation
\r
32467 \begin_inset space ~
\r
32471 \begin_inset CommandInset ref
\r
32472 LatexCommand eqref
\r
32473 reference "eq:chem-reaction"
\r
32478 \begin_inset Newline newline
\r
32489 \begin_layout Plain Layout
\r
32502 \begin_layout Plain Layout
\r
32515 \begin_layout Plain Layout
\r
32528 \begin_layout Plain Layout
\r
32541 \begin_layout Plain Layout
\r
32554 \begin_layout Plain Layout
\r
32566 \begin_layout Standard
\r
32567 To create multiline chemical equations first a multiline formula is created
\r
32569 \begin_inset CommandInset ref
\r
32571 reference "sec:Multiline-Formulas"
\r
32576 Afterwards the command
\r
32582 is used in every small blue box of the formula.
\r
32584 \begin_inset CommandInset ref
\r
32585 LatexCommand eqref
\r
32586 reference "eq:TEOS-reaction-1"
\r
32591 \begin_inset CommandInset ref
\r
32592 LatexCommand eqref
\r
32593 reference "eq:TEOS-reaction-2"
\r
32597 are an example of a multi-stage chemical reaction where every equation
\r
32598 has its own number.
\r
32599 \begin_inset Formula
\r
32601 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
\r
32602 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
\r
32610 \begin_layout Standard
\r
32621 package provides the command
\r
32628 \begin_inset Index idx
\r
32631 \begin_layout Plain Layout
\r
32639 that has to be used for special cases.
\r
32640 For more information about
\r
32646 and more examples have a look at the documentation of
\r
32651 \begin_inset CommandInset citation
\r
32652 LatexCommand cite
\r
32660 \begin_layout Section
\r
32664 \begin_layout Standard
\r
32665 LyX supports two types of commutative diagrams:
\r
32673 that are explained in the following.
\r
32676 \begin_layout Subsection
\r
32678 \begin_inset Index idx
\r
32681 \begin_layout Plain Layout
\r
32690 \begin_layout Standard
\r
32691 Diagrams of this type visualize relations by vertical and horizontal lines
\r
32693 \begin_inset Formula
\r
32695 \begin{CD}A@>>>B@>>>C\\
\r
32706 \begin_layout Standard
\r
32707 To get them, the command
\r
32712 \begin_inset Index idx
\r
32715 \begin_layout Plain Layout
\r
32725 is inserted to a formula.
\r
32726 A blue box appears with two dashed lines where further commands can be
\r
32729 \begin_inset Info
\r
32731 arg "newline-insert newline"
\r
32734 a new line is created.
\r
32735 Horizontal relations are inserted in odd, vertical in even formula lines.
\r
32738 \begin_layout Standard
\r
32739 To create the relations there are the following commands:
\r
32742 \begin_layout Itemize
\r
32747 creates a left arrow,
\r
32751 a right arrow and
\r
32755 a long equal sign
\r
32758 \begin_layout Itemize
\r
32763 creates an up arrow,
\r
32767 a down arrow and
\r
32771 a vertical equal sign
\r
32774 \begin_layout Itemize
\r
32780 is a placeholder for non-existent relations
\r
32783 \begin_layout Standard
\r
32784 All arrows can be labeled as follows:
\r
32787 \begin_layout Itemize
\r
32788 If text inserted between the first and second < or >, resp., it is placed
\r
32790 When it is inserted between the second and third one, it appears under
\r
32794 \begin_layout Itemize
\r
32795 When text for vertical arrows is inserted between the first and second A
\r
32796 or V, resp., it is placed left beside the arrow.
\r
32797 When it is inserted between the second and third one, it appears right
\r
32798 beside the arrow.
\r
32799 If the text contains an A or V, these letters must be set into a TeX-brace.
\r
32802 \begin_layout Standard
\r
32803 As example a diagram with all possible relations:
\r
32806 \begin_layout Standard
\r
32807 \begin_inset Formula
\r
32809 \begin{CD}A@>j>>B@>>k>C@=F\\
\r
32810 @AmAA@.@VV{V}V@|\\
\r
32820 \begin_layout Standard
\r
32821 The command for this is:
\r
32822 \begin_inset Newline newline
\r
32833 \begin_layout Plain Layout
\r
32842 A@>j>>B@>>k>C@=F Ctrl+Return
\r
32843 \begin_inset Newline newline
\r
32847 \begin_inset Phantom HPhantom
\r
32850 \begin_layout Plain Layout
\r
32859 \begin_layout Plain Layout
\r
32878 \begin_inset Formula $\to$
\r
32884 \begin_inset Newline newline
\r
32888 \begin_inset Phantom HPhantom
\r
32891 \begin_layout Plain Layout
\r
32900 \begin_layout Plain Layout
\r
32917 \begin_layout Subsection
\r
32918 Xymatrix Diagrams
\r
32919 \begin_inset Index idx
\r
32922 \begin_layout Plain Layout
\r
32923 Diagrams ! xymatrix
\r
32931 \begin_layout Standard
\r
32932 To be able to use xymatrices, the LaTeX-package
\r
32936 must be installed.
\r
32937 A xymatrix is created by inserting the command
\r
32944 Then you are able to add new matrix columns and rows like for normal matrices,
\r
32946 \begin_inset CommandInset ref
\r
32948 reference "sec:Matrices"
\r
32955 \begin_layout Standard
\r
32956 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
\r
32958 All possibilities to create commutative diagrams and decorations are explained
\r
32959 in detail in the
\r
32963 that you find in the menu
\r
32965 Help\SpecialChar \menuseparator
\r
32967 \begin_inset space ~
\r
32975 \begin_layout Subsection
\r
32981 \begin_inset Index idx
\r
32984 \begin_layout Plain Layout
\r
32985 Diagrams ! Feynman
\r
32993 \begin_layout Standard
\r
32994 To be able to use
\r
32998 -diagrams, the LaTeX-package
\r
33002 must be installed.
\r
33007 -diagram is created by inserting the command
\r
33014 Then you are able to add new matrix columns and rows like for normal matrices,
\r
33016 \begin_inset CommandInset ref
\r
33018 reference "sec:Matrices"
\r
33025 \begin_layout Standard
\r
33026 Examples how to create
\r
33030 diagrams in LyX is given in the
\r
33032 Feynman-diagram manual
\r
33034 that you find in the menu
\r
33036 Help\SpecialChar \menuseparator
\r
33038 \begin_inset space ~
\r
33046 \begin_layout Standard
\r
33047 \begin_inset Newpage newpage
\r
33053 \begin_layout Section
\r
33054 User-defined Commands
\r
33055 \begin_inset Index idx
\r
33058 \begin_layout Plain Layout
\r
33059 User-defined commands
\r
33067 \begin_layout Standard
\r
33068 \begin_inset Note Greyedout
\r
33071 \begin_layout Plain Layout
\r
33076 The names of user-defined commands and macros may only consist of Latin
\r
33085 \begin_layout Subsection
\r
33089 \begin_inset CommandInset label
\r
33090 LatexCommand label
\r
33091 name "sub:The-Command-newcommand"
\r
33096 \begin_inset Index idx
\r
33099 \begin_layout Plain Layout
\r
33100 User-defined commands !
\r
33108 \begin_inset Index idx
\r
33111 \begin_layout Plain Layout
\r
33122 \begin_layout Standard
\r
33123 Many LaTeX-commands are too long to be used frequently.
\r
33124 But it is possible to define with the command
\r
33130 new shorter commands.
\r
33133 \begin_layout Standard
\r
33134 The command scheme of
\r
33143 \begin_layout Standard
\r
33148 newcommand{new command name}[number of arguments][optional
\r
33153 \begin_inset Newline newline
\r
33157 \begin_inset Phantom HPhantom
\r
33160 \begin_layout Plain Layout
\r
33170 {command definition}
\r
33173 \begin_layout Standard
\r
33174 \begin_inset Note Greyedout
\r
33177 \begin_layout Plain Layout
\r
33182 Assure that the name of the new command is not already used in your document
\r
33183 or by LaTeX-packages that you use.
\r
33184 When you for example define the command
\r
33196 , you get an error message because
\r
33202 is already defined as command for
\r
33203 \begin_inset Quotes eld
\r
33207 \begin_inset Formula $\le$
\r
33211 \begin_inset Quotes erd
\r
33222 \begin_layout Standard
\r
33223 The number of arguments is an integer in the range 0
\r
33224 \begin_inset space \thinspace{}
\r
33228 \begin_inset space \thinspace{}
\r
33231 9 and specifies how many arguments the new command should have.
\r
33232 With the optional value a value for an optional argument can be predefined.
\r
33233 When this is done, the
\r
33241 rgument of the new command is automatically an optional one.
\r
33244 \begin_layout Standard
\r
33245 Here are some examples:
\r
33248 \begin_layout Itemize
\r
33249 To define the command
\r
33261 , the LaTeX-preamble line is:
\r
33262 \begin_inset VSpace medskip
\r
33266 \begin_inset Newline newline
\r
33280 \begin_layout Itemize
\r
33281 To define the command
\r
33293 , the argument (that should be underlined) must be taken into account.
\r
33294 For this the preamble line is:
\r
33295 \begin_inset VSpace medskip
\r
33299 \begin_inset Newline newline
\r
33313 \begin_inset VSpace medskip
\r
33317 \begin_inset Newline newline
\r
33324 acts as argument placeholder, the
\r
33328 behind it denotes that it is the placeholder for the first argument.
\r
33331 \begin_layout Itemize
\r
33339 \begin_inset space \thinspace{}
\r
33343 \begin_inset space \space{}
\r
33346 define the command
\r
33353 \begin_inset VSpace medskip
\r
33357 \begin_inset Newline newline
\r
33368 framebox#1#2{$#3$}}
\r
33371 \begin_inset VSpace medskip
\r
33375 \begin_inset Newline newline
\r
33378 The two Dollar signs creates the extra formula needed for
\r
33385 \begin_inset CommandInset ref
\r
33387 reference "sub:Boxes-with-Frame"
\r
33394 \begin_layout Itemize
\r
33395 To create a new command for
\r
33401 where the color for the box need not be specified, the argument for the
\r
33402 color is defined optional:
\r
33403 \begin_inset VSpace medskip
\r
33407 \begin_inset Newline newline
\r
33418 fcolorbox{#2}{#1}{$#3$}}
\r
33421 \begin_inset VSpace medskip
\r
33425 \begin_inset Newline newline
\r
33428 When the color is not specified when using
\r
33434 , the predefined color
\r
33441 \begin_layout Standard
\r
33442 A test of the new defined commands:
\r
33445 \begin_layout Standard
\r
33447 \begin_inset Tabular
\r
33448 <lyxtabular version="3" rows="6" columns="2">
\r
33449 <features tabularvalignment="middle">
\r
33450 <column alignment="center" valignment="top" width="0">
\r
33451 <column alignment="center" valignment="top" width="0">
\r
33453 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
33454 \begin_inset Text
\r
33456 \begin_layout Plain Layout
\r
33462 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
33463 \begin_inset Text
\r
33465 \begin_layout Plain Layout
\r
33467 \begin_inset Note Note
\r
33470 \begin_layout Plain Layout
\r
33477 is only used as spacer.
\r
33489 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
33490 \begin_inset Text
\r
33492 \begin_layout Plain Layout
\r
33499 \begin_layout Plain Layout
\r
33513 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
33514 \begin_inset Text
\r
33516 \begin_layout Plain Layout
\r
33517 \begin_inset Formula $A\gr B$
\r
33527 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
33528 \begin_inset Text
\r
33530 \begin_layout Plain Layout
\r
33538 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
33539 \begin_inset Text
\r
33541 \begin_layout Plain Layout
\r
33542 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
\r
33552 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
33553 \begin_inset Text
\r
33555 \begin_layout Plain Layout
\r
33559 \begin_inset Formula $\to$
\r
33565 \begin_inset Formula $\to$
\r
33576 \begin_layout Plain Layout
\r
33590 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
33591 \begin_inset Text
\r
33593 \begin_layout Plain Layout
\r
33594 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
\r
33604 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
33605 \begin_inset Text
\r
33607 \begin_layout Plain Layout
\r
33611 \begin_inset Formula $\to$
\r
33622 \begin_layout Plain Layout
\r
33636 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
33637 \begin_inset Text
\r
33639 \begin_layout Plain Layout
\r
33640 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
\r
33650 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
33651 \begin_inset Text
\r
33653 \begin_layout Plain Layout
\r
33659 \begin_inset Formula $\to$
\r
33670 \begin_layout Plain Layout
\r
33684 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
33685 \begin_inset Text
\r
33687 \begin_layout Plain Layout
\r
33688 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
\r
33704 \begin_layout Subsection
\r
33706 \begin_inset Index idx
\r
33709 \begin_layout Plain Layout
\r
33710 User-defined commands! Math macros
\r
33716 \begin_inset Index idx
\r
33719 \begin_layout Plain Layout
\r
33728 \begin_layout Standard
\r
33729 User-defined commands are especially convenient for complex expressions.
\r
33730 When you are for example dealing with a document that has quadratic equations,
\r
33731 the same solution type occurs several times.
\r
33732 The general form of a quadratic equation is
\r
33733 \begin_inset Formula
\r
33735 0=\lambda^{2}+p\lambda+q
\r
33740 The general form of the solution is
\r
33741 \begin_inset Formula
\r
33743 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
\r
33751 \begin_layout Standard
\r
33752 To define a command for the solution formula where only the three parameters
\r
33754 \begin_inset Formula $\lambda$
\r
33758 \begin_inset Formula $p$
\r
33762 \begin_inset Formula $q$
\r
33765 need to be specified and the index of
\r
33766 \begin_inset Formula $\lambda$
\r
33769 can be given optionally, the LaTeX-preamble line is
\r
33770 \begin_inset Newline newline
\r
33786 \begin_inset Newline newline
\r
33790 \begin_inset Phantom HPhantom
\r
33793 \begin_layout Plain Layout
\r
33807 frac{#3^{2}}{4}-#4}}
\r
33810 \begin_layout Standard
\r
33811 To create with this the solution formula, the command
\r
33812 \begin_inset Newline newline
\r
33822 \begin_inset Formula $\to$
\r
33828 \begin_inset Formula $\to$
\r
33835 is inserted to a formula
\r
33840 \begin_layout Standard
\r
33841 The definition of the new command is unintuitive because one has to know
\r
33842 the schemes of all used LaTeX commands, e.
\r
33843 \begin_inset space \thinspace{}
\r
33847 \begin_inset space \space{}
\r
33850 that a fraction is inserted in LaTeX as
\r
33854 frac{numerator}{denominator}
\r
33857 Furthermore one can easily forget a brace in the definition and cannot
\r
33858 see in LyX what the new command is doing.
\r
33859 To avoid these problems LyX offers the possibility to use math macros instead
\r
33869 \begin_layout Standard
\r
33870 A math macro is created by using the menu
\r
33872 Insert\SpecialChar \menuseparator
\r
33873 Math\SpecialChar \menuseparator
\r
33876 or the toolbar button
\r
33877 \begin_inset Graphics
\r
33878 filename ../images/math-macro_newmacroname_newcommand.png
\r
33884 The math macro toolbar appears together with the following box where the
\r
33885 macro is defined:
\r
33886 \begin_inset Newline newline
\r
33890 \begin_inset space \hspace*{\fill}
\r
33894 \begin_inset Graphics
\r
33895 filename clipart/macrobox.png
\r
33900 \begin_inset space \hspace*{\fill}
\r
33904 \begin_inset Newline newline
\r
33908 \begin_inset FormulaMacro
\r
33909 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
\r
33914 newmacroname is the default name of the macro that should be changed to
\r
33915 something sensible.
\r
33916 The wanted formula is inserted in the first blue box.
\r
33917 An argument placeholder is inserted with the command
\r
33924 \begin_inset space \thinspace{}
\r
33928 \begin_inset space \space{}
\r
33937 or by using the macro toolbar button
\r
33938 \begin_inset Graphics
\r
33939 filename ../images/math-macro-add-param.png
\r
33945 Argument placeholders are displayed red.
\r
33947 \begin_inset space ~
\r
33950 arguments are possible.
\r
33951 Optional arguments are created with the toolbar button
\r
33952 \begin_inset Graphics
\r
33953 filename ../images/math-macro-add-optional-param.png
\r
33959 The first non-optional argument can be transformed to an optional one with
\r
33960 the toolbar button
\r
33961 \begin_inset Graphics
\r
33962 filename ../images/math-macro-make-optional.png
\r
33968 In the second blue box the appearance of the macro in LyX can be defined.
\r
33969 Normally you want to see it as it is defined, so the box is kept empty.
\r
33970 But when you have created a macro that needs lot of space on the screen,
\r
33971 you can insert in the box for example
\r
33972 \begin_inset Newline newline
\r
34002 \begin_inset Newline newline
\r
34007 For the macro only the arguments with the macro name in front of them will
\r
34008 then be displayed in LyX, leading to a better overview.
\r
34009 The formula appears in the output as defined in the first box.
\r
34010 \begin_inset Newline newline
\r
34013 The appearance of macros in formulas can furthermore be changed for single
\r
34014 macros by setting the cursor in the macro and using the menu
\r
34016 View\SpecialChar \menuseparator
\r
34018 \begin_inset space ~
\r
34022 \begin_inset space ~
\r
34030 \begin_layout Standard
\r
34031 To use a macro, the macro name is inserted as command to a formula, in our
\r
34039 Our macro looks in LyX like this:
\r
34040 \begin_inset Newline newline
\r
34044 \begin_inset space \hspace*{\fill}
\r
34048 \begin_inset Graphics
\r
34049 filename clipart/macrouse.png
\r
34054 \begin_inset space \hspace*{\fill}
\r
34058 \begin_inset Newline newline
\r
34061 Here is our macro example with the arguments
\r
34062 \begin_inset Formula $x$
\r
34066 \begin_inset Formula $\ln(x)$
\r
34070 \begin_inset Formula $B$
\r
34076 \begin_layout Standard
\r
34077 \begin_inset Formula
\r
34087 \begin_layout Standard
\r
34088 LyX offers in the menu
\r
34090 Tools\SpecialChar \menuseparator
\r
34091 Preferences\SpecialChar \menuseparator
\r
34092 Editing\SpecialChar \menuseparator
\r
34095 different styles to edit macros.
\r
34096 To find the style that suits you the most, choose a style and set the cursor
\r
34097 in a macro formula to see the difference.
\r
34100 \begin_layout Standard
\r
34101 A math macro is transformed internally to a
\r
34107 command when exporting the document.
\r
34114 command is not placed in the LaTeX-preamble, therefore macros can only
\r
34115 be used in formulas that are in the document below the macro definition
\r
34119 \begin_layout Standard
\r
34120 Math macros can also be directly created from a
\r
34127 When writing for example the command
\r
34130 \begin_inset Newline newline
\r
34139 xleftarrow[#2]{#1}}
\r
34140 \begin_inset Newline newline
\r
34145 in LyX as normal text, highlighting it completely and using then the shortcut
\r
34150 , the command will be transformed to a math macro.
\r
34151 Using this method you need to be careful that the
\r
34157 command is typed correctly, otherwise you get a faulty macro leading to
\r
34161 \begin_layout Standard
\r
34162 Math macros currently have the problem that further formulas in macro definition
\r
34163 s are handled wrongly.
\r
34164 Therefore the example
\r
34171 \begin_inset CommandInset ref
\r
34173 reference "sub:The-Command-newcommand"
\r
34177 cannot be created as macro.
\r
34180 \begin_layout Standard
\r
34181 When the cursor is in a macro definition box, you will see the macro toolbar
\r
34185 \begin_layout Standard
\r
34186 \begin_inset VSpace defskip
\r
34192 \begin_layout Standard
\r
34193 \begin_inset Graphics
\r
34194 filename clipart/MacroToolbar.png
\r
34199 \begin_inset Index idx
\r
34202 \begin_layout Plain Layout
\r
34211 \begin_layout Standard
\r
34212 \begin_inset VSpace defskip
\r
34218 \begin_layout Standard
\r
34219 The macro toolbar contains from left to right the following buttons:
\r
34222 \begin_layout Standard
\r
34223 \begin_inset VSpace defskip
\r
34229 \begin_layout Standard
\r
34230 \begin_inset Tabular
\r
34231 <lyxtabular version="3" rows="9" columns="2">
\r
34232 <features islongtable="true" longtabularalignment="center">
\r
34233 <column alignment="left" valignment="top" width="0">
\r
34234 <column alignment="left" valignment="top" width="85col%">
\r
34235 <row interlinespace="2.5mm">
\r
34236 <cell alignment="center" valignment="top" usebox="none">
\r
34237 \begin_inset Text
\r
34239 \begin_layout Plain Layout
\r
34240 \begin_inset Graphics
\r
34241 filename ../images/math-macro-remove-param.png
\r
34242 rotateOrigin center
\r
34251 <cell alignment="center" valignment="top" usebox="none">
\r
34252 \begin_inset Text
\r
34254 \begin_layout Plain Layout
\r
34257 Edit\SpecialChar \menuseparator
\r
34258 Math\SpecialChar \menuseparator
\r
34260 \begin_inset space ~
\r
34263 Definition\SpecialChar \menuseparator
\r
34264 Remove Last Argument
\r
34270 <row interlinespace="2.5mm">
\r
34271 <cell alignment="center" valignment="top" usebox="none">
\r
34272 \begin_inset Text
\r
34274 \begin_layout Plain Layout
\r
34275 \begin_inset Graphics
\r
34276 filename ../images/math-macro-add-param.png
\r
34277 rotateOrigin center
\r
34286 <cell alignment="center" valignment="top" usebox="none">
\r
34287 \begin_inset Text
\r
34289 \begin_layout Plain Layout
\r
34292 Edit\SpecialChar \menuseparator
\r
34293 Math\SpecialChar \menuseparator
\r
34295 \begin_inset space ~
\r
34298 Definition\SpecialChar \menuseparator
\r
34305 <row interlinespace="2.5mm">
\r
34306 <cell alignment="center" valignment="top" usebox="none">
\r
34307 \begin_inset Text
\r
34309 \begin_layout Plain Layout
\r
34310 \begin_inset Graphics
\r
34311 filename ../images/math-macro-make-optional.png
\r
34312 rotateOrigin center
\r
34321 <cell alignment="center" valignment="top" usebox="none">
\r
34322 \begin_inset Text
\r
34324 \begin_layout Plain Layout
\r
34327 Edit\SpecialChar \menuseparator
\r
34328 Math\SpecialChar \menuseparator
\r
34330 \begin_inset space ~
\r
34333 Definition\SpecialChar \menuseparator
\r
34334 Make First Non-Optional into
\r
34335 \begin_inset Newline newline
\r
34339 \begin_inset Phantom HPhantom
\r
34342 \begin_layout Plain Layout
\r
34345 Edit\SpecialChar \menuseparator
\r
34346 Math\SpecialChar \menuseparator
\r
34348 \begin_inset space ~
\r
34351 Definition\SpecialChar \menuseparator
\r
34357 Optional Argument
\r
34363 <row interlinespace="2.5mm">
\r
34364 <cell alignment="center" valignment="top" usebox="none">
\r
34365 \begin_inset Text
\r
34367 \begin_layout Plain Layout
\r
34368 \begin_inset Graphics
\r
34369 filename ../images/math-macro-make-nonoptional.png
\r
34370 rotateOrigin center
\r
34379 <cell alignment="center" valignment="top" usebox="none">
\r
34380 \begin_inset Text
\r
34382 \begin_layout Plain Layout
\r
34385 Edit\SpecialChar \menuseparator
\r
34386 Math\SpecialChar \menuseparator
\r
34388 \begin_inset space ~
\r
34391 Definition\SpecialChar \menuseparator
\r
34392 Make Last Optional into
\r
34393 \begin_inset Newline newline
\r
34397 \begin_inset Phantom HPhantom
\r
34400 \begin_layout Plain Layout
\r
34403 Edit\SpecialChar \menuseparator
\r
34404 Math\SpecialChar \menuseparator
\r
34406 \begin_inset space ~
\r
34409 Definition\SpecialChar \menuseparator
\r
34415 Non-Optional Argument
\r
34421 <row interlinespace="2.5mm">
\r
34422 <cell alignment="center" valignment="top" usebox="none">
\r
34423 \begin_inset Text
\r
34425 \begin_layout Plain Layout
\r
34426 \begin_inset Graphics
\r
34427 filename ../images/math-macro-remove-optional-param.png
\r
34428 rotateOrigin center
\r
34437 <cell alignment="center" valignment="top" usebox="none">
\r
34438 \begin_inset Text
\r
34440 \begin_layout Plain Layout
\r
34443 Edit\SpecialChar \menuseparator
\r
34444 Math\SpecialChar \menuseparator
\r
34446 \begin_inset space ~
\r
34449 Definition\SpecialChar \menuseparator
\r
34450 Remove Optional Argument
\r
34456 <row interlinespace="2.5mm">
\r
34457 <cell alignment="center" valignment="top" usebox="none">
\r
34458 \begin_inset Text
\r
34460 \begin_layout Plain Layout
\r
34461 \begin_inset Graphics
\r
34462 filename ../images/math-macro-add-optional-param.png
\r
34463 rotateOrigin center
\r
34472 <cell alignment="center" valignment="top" usebox="none">
\r
34473 \begin_inset Text
\r
34475 \begin_layout Plain Layout
\r
34478 Edit\SpecialChar \menuseparator
\r
34479 Math\SpecialChar \menuseparator
\r
34481 \begin_inset space ~
\r
34484 Definition\SpecialChar \menuseparator
\r
34485 Insert Optional Argument
\r
34491 <row interlinespace="2.5mm">
\r
34492 <cell alignment="center" valignment="top" usebox="none">
\r
34493 \begin_inset Text
\r
34495 \begin_layout Plain Layout
\r
34496 \begin_inset Graphics
\r
34497 filename ../images/math-macro-remove-greedy-param.png
\r
34498 rotateOrigin center
\r
34507 <cell alignment="center" valignment="top" usebox="none">
\r
34508 \begin_inset Text
\r
34510 \begin_layout Plain Layout
\r
34513 Edit\SpecialChar \menuseparator
\r
34514 Math\SpecialChar \menuseparator
\r
34516 \begin_inset space ~
\r
34519 Definition\SpecialChar \menuseparator
\r
34520 Remove Last Argument
\r
34521 \begin_inset Newline newline
\r
34525 \begin_inset Phantom HPhantom
\r
34528 \begin_layout Plain Layout
\r
34531 Edit\SpecialChar \menuseparator
\r
34532 Math\SpecialChar \menuseparator
\r
34534 \begin_inset space ~
\r
34537 Definition\SpecialChar \menuseparator
\r
34543 Spitting Out To The Right
\r
34549 <row interlinespace="2.5mm">
\r
34550 <cell alignment="center" valignment="top" usebox="none">
\r
34551 \begin_inset Text
\r
34553 \begin_layout Plain Layout
\r
34554 \begin_inset Graphics
\r
34555 filename ../images/math-macro-append-greedy-param.png
\r
34556 rotateOrigin center
\r
34565 <cell alignment="center" valignment="top" usebox="none">
\r
34566 \begin_inset Text
\r
34568 \begin_layout Plain Layout
\r
34571 Edit\SpecialChar \menuseparator
\r
34572 Math\SpecialChar \menuseparator
\r
34574 \begin_inset space ~
\r
34577 Definition\SpecialChar \menuseparator
\r
34579 \begin_inset Newline newline
\r
34583 \begin_inset Phantom HPhantom
\r
34586 \begin_layout Plain Layout
\r
34589 Edit\SpecialChar \menuseparator
\r
34590 Math\SpecialChar \menuseparator
\r
34592 \begin_inset space ~
\r
34595 Definition\SpecialChar \menuseparator
\r
34601 Eating From The Right
\r
34607 <row interlinespace="2.5mm">
\r
34608 <cell alignment="center" valignment="top" usebox="none">
\r
34609 \begin_inset Text
\r
34611 \begin_layout Plain Layout
\r
34612 \begin_inset Graphics
\r
34613 filename ../images/math-macro-add-greedy-optional-param.png
\r
34614 rotateOrigin center
\r
34623 <cell alignment="center" valignment="top" usebox="none">
\r
34624 \begin_inset Text
\r
34626 \begin_layout Plain Layout
\r
34629 Edit\SpecialChar \menuseparator
\r
34630 Math\SpecialChar \menuseparator
\r
34632 \begin_inset space ~
\r
34635 Definition\SpecialChar \menuseparator
\r
34636 Append Optional Argument
\r
34637 \begin_inset Newline newline
\r
34641 \begin_inset Phantom HPhantom
\r
34644 \begin_layout Plain Layout
\r
34647 Edit\SpecialChar \menuseparator
\r
34648 Math\SpecialChar \menuseparator
\r
34650 \begin_inset space ~
\r
34653 Definition\SpecialChar \menuseparator
\r
34659 Eating From The Right
\r
34672 \begin_layout Section
\r
34673 Computer Algebra Systems
\r
34676 \begin_layout Standard
\r
34677 LyX offers the exchange between mathematical expressions written in LyX's
\r
34678 math editor and external applications or user defined scripts.
\r
34679 Currently supported applications are
\r
34696 Note that the set of supported mathematical constructs is limited only
\r
34697 to very simple cases.
\r
34700 \begin_layout Subsection
\r
34704 \begin_layout Standard
\r
34705 Write some expression in a formula, go to the
\r
34707 Edit\SpecialChar \menuseparator
\r
34708 Math\SpecialChar \menuseparator
\r
34709 Use Computer Algebra System
\r
34711 menu and choose the application you have installed on the computer.
\r
34712 After that the result of computation should show on the right side of the
\r
34713 expression together with the
\r
34714 \begin_inset Quotes eld
\r
34718 \begin_inset Quotes erd
\r
34724 \begin_layout Standard
\r
34725 Here are few simple examples (with results from
\r
34726 \family typewriter
\r
34729 ) to show what kind of computations can be performed:
\r
34732 \begin_layout Itemize
\r
34733 \begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$
\r
34739 \begin_layout Itemize
\r
34740 \begin_inset Formula $\frac{37.0}{3}=12.33333333333333$
\r
34746 \begin_layout Itemize
\r
34747 \begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$
\r
34753 \begin_layout Itemize
\r
34754 \begin_inset Formula $\det\left[\begin{array}{ccc}
\r
34758 \end{array}\right]=-56$
\r
34764 \begin_layout Itemize
\r
34765 \begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$
\r
34771 \begin_layout Subsection
\r
34772 Keyboard shortcut
\r
34775 \begin_layout Standard
\r
34776 Currently there is no keyboard shortcut for calling the algebra applications.
\r
34777 One can easily bind a shortcut to the
\r
34781 LyX function (see the
\r
34789 \begin_inset space \thinspace{}
\r
34793 \begin_inset space \space{}
\r
34800 key inside the math editor.
\r
34802 \family typewriter
\r
34805 one would use this shortcut definition command:
\r
34808 \begin_layout Standard
\r
34811 command-alternatives break-paragraph;math-extern maxima
\r
34814 \begin_layout Section
\r
34816 \begin_inset Index idx
\r
34819 \begin_layout Plain Layout
\r
34828 \begin_layout Subsection
\r
34830 \begin_inset Index idx
\r
34833 \begin_layout Plain Layout
\r
34834 Numbers ! negative
\r
34842 \begin_layout Standard
\r
34843 Negative numbers often look ugly in formulas because the minus sign before
\r
34844 the number is set with the same length as the minus operator sign.
\r
34845 When writing the negative number in normal text, the minus sign appears
\r
34849 \begin_layout Standard
\r
34850 Thus, the problem disappears when converting the minus sign to mathematical
\r
34854 \begin_layout Standard
\r
34855 An example to visualize the problem:
\r
34858 \begin_layout Standard
\r
34860 \begin_inset Tabular
\r
34861 <lyxtabular version="3" rows="3" columns="2">
\r
34862 <features tabularvalignment="middle">
\r
34863 <column alignment="right" valignment="top" width="0">
\r
34864 <column alignment="left" valignment="top" width="0">
\r
34866 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
34867 \begin_inset Text
\r
34869 \begin_layout Plain Layout
\r
34875 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
\r
34876 \begin_inset Text
\r
34878 \begin_layout Plain Layout
\r
34886 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
34887 \begin_inset Text
\r
34889 \begin_layout Plain Layout
\r
34895 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
\r
34896 \begin_inset Text
\r
34898 \begin_layout Plain Layout
\r
34899 \begin_inset Formula $x=-2$
\r
34909 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
34910 \begin_inset Text
\r
34912 \begin_layout Plain Layout
\r
34918 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
\r
34919 \begin_inset Text
\r
34921 \begin_layout Plain Layout
\r
34922 \begin_inset Formula $x=\textrm{-}2$
\r
34938 \begin_layout Subsection
\r
34939 Comma as decimal Separator
\r
34940 \begin_inset Index idx
\r
34943 \begin_layout Plain Layout
\r
34952 \begin_layout Standard
\r
34953 In LaTeX a comma inside a formula is used, according to the English convention,
\r
34954 as number group separator.
\r
34955 So there will be space added behind all commas in formulas.
\r
34958 \begin_layout Standard
\r
34959 To avoid this, the comma is highlighted and changed to mathematical text
\r
34961 \begin_inset Info
\r
34969 \begin_layout Standard
\r
34970 To use all formula commas in the document as decimal separator, the file
\r
34976 \begin_inset Foot
\r
34979 \begin_layout Plain Layout
\r
34984 is part of the LaTeX-package
\r
34989 \begin_inset Index idx
\r
34992 \begin_layout Plain Layout
\r
34997 \begin_layout Plain Layout
\r
35017 \begin_inset Index idx
\r
35020 \begin_layout Plain Layout
\r
35021 Packages ! icomma
\r
35026 is loaded with the LaTeX-preamble line
\r
35029 \begin_layout Standard
\r
35034 usepackage{icomma}
\r
35037 \begin_layout Subsection
\r
35039 \begin_inset CommandInset label
\r
35040 LatexCommand label
\r
35041 name "sub:Physical-Vectors"
\r
35046 \begin_inset Index idx
\r
35049 \begin_layout Plain Layout
\r
35050 Vectors ! physical
\r
35058 \begin_layout Standard
\r
35059 Predefined vectors are offered by the LaTeX-package
\r
35064 \begin_inset Index idx
\r
35067 \begin_layout Plain Layout
\r
35068 Packages ! braket
\r
35073 that is loaded with the LaTeX-preamble line
\r
35076 \begin_layout Standard
\r
35081 usepackage{braket}
\r
35084 \begin_layout Standard
\r
35088 \begin_layout Plain Layout
\r
35098 \begin_inset Note Note
\r
35101 \begin_layout Plain Layout
\r
35102 The following table will only be displayed when the LaTeX-package
\r
35114 \begin_layout Standard
\r
35115 The following commands are defined:
\r
35118 \begin_layout Standard
\r
35120 \begin_inset Tabular
\r
35121 <lyxtabular version="3" rows="4" columns="2">
\r
35122 <features tabularvalignment="middle">
\r
35123 <column alignment="center" valignment="top" width="0">
\r
35124 <column alignment="center" valignment="top" width="0">
\r
35126 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
35127 \begin_inset Text
\r
35129 \begin_layout Plain Layout
\r
35135 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
35136 \begin_inset Text
\r
35138 \begin_layout Plain Layout
\r
35146 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
35147 \begin_inset Text
\r
35149 \begin_layout Plain Layout
\r
35159 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
35160 \begin_inset Text
\r
35162 \begin_layout Plain Layout
\r
35163 \begin_inset Formula $\Bra{\psi}$
\r
35173 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
35174 \begin_inset Text
\r
35176 \begin_layout Plain Layout
\r
35186 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
35187 \begin_inset Text
\r
35189 \begin_layout Plain Layout
\r
35190 \begin_inset Formula $\Ket{\psi}$
\r
35200 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
35201 \begin_inset Text
\r
35203 \begin_layout Plain Layout
\r
35215 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
35216 \begin_inset Text
\r
35218 \begin_layout Plain Layout
\r
35219 \begin_inset Formula $\Braket{\psi|\phi}$
\r
35235 \begin_layout Standard
\r
35242 assures that all vertical bars are set in the size of the surrounding brackets:
\r
35243 \begin_inset Formula
\r
35245 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}
\r
35254 \begin_layout Plain Layout
\r
35264 \begin_inset Note Note
\r
35267 \begin_layout Plain Layout
\r
35268 The following will be displayed when the LaTeX-package
\r
35272 is not installed:
\r
35280 \begin_layout Standard
\r
35281 You need to install the LaTeX-package
\r
35285 to see the rest of this subsection in the output.
\r
35288 \begin_layout Standard
\r
35292 \begin_layout Plain Layout
\r
35304 \begin_layout Standard
\r
35311 can also be achieved using the command
\r
35317 , that is described in
\r
35318 \begin_inset CommandInset ref
\r
35320 reference "sub:Automatic-Bracket-Size"
\r
35327 \begin_layout Subsection
\r
35328 Self-defined Fractions
\r
35329 \begin_inset CommandInset label
\r
35330 LatexCommand label
\r
35331 name "sub:Self-defined-Fractions"
\r
35336 \begin_inset Index idx
\r
35339 \begin_layout Plain Layout
\r
35340 Fractions ! self-defined
\r
35348 \begin_layout Standard
\r
35349 To define custom commands for fractions, the command
\r
35356 \begin_inset Index idx
\r
35359 \begin_layout Plain Layout
\r
35366 \begin_layout Plain Layout
\r
35380 is used in the following scheme:
\r
35383 \begin_layout Standard
\r
35396 bracket}{fraction bar thickness}{style}
\r
35397 \begin_inset Newline newline
\r
35401 \begin_inset Phantom HPhantom
\r
35404 \begin_layout Plain Layout
\r
35414 {numerator}{denominator}
\r
35417 \begin_layout Standard
\r
35418 The style is a number in the range of 0
\r
35419 \begin_inset space \thinspace{}
\r
35423 \begin_inset space \thinspace{}
\r
35429 \begin_layout Standard
\r
35431 \begin_inset Tabular
\r
35432 <lyxtabular version="3" rows="5" columns="2">
\r
35433 <features tabularvalignment="middle">
\r
35434 <column alignment="center" valignment="top" width="0">
\r
35435 <column alignment="center" valignment="top" width="0">
\r
35437 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
35438 \begin_inset Text
\r
35440 \begin_layout Plain Layout
\r
35446 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
35447 \begin_inset Text
\r
35449 \begin_layout Plain Layout
\r
35457 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
35458 \begin_inset Text
\r
35460 \begin_layout Plain Layout
\r
35466 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
35467 \begin_inset Text
\r
35469 \begin_layout Plain Layout
\r
35470 display style formula
\r
35477 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
35478 \begin_inset Text
\r
35480 \begin_layout Plain Layout
\r
35486 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
35487 \begin_inset Text
\r
35489 \begin_layout Plain Layout
\r
35497 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
35498 \begin_inset Text
\r
35500 \begin_layout Plain Layout
\r
35506 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
35507 \begin_inset Text
\r
35509 \begin_layout Plain Layout
\r
35517 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
35518 \begin_inset Text
\r
35520 \begin_layout Plain Layout
\r
35526 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
35527 \begin_inset Text
\r
35529 \begin_layout Plain Layout
\r
35543 \begin_layout Standard
\r
35544 When no style is given, the size is adjusted to the surrounding environment
\r
35545 like for the command
\r
35554 \begin_layout Standard
\r
35555 When no fraction bar thickness is given, the predefined value of 0.4
\r
35556 \begin_inset space \thinspace{}
\r
35562 \begin_layout Standard
\r
35563 \begin_inset VSpace medskip
\r
35566 For example, the commands
\r
35579 \begin_inset CommandInset ref
\r
35581 reference "sub:Fractions"
\r
35585 are defined with the commands
\r
35588 \begin_layout Standard
\r
35597 genfrac{}{}{}{0}{#1}{#2}}
\r
35600 \begin_layout Standard
\r
35604 \begin_layout Standard
\r
35613 genfrac{(}{)}{0pt}{1}{#1}{#2}}
\r
35616 \begin_layout Standard
\r
35617 \begin_inset VSpace medskip
\r
35620 To define a fraction where the fraction bar thickness can be given as optional
\r
35621 argument, the following line is inserted to the LaTeX-preamble:
\r
35624 \begin_layout Standard
\r
35633 genfrac{}{}{#1}{}{#2}{#3}}
\r
35636 \begin_layout Standard
\r
35638 \begin_inset Formula
\r
35640 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
\r
35641 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
\r
35646 As one can see, the distance of the numerator and the denominator to the
\r
35647 fraction bar is round about three times the bar thickness.
\r
35650 \begin_layout Subsection
\r
35651 Canceled Formulas
\r
35652 \begin_inset Index idx
\r
35655 \begin_layout Plain Layout
\r
35656 Formula ! canceled
\r
35664 \begin_layout Standard
\r
35665 To cancel formulas or formula parts, the LaTeX-package
\r
35670 \begin_inset Index idx
\r
35673 \begin_layout Plain Layout
\r
35674 Packages ! cancel
\r
35679 has to be loaded with the LaTeX-preamble line
\r
35682 \begin_layout Standard
\r
35687 usepackage{cancel}
\r
35690 \begin_layout Standard
\r
35694 \begin_layout Plain Layout
\r
35704 \begin_inset Note Note
\r
35707 \begin_layout Plain Layout
\r
35708 The following table will only be displayed when the LaTeX-package
\r
35720 \begin_layout Standard
\r
35721 There are four ways to cancel formulas:
\r
35724 \begin_layout Standard
\r
35726 \begin_inset Tabular
\r
35727 <lyxtabular version="3" rows="5" columns="2">
\r
35728 <features tabularvalignment="middle">
\r
35729 <column alignment="center" valignment="top" width="0">
\r
35730 <column alignment="center" valignment="top" width="0">
\r
35732 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
35733 \begin_inset Text
\r
35735 \begin_layout Plain Layout
\r
35741 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
35742 \begin_inset Text
\r
35744 \begin_layout Plain Layout
\r
35746 \begin_inset Note Note
\r
35749 \begin_layout Plain Layout
\r
35756 are used here as spacer.
\r
35768 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
35769 \begin_inset Text
\r
35771 \begin_layout Plain Layout
\r
35780 \begin_layout Plain Layout
\r
35794 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
35795 \begin_inset Text
\r
35797 \begin_layout Plain Layout
\r
35798 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
\r
35808 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
35809 \begin_inset Text
\r
35811 \begin_layout Plain Layout
\r
35820 \begin_layout Plain Layout
\r
35834 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
35835 \begin_inset Text
\r
35837 \begin_layout Plain Layout
\r
35838 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
\r
35848 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
35849 \begin_inset Text
\r
35851 \begin_layout Plain Layout
\r
35860 \begin_layout Plain Layout
\r
35874 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
35875 \begin_inset Text
\r
35877 \begin_layout Plain Layout
\r
35878 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
\r
35888 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
35889 \begin_inset Text
\r
35891 \begin_layout Plain Layout
\r
35895 \begin_inset Formula $\to$
\r
35906 \begin_layout Plain Layout
\r
35920 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
35921 \begin_inset Text
\r
35923 \begin_layout Plain Layout
\r
35924 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
\r
35940 \begin_layout Standard
\r
35947 is especially suitable to visualize the reduction of fractions within formulas:
\r
35948 \begin_inset Formula
\r
35950 \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}}}
\r
35958 \begin_layout Standard
\r
35959 To change the size of
\r
35966 \begin_inset Quotes eld
\r
35970 \begin_inset Quotes erd
\r
35973 value one can load the package
\r
35977 with either the option
\r
35981 which leads to the same size as for the canceled value or with the option
\r
35986 which makes is it a bit smaller than the size one gets without using a
\r
35988 In this document
\r
35992 was loaded with this line:
\r
35995 \begin_layout Standard
\r
36000 usepackage[samesize]{cancel}
\r
36003 \begin_layout Standard
\r
36004 To color the cancellation bar one adds this command as TeX code:
\r
36007 \begin_layout Standard
\r
36019 \begin_layout Standard
\r
36024 can be replaced by a color of your choice.
\r
36027 \begin_layout Standard
\r
36031 \begin_layout Plain Layout
\r
36047 \begin_layout Standard
\r
36048 \begin_inset Formula
\r
36050 \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}}}
\r
36058 \begin_layout Standard
\r
36062 \begin_layout Plain Layout
\r
36076 \begin_inset Note Note
\r
36079 \begin_layout Plain Layout
\r
36088 \begin_layout Standard
\r
36089 For further customizations, see the documentation of the package
\r
36094 \begin_inset CommandInset citation
\r
36095 LatexCommand cite
\r
36103 \begin_layout Standard
\r
36107 \begin_layout Plain Layout
\r
36117 \begin_inset Note Note
\r
36120 \begin_layout Plain Layout
\r
36121 The following will be displayed when the LaTeX-package
\r
36125 is not installed:
\r
36133 \begin_layout Standard
\r
36134 You need to install the LaTeX-package
\r
36138 to see the rest of this subsection in the output.
\r
36141 \begin_layout Standard
\r
36145 \begin_layout Plain Layout
\r
36157 \begin_layout Standard
\r
36158 \begin_inset Newpage newpage
\r
36164 \begin_layout Subsection
\r
36165 Formulas in Section Headings
\r
36166 \begin_inset CommandInset label
\r
36167 LatexCommand label
\r
36168 name "sub:Formulas-in-Section"
\r
36173 \begin_inset Index idx
\r
36176 \begin_layout Plain Layout
\r
36177 Formula ! in section headings
\r
36185 \begin_layout Standard
\r
36186 When formulas are used in section headings, the following has to be taken
\r
36190 \begin_layout Standard
\r
36191 \begin_inset Note Greyedout
\r
36194 \begin_layout Plain Layout
\r
36200 \begin_inset Index idx
\r
36203 \begin_layout Plain Layout
\r
36204 Packages ! hyperref
\r
36209 support is enabled in the document settings dialog under
\r
36212 \begin_inset space ~
\r
36217 , PDF-bookmarks are created for every section heading in the table of contents.
\r
36218 If a section heading contains formulas, they are incorrectly displayed
\r
36219 in the bookmark text, because formulas in bookmarks infringe the PDF convention
\r
36228 \begin_layout Standard
\r
36229 Both problems can be solved by inserting at the end of the section heading
\r
36230 a short title with the menu
\r
36232 Insert\SpecialChar \menuseparator
\r
36234 \begin_inset space ~
\r
36240 Short titles are used as alternative for multiline section headings to
\r
36241 keep the table of contents clearly arranged.
\r
36242 Only the short title appears in the table of contents and therefore also
\r
36243 in the PDF-bookmark.
\r
36246 \begin_layout Standard
\r
36247 When formulas should be used in the table of contents but
\r
36251 is used, one can use the following command in TeX-mode:
\r
36254 \begin_layout Standard
\r
36259 texorpdfstring{part}{alternative}
\r
36260 \begin_inset Index idx
\r
36263 \begin_layout Plain Layout
\r
36274 \begin_layout Standard
\r
36275 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
\r
36276 This can be characters, formulas, footnotes, but also cross-references.
\r
36277 The alternative is used instead of the part for the bookmark.
\r
36280 \begin_layout Standard
\r
36281 Here are two example headings:
\r
36282 \begin_inset VSpace -3mm
\r
36289 \begin_layout Plain Layout
\r
36301 \begin_layout Subsubsection
\r
36302 Heading without formula in table of contents
\r
36303 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
\r
36307 \begin_inset Argument
\r
36310 \begin_layout Plain Layout
\r
36311 Heading without formula in table of contents
\r
36319 \begin_layout Subsubsection
\r
36320 Heading with formula in table of contents
\r
36324 \begin_layout Plain Layout
\r
36334 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
\r
36341 \begin_layout Plain Layout
\r
36351 \begin_layout Standard
\r
36355 \begin_layout Plain Layout
\r
36364 In the first heading a short title was used, in the second one
\r
36373 \begin_layout Standard
\r
36374 To get the same formatting as for the other headings, the complete heading
\r
36380 \begin_inset Foot
\r
36383 \begin_layout Plain Layout
\r
36385 \begin_inset CommandInset ref
\r
36387 reference "sub:Bold-Formulas"
\r
36399 \begin_layout Subsection
\r
36400 Formulas in multi-column Text
\r
36401 \begin_inset Index idx
\r
36404 \begin_layout Plain Layout
\r
36405 Formula ! in multi-column text
\r
36413 \begin_layout Standard
\r
36414 Formulas in multi-column text are often too wide to fit into a column and
\r
36415 thus need to be set over the whole page width.
\r
36416 This is done by using the LaTeX-package
\r
36421 \begin_inset Foot
\r
36424 \begin_layout Plain Layout
\r
36429 is part of every LaTeX standard installation.
\r
36435 \begin_inset Index idx
\r
36438 \begin_layout Plain Layout
\r
36439 Packages ! multicol
\r
36444 , that is loaded with the LaTeX-preamble line
\r
36447 \begin_layout Standard
\r
36452 usepackage{multicol}
\r
36455 \begin_layout Standard
\r
36456 \begin_inset Note Greyedout
\r
36459 \begin_layout Plain Layout
\r
36460 Note that in this case the setting
\r
36463 \begin_inset space ~
\r
36470 Document\SpecialChar \menuseparator
\r
36476 \begin_inset space ~
\r
36496 \begin_layout Standard
\r
36497 Before the multi-column text the command
\r
36500 \begin_layout Standard
\r
36505 begin{multicols}{column number}
\r
36508 \begin_layout Standard
\r
36509 is written in TeX-mode.
\r
36510 The column number is a number in the range of 2
\r
36511 \begin_inset space \thinspace{}
\r
36515 \begin_inset space \thinspace{}
\r
36519 Before the formula the multi-column text is ended by inserting the command
\r
36522 \begin_layout Standard
\r
36530 \begin_layout Standard
\r
36534 \begin_layout Standard
\r
36535 Due to the command some space is automatically added before the formula.
\r
36536 To revert this, -6
\r
36537 \begin_inset space \thinspace{}
\r
36540 mm vertical space is inserted before the formula.
\r
36541 When the formula style
\r
36544 \begin_inset Foot
\r
36547 \begin_layout Plain Layout
\r
36548 formula styles see
\r
36549 \begin_inset CommandInset ref
\r
36551 reference "sec:Formula-Styles"
\r
36563 \begin_inset space \thinspace{}
\r
36566 mm space is inserted instead.
\r
36569 \begin_layout Standard
\r
36570 As example a multi-column text with a displayed formula:
\r
36573 \begin_layout Standard
\r
36579 \begin_layout Plain Layout
\r
36583 begin{multicols}{2}
\r
36588 Das Spektrum wird fouriertransformiert.
\r
36589 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
\r
36590 , Lösungsmittel) zu trennen.
\r
36591 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
\r
36592 nun das Aussehen des Ausgangssignals.
\r
36593 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
\r
36594 über alle Phasen integrieren muss.
\r
36596 \begin_inset Formula $S$
\r
36599 unser normiertes Ausgangssignal und
\r
36600 \begin_inset Formula $P$
\r
36603 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
\r
36607 \begin_layout Plain Layout
\r
36617 \begin_inset VSpace -6mm
\r
36621 \begin_inset Formula
\r
36623 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
\r
36632 \begin_layout Plain Layout
\r
36636 begin{multicols}{2}
\r
36642 \begin_inset Formula $S_{0}$
\r
36645 das Signal ohne Gradient ist und die Normierungsbedingung
\r
36646 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
\r
36650 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
\r
36652 \begin_inset Formula $\nicefrac{\pi}{2}$
\r
36656 \begin_inset space \thinspace{}
\r
36659 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
\r
36660 das Signal zusätzlich abschwächt.
\r
36661 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
\r
36663 \begin_inset Formula $T_{2}$
\r
36669 \begin_layout Standard
\r
36675 \begin_layout Plain Layout
\r
36687 \begin_layout Subsection
\r
36688 Formulas with Description of Variables
\r
36689 \begin_inset Index idx
\r
36692 \begin_layout Plain Layout
\r
36693 Formula ! with description of variables
\r
36701 \begin_layout Standard
\r
36702 To describe variables within a formula, like in formula
\r
36703 \begin_inset CommandInset ref
\r
36704 LatexCommand eqref
\r
36705 reference "eq:within"
\r
36714 \begin_inset Formula $n$
\r
36718 \begin_inset space ~
\r
36721 matrix is used with left aligned columns for the
\r
36722 \begin_inset Formula $n$
\r
36726 \begin_inset Foot
\r
36729 \begin_layout Plain Layout
\r
36731 \begin_inset CommandInset ref
\r
36733 reference "sec:Matrices"
\r
36742 To set the description in a smaller size, before the matrix e.
\r
36743 \begin_inset space \thinspace{}
\r
36747 \begin_inset space \space{}
\r
36757 \begin_inset Foot
\r
36760 \begin_layout Plain Layout
\r
36762 \begin_inset CommandInset ref
\r
36764 reference "sub:Font-Sizes"
\r
36776 \begin_layout Standard
\r
36777 When the formula style
\r
36780 \begin_inset Foot
\r
36783 \begin_layout Plain Layout
\r
36784 formula styles see
\r
36785 \begin_inset CommandInset ref
\r
36787 reference "sec:Formula-Styles"
\r
36805 \begin_inset Foot
\r
36808 \begin_layout Plain Layout
\r
36815 only works in formulas with the style
\r
36820 \begin_inset CommandInset ref
\r
36822 reference "sub:Variable-Space"
\r
36831 is inserted before and after the matrix to have the same separation of
\r
36832 the matrix from the equation and the side margin.
\r
36835 \begin_layout Standard
\r
36836 When the formula style
\r
36840 is used, the method described in
\r
36841 \begin_inset CommandInset ref
\r
36843 reference "sub:Flalign-Environment"
\r
36847 is used to indent formulas.
\r
36849 \begin_inset CommandInset ref
\r
36850 LatexCommand eqref
\r
36851 reference "eq:within"
\r
36855 consists of five columns where in the first two columns contain the equation,
\r
36856 the third the matrix and the last one an empty TeX-brace.
\r
36857 \begin_inset Formula
\r
36859 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
\r
36860 \rho & \textrm{density}\\
\r
36861 V & \textrm{volume}\\
\r
36862 g & \textrm{gravitational acceleration}
\r
36863 \end{array} & & {}\label{eq:within}
\r
36871 \begin_layout Subsection
\r
36872 Upright small Greek Letters
\r
36873 \begin_inset CommandInset label
\r
36874 LatexCommand label
\r
36875 name "sub:Upright-small-Greek"
\r
36880 \begin_inset Index idx
\r
36883 \begin_layout Plain Layout
\r
36884 Greek letters ! upright
\r
36892 \begin_layout Standard
\r
36893 Most of the math fonts only provide italic small Greek letters.
\r
36894 But for symbols of elementary particles like pions and neutrinos, upright
\r
36895 Greek letters are needed.
\r
36901 \begin_inset Foot
\r
36904 \begin_layout Plain Layout
\r
36909 is part of the LaTeX-package
\r
36914 \begin_inset Index idx
\r
36917 \begin_layout Plain Layout
\r
36922 \begin_layout Plain Layout
\r
36942 \begin_inset Index idx
\r
36945 \begin_layout Plain Layout
\r
36946 Packages ! upgreek
\r
36951 that is loaded with the LaTeX-preamble line
\r
36954 \begin_layout Standard
\r
36959 usepackage{upgreek}
\r
36962 \begin_layout Standard
\r
36968 \begin_layout Plain Layout
\r
36978 \begin_inset Note Note
\r
36981 \begin_layout Plain Layout
\r
36982 The following table will only be displayed when the LaTeX-package
\r
36991 They are created when the command for a small Greek letter is started with
\r
36997 For example the command
\r
37004 \begin_inset Formula $\uptau$
\r
37010 \begin_layout Standard
\r
37011 With these commands reactions of elementary particles can be typeset:
\r
37012 \begin_inset Formula
\r
37014 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
\r
37022 \begin_layout Standard
\r
37023 The upright letters are more bold and wider than the italic ones.
\r
37024 They should therefore not be used for units like
\r
37025 \begin_inset Quotes eld
\r
37029 \begin_inset Quotes erd
\r
37035 \begin_layout Standard
\r
37039 \begin_layout Plain Layout
\r
37049 \begin_inset Note Note
\r
37052 \begin_layout Plain Layout
\r
37053 The following will be displayed when the LaTeX-package
\r
37057 is not installed:
\r
37065 \begin_layout Standard
\r
37066 You need to install the LaTeX-package
\r
37070 to see the rest of this subsection in the output.
\r
37073 \begin_layout Standard
\r
37077 \begin_layout Plain Layout
\r
37089 \begin_layout Subsection
\r
37090 Text Characters in Formulas
\r
37091 \begin_inset CommandInset label
\r
37092 LatexCommand label
\r
37093 name "sub:Text-Characters-in"
\r
37098 \begin_inset Index idx
\r
37101 \begin_layout Plain Layout
\r
37102 Text ! in formulas
\r
37110 \begin_layout Standard
\r
37111 In some cases you might want to insert text characters directly into formulas.
\r
37112 When for example the centered dot · is often used in formulas like
\r
37113 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
\r
37116 , one would have to insert the command
\r
37123 \begin_inset Foot
\r
37126 \begin_layout Plain Layout
\r
37128 \begin_inset CommandInset ref
\r
37130 reference "sub:Binary-Operators"
\r
37139 all the time, because this character is defined in all encodings as text
\r
37141 But the encoding can be changed by this LaTeX-preamble line:
\r
37144 \begin_layout Standard
\r
37149 Declare Inputtext{183}{
\r
37157 textperiodcentered
\r
37159 f\SpecialChar \textcompwordmark{}
\r
37163 \begin_layout Standard
\r
37164 The character encoding (menu
\r
37166 Document\SpecialChar \menuseparator
\r
37167 Settings\SpecialChar \menuseparator
\r
37170 ) specifies what character appears when a keyboard key is pressed.
\r
37171 When the key for the character '·' is pressed, internally the command
\r
37175 textperiodcentered
\r
37178 But this command is not available in a formula so that you would get LaTeX-erro
\r
37180 With the changed encoding the right command is chosen automatically, depending
\r
37181 on if the character was inserted into a formula or not.
\r
37184 \begin_layout Standard
\r
37185 The encoding of several characters is saved in definition files.
\r
37186 For example the encoding
\r
37190 is defined in the file
\r
37194 which is in the installation folder of LaTeX.
\r
37195 Encodings should only be changed via the LaTeX-preamble and not in the
\r
37196 definition files.
\r
37197 Otherwise documents could not be edited by other LyX users working on other
\r
37201 \begin_layout Standard
\r
37202 \begin_inset VSpace medskip
\r
37205 Besides the centered dot, in this document the degree sign ° is defined
\r
37206 with the following LaTeX-preamble line so that it can be directly inserted
\r
37210 \begin_layout Standard
\r
37215 DeclareInputtext{176}{
\r
37225 f\SpecialChar \textcompwordmark{}
\r
37229 \begin_layout Standard
\r
37230 \begin_inset Newpage newpage
\r
37236 \begin_layout Section
\r
37237 \start_of_appendix
\r
37238 Typographic Advice
\r
37239 \begin_inset Index idx
\r
37242 \begin_layout Plain Layout
\r
37243 Typographic advice
\r
37251 \begin_layout Standard
\r
37252 This section is a summary of the most important typographic rules, listed
\r
37254 \begin_inset Foot
\r
37257 \begin_layout Plain Layout
\r
37258 This collection was partly taken from the German semi-official dictionary
\r
37260 \begin_inset Quotes eld
\r
37264 \begin_inset Quotes erd
\r
37268 \begin_inset CommandInset citation
\r
37269 LatexCommand cite
\r
37274 that lists some of the ISO rules.
\r
37275 More rules are listed in
\r
37276 \begin_inset CommandInset citation
\r
37277 LatexCommand cite
\r
37290 \begin_layout Itemize
\r
37291 Physical units are
\r
37296 \begin_inset Foot
\r
37299 \begin_layout Plain Layout
\r
37300 done with font styles, see
\r
37301 \begin_inset CommandInset ref
\r
37303 reference "sub:Font-Styles"
\r
37312 , no matter if they appear in italic text: 30
\r
37313 \begin_inset space \thinspace{}
\r
37317 \begin_inset Newline newline
\r
37320 Between the value and the unit is the smallest space, see
\r
37321 \begin_inset CommandInset ref
\r
37323 reference "sub:Predefined-Space"
\r
37328 \begin_inset Newline newline
\r
37331 This convention is automatically fulfilled when the command
\r
37338 When it is entered to a formula, two boxes appear.
\r
37339 In the first one the value is inserted, in the second one the unit, and
\r
37340 one gets as above:
\r
37341 \begin_inset Formula $\unit[30]{km/h}$
\r
37345 \begin_inset space \thinspace{}
\r
37355 is not a real LaTeX command but the command
\r
37359 unit[value]{unit}
\r
37361 , therefore you cannot use it in TeX code.
\r
37364 \begin_layout Itemize
\r
37365 Percent and perthousand signs are set like physical units:
\r
37366 \begin_inset Newline newline
\r
37370 \begin_inset space \thinspace{}
\r
37373 ‰ alcohol in blood
\r
37376 \begin_layout Itemize
\r
37377 The degree sign follows directly on the value: 15°, but not when it is used
\r
37379 \begin_inset space \thinspace{}
\r
37385 \begin_layout Itemize
\r
37386 In numbers with more than four digits the smallest space is inserted before
\r
37387 every third digit to group them:
\r
37397 \begin_inset space \thinspace{}
\r
37401 \begin_inset space \thinspace{}
\r
37407 \begin_layout Itemize
\r
37408 For dimensions like 120×90×40
\r
37409 \begin_inset space \thinspace{}
\r
37412 cm the multiplication sign
\r
37413 \begin_inset Quotes eld
\r
37417 \begin_inset Quotes erd
\r
37421 It is available either via the command
\r
37429 Insert\SpecialChar \menuseparator
\r
37430 Special Character\SpecialChar \menuseparator
\r
37436 \begin_layout Itemize
\r
37437 Functions with names consisting of several letters are set upright to avoid
\r
37439 \begin_inset CommandInset ref
\r
37441 reference "sub:Predefined-Functions"
\r
37448 \begin_layout Itemize
\r
37449 Indices consisting of several letters, are set upright:
\r
37450 \begin_inset Formula $E_{\mathrm{kin}}$
\r
37454 \begin_inset Newline newline
\r
37457 Components of matrices are set italic:
\r
37458 \begin_inset Formula $\hat{H}_{kl}$
\r
37464 \begin_layout Itemize
\r
37465 The differentiation/integration operator 'd', the Euler's number 'e' and
\r
37466 the imaginary unit 'i' should be set upright, to avoid mixing them up with
\r
37470 \begin_layout Itemize
\r
37471 The character that denotes a
\r
37475 transformation is inserted either by the command
\r
37483 \begin_layout Plain Layout
\r
37496 Insert\SpecialChar \menuseparator
\r
37497 Special Character\SpecialChar \menuseparator
\r
37498 Symbols\SpecialChar \menuseparator
\r
37500 \begin_inset space ~
\r
37506 \begin_inset Formula $\mathscr{F}$
\r
37512 \begin_layout Standard
\r
37513 \begin_inset Newpage newpage
\r
37519 \begin_layout Section
\r
37521 \begin_inset Index idx
\r
37524 \begin_layout Plain Layout
\r
37533 \begin_layout Standard
\r
37534 Some characters and symbols can be created with several commands.
\r
37535 Here is a list of the synonym commands:
\r
37538 \begin_layout Standard
\r
37539 \begin_inset VSpace bigskip
\r
37543 \begin_inset space \hfill{}
\r
37547 \begin_inset Tabular
\r
37548 <lyxtabular version="3" rows="12" columns="2">
\r
37549 <features tabularvalignment="middle">
\r
37550 <column alignment="center" valignment="top" width="0pt">
\r
37551 <column alignment="center" valignment="top" width="0pt">
\r
37553 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
37554 \begin_inset Text
\r
37556 \begin_layout Plain Layout
\r
37562 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
37563 \begin_inset Text
\r
37565 \begin_layout Plain Layout
\r
37567 \begin_inset Note Note
\r
37570 \begin_layout Plain Layout
\r
37577 is only used as spacer.
\r
37589 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
37590 \begin_inset Text
\r
37592 \begin_layout Plain Layout
\r
37600 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
37601 \begin_inset Text
\r
37603 \begin_layout Plain Layout
\r
37607 \begin_layout Plain Layout
\r
37611 raisebox{-1.2mm}{
\r
37620 \begin_layout Plain Layout
\r
37634 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
37635 \begin_inset Text
\r
37637 \begin_layout Plain Layout
\r
37645 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
37646 \begin_inset Text
\r
37648 \begin_layout Plain Layout
\r
37658 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
37659 \begin_inset Text
\r
37661 \begin_layout Plain Layout
\r
37669 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
37670 \begin_inset Text
\r
37672 \begin_layout Plain Layout
\r
37682 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
37683 \begin_inset Text
\r
37685 \begin_layout Plain Layout
\r
37693 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
37694 \begin_inset Text
\r
37696 \begin_layout Plain Layout
\r
37704 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
37705 \begin_inset Text
\r
37707 \begin_layout Plain Layout
\r
37715 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
37716 \begin_inset Text
\r
37718 \begin_layout Plain Layout
\r
37726 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
37727 \begin_inset Text
\r
37729 \begin_layout Plain Layout
\r
37737 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
37738 \begin_inset Text
\r
37740 \begin_layout Plain Layout
\r
37750 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
37751 \begin_inset Text
\r
37753 \begin_layout Plain Layout
\r
37761 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
37762 \begin_inset Text
\r
37764 \begin_layout Plain Layout
\r
37774 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
37775 \begin_inset Text
\r
37777 \begin_layout Plain Layout
\r
37785 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
37786 \begin_inset Text
\r
37788 \begin_layout Plain Layout
\r
37798 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
37799 \begin_inset Text
\r
37801 \begin_layout Plain Layout
\r
37809 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
37810 \begin_inset Text
\r
37812 \begin_layout Plain Layout
\r
37822 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
37823 \begin_inset Text
\r
37825 \begin_layout Plain Layout
\r
37833 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
37834 \begin_inset Text
\r
37836 \begin_layout Plain Layout
\r
37844 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
37845 \begin_inset Text
\r
37847 \begin_layout Plain Layout
\r
37855 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
37856 \begin_inset Text
\r
37858 \begin_layout Plain Layout
\r
37870 \begin_inset space \hfill{}
\r
37874 \begin_inset Tabular
\r
37875 <lyxtabular version="3" rows="12" columns="2">
\r
37876 <features tabularvalignment="middle">
\r
37877 <column alignment="center" valignment="top" width="0pt">
\r
37878 <column alignment="center" valignment="top" width="0pt">
\r
37880 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
37881 \begin_inset Text
\r
37883 \begin_layout Plain Layout
\r
37889 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
37890 \begin_inset Text
\r
37892 \begin_layout Plain Layout
\r
37900 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
37901 \begin_inset Text
\r
37903 \begin_layout Plain Layout
\r
37911 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
37912 \begin_inset Text
\r
37914 \begin_layout Plain Layout
\r
37926 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
37927 \begin_inset Text
\r
37929 \begin_layout Plain Layout
\r
37937 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
37938 \begin_inset Text
\r
37940 \begin_layout Plain Layout
\r
37950 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
37951 \begin_inset Text
\r
37953 \begin_layout Plain Layout
\r
37961 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
37962 \begin_inset Text
\r
37964 \begin_layout Plain Layout
\r
37974 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
37975 \begin_inset Text
\r
37977 \begin_layout Plain Layout
\r
37985 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
37986 \begin_inset Text
\r
37988 \begin_layout Plain Layout
\r
37996 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
37997 \begin_inset Text
\r
37999 \begin_layout Plain Layout
\r
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38150 \begin_inset Text
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38152 \begin_layout Plain Layout
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38166 \begin_inset space \hfill{}
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38172 \begin_layout Standard
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38173 \begin_inset Newpage newpage
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38179 \begin_layout Bibliography
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38180 \begin_inset CommandInset bibitem
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38193 The LaTeX Companion
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38196 Addison Wesley, 2004
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38201 LatexCommand bibitem
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38207 \begin_inset CommandInset href
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38208 LatexCommand href
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38209 name "Description"
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38210 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
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38214 of LaTeX's math abilities
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38217 \begin_layout Bibliography
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38219 LatexCommand bibitem
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38227 name "Description"
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38228 target "ftp://ftp.ams.org/pub/tex/doc/amsmath/amsldoc.pdf"
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38257 LatexCommand href
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38259 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
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38263 of all symbols available with LaTeX-packages
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38266 \begin_layout Bibliography
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38268 LatexCommand bibitem
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38276 name "Documentation"
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38277 target "http://mirrors.ctan.org/macros/latex/contrib/cancel/cancel.pdf"
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38281 of the LaTeX-package
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38286 \begin_inset Index idx
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38290 Packages ! cancel
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38300 LatexCommand bibitem
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38306 \begin_inset CommandInset href
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38307 LatexCommand href
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38308 name "Documentation"
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38309 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
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38313 of the LaTeX-package
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38322 Packages ! hyperref
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38340 name "Documentation"
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38341 target "http://www.ctan.org/tex-archive/macros/latex/contrib/mhchem/mhchem.pdf"
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38345 of the LaTeX-package
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38354 Packages ! mhchem
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38372 name "Description"
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38373 target "http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf"
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38384 \begin_inset CommandInset ref
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38386 reference "sub:Operator-Limits"
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38391 \begin_inset Index idx
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38418 Auflage, Duden 2001
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38421 \begin_layout Bibliography
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38422 \begin_inset CommandInset bibitem
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38423 LatexCommand bibitem
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38429 \begin_inset CommandInset href
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38430 LatexCommand href
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38431 name "Check list"
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38432 target "http://physics.nist.gov/Document/checklist.pdf"
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38436 for reviewing manuscripts
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38439 \begin_layout Standard
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38440 \begin_inset CommandInset index_print
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38441 LatexCommand printindex
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projects / lyx.git / blob