1 #LyX 2.1 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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151 \font_roman default
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153 \font_typewriter default
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155 \font_default_family default
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156 \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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175 \pdf_bookmarksopen true
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176 \pdf_bookmarksopenlevel 1
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182 \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false"
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184 \use_geometry false
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185 \use_package amsmath 2
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186 \use_package amssymb 2
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187 \use_package cancel 0
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188 \use_package esint 1
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189 \use_package mathdots 1
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190 \use_package mathtools 0
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191 \use_package mhchem 1
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192 \use_package stackrel 0
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193 \use_package stmaryrd 0
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194 \use_package undertilde 0
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196 \cite_engine_type default
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197 \biblio_style plain
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200 \paperorientation portrait
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201 \suppress_date false
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202 \justification true
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204 \notefontcolor #0000ff
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211 \paragraph_separation skip
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213 \quotes_language english
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216 \paperpagestyle plain
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220 \tracking_changes false
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221 \output_changes false
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222 \html_math_output 0
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223 \html_css_as_file 0
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224 \html_be_strict false
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229 \begin_layout Title
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230 LyX's detailed Math manual
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233 \begin_layout Author
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238 \begin_layout Plain Layout
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240 If you have comments or error corrections, please send them to the LyX Documenta
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241 tion mailing list:
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244 \begin_inset CommandInset href
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246 name "lyx-docs@lists.lyx.org"
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247 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
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258 \begin_inset Note Note
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261 \begin_layout Plain Layout
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268 \begin_inset Newline newline
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272 \begin_inset Newline newline
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280 \begin_layout Standard
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281 \begin_inset CommandInset toc
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282 LatexCommand tableofcontents
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289 \begin_layout Standard
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290 \begin_inset Note Note
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293 \begin_layout Plain Layout
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294 To export this document to PDF, PS or DVI the LaTeX-packages
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296 braket, cancel, eurosym, mathdots, mhchem
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302 should be installed.
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303 If they are not installed the document can be exported anyway but the sections
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304 where the packages are required will not appear in the output.
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309 ; if it is not installed, this file cannot be exported.
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312 \begin_layout Plain Layout
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313 The latest PDF-version of this document can be found here:
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314 \begin_inset Newline newline
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319 http://wiki.lyx.org/LyX/DocumentationDevelopment#Math
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327 \begin_layout Standard
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328 \begin_inset Newpage newpage
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334 \begin_layout Section
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338 \begin_layout Standard
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339 This document explains LyX's math features and is furthermore a collection
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340 of LaTeX-commands used for mathematical characters and constructs.
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341 The explanations are designed for the usage of commands.
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342 It is therefore required that you have read the section
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345 \begin_inset space ~
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350 of the User's Guide.
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353 \begin_layout Standard
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354 Most of the characters and many constructs explained in this manual are
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355 also accessible via the menu
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359 \SpecialChar \menuseparator
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375 But everybody who has to write lots of formulas will notice that it is
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376 much faster to use commands instead of the math toolbar.
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377 Therefore this manual is focused on commands but also mentions the correspondin
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378 g toolbar buttons when available.
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381 \begin_layout Standard
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382 If not specially mentioned the commands are only available within formulas.
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383 To be able to use all commands explained in this document, the option
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385 Use AMS math package
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387 must be checked in the document settings (menu
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389 Document\SpecialChar \menuseparator
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390 Settings\SpecialChar \menuseparator
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392 \begin_inset space ~
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401 \begin_layout Plain Layout
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404 Use AMS math package automatically
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410 \begin_layout Plain Layout
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419 -math when math constructs are found that are supported by LyX.
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427 \begin_layout Standard
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428 This document doesn't list all
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432 \begin_layout Plain Layout
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445 \begin_layout Plain Layout
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450 \begin_layout Plain Layout
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459 -math commands is in the file
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462 \begin_inset CommandInset href
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465 target "ftp://ftp.ams.org/pub/tex/doc/amstex/amsguide.pdf"
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471 , which is part of every LaTeX standard installation.
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476 for lucidity reasons.
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479 \begin_layout Section
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480 General Instructions
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483 \begin_layout Standard
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484 To create an inline formula
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485 \begin_inset Index idx
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488 \begin_layout Plain Layout
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494 that is embedded into a text line, use one of the shortcuts
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500 or the toolbar button
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501 \begin_inset Graphics
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502 filename ../images/math-mode.png
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508 \begin_inset Newline newline
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511 To create a display style formula
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512 \begin_inset Index idx
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515 \begin_layout Plain Layout
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516 Formula ! display style
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521 which will appear bigger, has a different format, and will be in a separate
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522 paragraph, use one of these shortcuts:
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531 \begin_layout Standard
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532 To change a display style formula to an inline formula, set the cursor into
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533 the formula and use one of the shortcuts
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541 Edit\SpecialChar \menuseparator
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542 Math\SpecialChar \menuseparator
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543 Change formula type
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546 The same way is used to change an inline formula to a display style formula.
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549 \begin_layout Standard
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550 To display parts of an inline formula in the size of a display style formula,
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558 \begin_inset Index idx
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561 \begin_layout Plain Layout
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570 Then a new blue box appears in which the desired formula part is inserted.
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573 \begin_layout Standard
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574 Only inline formulas are allowed inside tables.
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577 \begin_layout Standard
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582 can be turned on in the menu
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584 View\SpecialChar \menuseparator
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588 When you click there on
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589 \begin_inset Quotes eld
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593 \begin_inset Quotes erd
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596 the toolbar will be shown permanently at the bottom; this state is visualized
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601 menu with a checkmark.
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602 When you click in this state again on
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603 \begin_inset Quotes eld
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607 \begin_inset Quotes erd
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618 is only shown when the cursor is within a formula; this state is visualized
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619 by the renaming of the menu entry from
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620 \begin_inset Quotes eld
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624 \begin_inset Quotes erd
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628 \begin_inset Quotes eld
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632 \begin_inset space ~
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636 \begin_inset Quotes erd
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642 \begin_layout Standard
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644 \begin_inset Index idx
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647 \begin_layout Plain Layout
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653 is invoked by pressing the toolbar button
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654 \begin_inset Graphics
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655 filename ../images/ert-insert.png
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660 or by using the menu
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662 Insert\SpecialChar \menuseparator
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667 \begin_layout Plain Layout
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683 \begin_inset Note Note
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686 \begin_layout Plain Layout
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687 In LyX there are three
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688 \begin_inset Quotes eld
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692 \begin_inset Quotes erd
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695 that appear in the output with sub- and superscript letters: TeX, LaTeX
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699 \begin_layout Plain Layout
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700 To avoid that these names are recognized as proper names, a TeX-brace pair
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709 \begin_layout Standard
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710 To change the LaTeX-preamble
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711 \begin_inset Index idx
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714 \begin_layout Plain Layout
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722 Document\SpecialChar \menuseparator
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723 Settings\SpecialChar \menuseparator
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728 \begin_layout Plain Layout
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744 \begin_layout Standard
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745 To edit matrices, case differentiations and multiline formulas subsequently,
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748 Edit\SpecialChar \menuseparator
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753 Edit\SpecialChar \menuseparator
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755 \begin_inset space \thinspace{}
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759 \begin_inset space \thinspace{}
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769 When lines and columns are swapped via the menu, the column or line where
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770 the cursor is in is exchanged with the column to the right or the line
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771 below, respectively.
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772 Is the cursor in the last column or row, the exchange is done with the
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773 column to the left or the line above.
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776 \begin_layout Standard
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777 To write text in formulas
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781 \begin_layout Plain Layout
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782 For multiline formulas the command
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789 \begin_inset CommandInset ref
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791 reference "sub:Text-in-multiline"
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805 \begin_inset Index idx
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808 \begin_layout Plain Layout
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815 \begin_inset Index idx
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818 \begin_layout Plain Layout
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825 This mode is invoked with the shortcut
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831 or by the insertion of the command
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838 \begin_inset Index idx
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841 \begin_layout Plain Layout
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850 The text appears black in LyX and can therefore be distinguished from the
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851 other formula parts which appear blue.
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852 In the output mathematical text is set upright, in contrary to other formula
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856 \begin_layout Subsection*
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860 \begin_layout Standard
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861 Most of the LaTeX-commands for math constructs have the following scheme:
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864 \begin_layout Standard
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869 commandname[optional
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880 \begin_layout Standard
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881 A command always starts with a backslash
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882 \begin_inset Quotes gld
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892 \begin_inset Quotes grd
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896 To omit optional arguments, also omit the associated brackets.
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897 The braces around the required arguments are named in this document as
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899 \begin_inset Index idx
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902 \begin_layout Plain Layout
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909 If you add in a formula a left brace to a command name, LyX automatically
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910 creates a TeX-brace.
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911 In all other cases TeX-braces are created in formulas with the command
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919 TeX-braces appear red in LyX, in contrary to normal braces which appear
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921 In TeX-mode no command is needed to get TeX-braces.
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922 TeX-braces don't appear in the output.
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925 \begin_layout Standard
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926 When commands without arguments, like commands for symbols are entered in
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927 TeX-mode, a space character must
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931 be behind the command to end it.
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932 This space doesn't appear in the output.
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933 When the space should appear in the output, the space must be followed
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934 by a protected space in normal text.
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937 \begin_layout Standard
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938 A protected space is inserted with
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941 arg "command-alternatives space-insert protected ; math-space"
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947 \begin_layout Subsection*
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948 \begin_inset Newpage newpage
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954 \begin_layout Itemize
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959 \begin_layout Plain Layout
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960 This visible space character can be created with the command
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967 \begin_inset Index idx
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970 \begin_layout Plain Layout
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978 , inserted in TeX-mode.
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987 \begin_layout Plain Layout
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997 \begin_inset space ~
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1000 denotes a space character to be input.
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1003 \begin_layout Itemize
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1005 \begin_inset Formula $\to$
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1008 denotes the usage of the corresponding arrow key on the keyboard.
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1013 key can often be used instead of
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1014 \begin_inset Formula $\to$
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1018 \begin_inset Formula $\downarrow$
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1026 \begin_inset Formula $\leftarrow$
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1030 \begin_inset Formula $\uparrow$
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1036 \begin_layout Subsection*
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1040 \begin_layout Standard
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1042 \begin_inset Float table
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1048 \begin_layout Plain Layout
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1052 \begin_layout Plain Layout
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1054 LatexCommand label
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1200 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
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1203 \begin_layout Plain Layout
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1209 \begin_inset space \thinspace{}
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1231 \begin_layout Plain Layout
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1232 scaled point (65536
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1256 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
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1259 \begin_layout Plain Layout
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1261 \begin_inset space \thinspace{}
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1265 \begin_inset space \thinspace{}
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1284 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
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1287 \begin_layout Plain Layout
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1289 \begin_inset space \thinspace{}
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1293 \begin_inset Formula $\approx$
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1297 \begin_inset space \thinspace{}
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1307 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
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1310 \begin_layout Plain Layout
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1325 \begin_inset space \thinspace{}
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1338 \begin_layout Plain Layout
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1344 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
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1347 \begin_layout Plain Layout
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1351 \begin_inset Quotes eld
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1357 \begin_inset Quotes erd
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1376 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
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1379 \begin_layout Plain Layout
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1381 \begin_inset Quotes eld
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1389 \begin_inset Quotes erd
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1392 in the current font
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1399 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
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1402 \begin_layout Plain Layout
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1408 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
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1411 \begin_layout Plain Layout
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1413 \begin_inset space \thinspace{}
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1417 \begin_inset Formula $\nicefrac{1}{18}$
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1421 \begin_inset space \thinspace{}
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1442 \begin_layout Standard
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1443 \begin_inset Newpage newpage
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1449 \begin_layout Section
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1453 \begin_layout Subsection
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1458 \begin_layout Plain Layout
\r
1465 \begin_inset Index idx
\r
1468 \begin_layout Plain Layout
\r
1475 \begin_inset Index idx
\r
1478 \begin_layout Plain Layout
\r
1483 \begin_layout Plain Layout
\r
1494 \begin_layout Plain Layout
\r
1507 \begin_inset Index idx
\r
1510 \begin_layout Plain Layout
\r
1515 \begin_layout Plain Layout
\r
1526 \begin_layout Plain Layout
\r
1541 \begin_layout Standard
\r
1542 Indices are created with an underscore
\r
1543 \begin_inset Quotes eld
\r
1547 \begin_inset Quotes erd
\r
1550 or via the math toolbar button
\r
1551 \begin_inset Graphics
\r
1552 filename ../images/math-subscript.png
\r
1557 , exponents with a caret
\r
1558 \begin_inset Quotes eld
\r
1562 \begin_inset Quotes erd
\r
1565 or via the math toolbar button
\r
1566 \begin_inset Graphics
\r
1567 filename ../images/math-superscript.png
\r
1575 \begin_layout Standard
\r
1577 \begin_inset Tabular
\r
1578 <lyxtabular version="3" rows="4" columns="2">
\r
1579 <features rotate="0" tabularvalignment="middle">
\r
1580 <column alignment="center" valignment="top" width="0pt">
\r
1581 <column alignment="center" valignment="top" width="0pt">
\r
1583 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
1586 \begin_layout Plain Layout
\r
1592 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
1595 \begin_layout Plain Layout
\r
1597 \begin_inset Note Note
\r
1600 \begin_layout Plain Layout
\r
1607 is only used as spacer.
\r
1619 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
1622 \begin_layout Plain Layout
\r
1628 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
1631 \begin_layout Plain Layout
\r
1632 \begin_inset Formula $B_{V}$
\r
1642 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
1645 \begin_layout Plain Layout
\r
1651 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
1654 \begin_layout Plain Layout
\r
1655 \begin_inset Formula $\raisebox{5mm}{}B^{V}$
\r
1665 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
1668 \begin_layout Plain Layout
\r
1673 \begin_layout Plain Layout
\r
1687 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
1690 \begin_layout Plain Layout
\r
1691 \begin_inset Formula $\raisebox{5mm}{}B^{A}$
\r
1707 \begin_layout Standard
\r
1708 As the caret is in some languages an accent, vowels will be accentuated
\r
1709 in this case and not set as exponents
\r
1713 \begin_layout Plain Layout
\r
1714 Depending on the used keyboard settings this can also happen for characters
\r
1715 other than vowels.
\r
1721 To get exponents in this case, press
\r
1725 after the caret as in the last example.
\r
1728 \begin_layout Subsection
\r
1730 \begin_inset CommandInset label
\r
1731 LatexCommand label
\r
1732 name "sub:Fractions"
\r
1737 \begin_inset Index idx
\r
1740 \begin_layout Plain Layout
\r
1749 \begin_layout Standard
\r
1750 Fractions are generated with the command
\r
1757 \begin_inset Index idx
\r
1760 \begin_layout Plain Layout
\r
1768 or via the math toolbar button
\r
1769 \begin_inset Graphics
\r
1770 filename ../images/math/frac.png
\r
1776 The font size is adjusted automatically, depending on whether the fraction
\r
1777 is in an inline or display style formula.
\r
1778 With the math toolbar button
\r
1779 \begin_inset Graphics
\r
1780 filename ../images/math/frac-square.png
\r
1785 you can select different fraction types.
\r
1788 \begin_layout Standard
\r
1796 \begin_inset Index idx
\r
1799 \begin_layout Plain Layout
\r
1807 a fraction can be created that always has the size of a display style formula.
\r
1815 \begin_inset Index idx
\r
1818 \begin_layout Plain Layout
\r
1826 the fraction appears always with the size of an inline formula.
\r
1830 \begin_layout Standard
\r
1831 A line with the fraction
\r
1832 \begin_inset Formula $\frac{1}{2}$
\r
1835 that was created with the command
\r
1844 \begin_layout Standard
\r
1845 A line with the fraction
\r
1846 \begin_inset Formula $\dfrac{1}{2}$
\r
1849 that was created with the command
\r
1858 \begin_layout Standard
\r
1860 \begin_inset Tabular
\r
1861 <lyxtabular version="3" rows="4" columns="2">
\r
1862 <features rotate="0" tabularvalignment="middle">
\r
1863 <column alignment="center" valignment="top" width="0pt">
\r
1864 <column alignment="center" valignment="top" width="0pt">
\r
1866 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
1869 \begin_layout Plain Layout
\r
1875 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
1878 \begin_layout Plain Layout
\r
1880 \begin_inset Note Note
\r
1883 \begin_layout Plain Layout
\r
1890 is only used as spacer.
\r
1902 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
1905 \begin_layout Plain Layout
\r
1912 \begin_layout Plain Layout
\r
1922 \begin_inset Formula $\downarrow$
\r
1930 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
1933 \begin_layout Plain Layout
\r
1934 \begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$
\r
1944 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
1947 \begin_layout Plain Layout
\r
1954 \begin_layout Plain Layout
\r
1964 \begin_inset Formula $\downarrow$
\r
1972 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
1975 \begin_layout Plain Layout
\r
1976 \begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$
\r
1986 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
1989 \begin_layout Plain Layout
\r
1996 \begin_layout Plain Layout
\r
2011 \begin_layout Plain Layout
\r
2021 \begin_inset Formula $\downarrow$
\r
2025 \begin_inset Formula $\downarrow\downarrow$
\r
2033 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
2036 \begin_layout Plain Layout
\r
2037 \begin_inset Formula $\raisebox{8mm}{}\dfrac{e^{\frac{1}{2}}}{3}\raisebox{-4mm}{}$
\r
2053 \begin_layout Standard
\r
2054 \begin_inset VSpace bigskip
\r
2058 \begin_inset Newpage newpage
\r
2061 For nested fractions the command
\r
2068 \begin_inset Index idx
\r
2071 \begin_layout Plain Layout
\r
2080 Here is an example:
\r
2081 \begin_inset VSpace -3mm
\r
2087 \begin_layout Standard
\r
2088 \begin_inset Formula
\r
2090 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
\r
2091 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}
\r
2099 \begin_layout Standard
\r
2100 The command for the example above is:
\r
2103 \begin_layout Standard
\r
2112 \begin_layout Plain Layout
\r
2122 \begin_inset Formula $\downarrow$
\r
2131 \begin_layout Plain Layout
\r
2146 \begin_layout Plain Layout
\r
2156 \begin_inset Formula $\downarrow$
\r
2160 \begin_inset Formula $\downarrow$
\r
2166 \begin_layout Standard
\r
2167 \begin_inset VSpace medskip
\r
2173 \begin_layout Standard
\r
2180 sets the fraction always in the size of a displayed formula, also when
\r
2181 it is part of another fraction.
\r
2184 \begin_layout Standard
\r
2185 It is possible to specify the alignment of the numerator.
\r
2192 is used to left align it, the command
\r
2198 to right-align it.
\r
2205 centers the numerator.
\r
2206 These fractions demonstrate the different alignments:
\r
2209 \begin_layout Standard
\r
2212 \begin_inset Formula
\r
2214 \cfrac[l]{A}{B+C}\,,\,\cfrac{A}{B+C}\,,\,\cfrac[r]{A}{B+C}
\r
2222 \begin_layout Standard
\r
2223 \begin_inset Note Greyedout
\r
2226 \begin_layout Plain Layout
\r
2243 are no real LaTeX commands but represent the command
\r
2247 cfrac[alignment]{numerator}{denominator}
\r
2250 Therefore you cannot use them in TeX code.
\r
2258 \begin_layout Standard
\r
2259 \begin_inset VSpace medskip
\r
2262 It is often advantageous to combine
\r
2275 \begin_inset Formula
\r
2277 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}
\r
2285 \begin_layout Standard
\r
2286 For inline fractions with a sloped fraction stroke you can use the command
\r
2294 \begin_inset Index idx
\r
2297 \begin_layout Plain Layout
\r
2306 \begin_inset Formula $\nicefrac{5}{31}$
\r
2316 \begin_inset Index idx
\r
2319 \begin_layout Plain Layout
\r
2328 \begin_inset Formula $\unitfrac{5}{31}$
\r
2331 There is furthermore the command
\r
2337 that offers to write a fraction in combination with a number:
\r
2338 \begin_inset Formula $\unitfrac[2]{1}{3}$
\r
2344 \begin_layout Standard
\r
2345 \begin_inset Note Greyedout
\r
2348 \begin_layout Plain Layout
\r
2359 is not a real LaTeX command but the command
\r
2360 \begin_inset Newline newline
\r
2367 unitfrac[number]{numerator}{denominator}
\r
2370 Therefore you cannot use it in TeX code.
\r
2378 \begin_layout Standard
\r
2379 How to define own fractions where the fraction stroke can be changed, is
\r
2381 \begin_inset CommandInset ref
\r
2383 reference "sub:Self-defined-Fractions"
\r
2390 \begin_layout Standard
\r
2391 \begin_inset Newpage newpage
\r
2397 \begin_layout Subsection
\r
2399 \begin_inset Index idx
\r
2402 \begin_layout Plain Layout
\r
2411 \begin_layout Standard
\r
2412 Square roots are created with
\r
2419 \begin_inset Index idx
\r
2422 \begin_layout Plain Layout
\r
2430 or the math toolbar button
\r
2431 \begin_inset Graphics
\r
2432 filename ../images/math/sqrt.png
\r
2437 , all other roots with the command
\r
2444 \begin_inset Index idx
\r
2447 \begin_layout Plain Layout
\r
2455 or with the math toolbar button
\r
2456 \begin_inset Graphics
\r
2457 filename ../images/math/root.png
\r
2465 \begin_layout Standard
\r
2467 \begin_inset Tabular
\r
2468 <lyxtabular version="3" rows="3" columns="2">
\r
2469 <features rotate="0" tabularvalignment="middle">
\r
2470 <column alignment="center" valignment="top" width="0pt">
\r
2471 <column alignment="center" valignment="top" width="0pt">
\r
2473 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
2476 \begin_layout Plain Layout
\r
2482 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
2485 \begin_layout Plain Layout
\r
2487 \begin_inset Note Note
\r
2490 \begin_layout Plain Layout
\r
2497 is only used as spacer.
\r
2509 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
2512 \begin_layout Plain Layout
\r
2519 \begin_layout Plain Layout
\r
2533 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
2536 \begin_layout Plain Layout
\r
2537 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$
\r
2547 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
2550 \begin_layout Plain Layout
\r
2557 \begin_layout Plain Layout
\r
2567 \begin_inset Formula $\downarrow$
\r
2575 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
2578 \begin_layout Plain Layout
\r
2579 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$
\r
2595 \begin_layout Standard
\r
2596 A square root can also be created with
\r
2602 when the root index field is left empty.
\r
2605 \begin_layout Standard
\r
2606 With certain indices the distance to the root is too small, like in this
\r
2608 \begin_inset Formula $\sqrt[\beta]{B}$
\r
2612 \begin_inset Newline newline
\r
2616 \begin_inset Formula $\beta$
\r
2620 To avoid this, the commands
\r
2627 \begin_inset Index idx
\r
2630 \begin_layout Plain Layout
\r
2645 \begin_inset Index idx
\r
2648 \begin_layout Plain Layout
\r
2656 are used with the following scheme:
\r
2659 \begin_layout Standard
\r
2664 leftroot{distance}
\r
2673 \begin_layout Standard
\r
2674 Distance is the number of Big Points (unit bp;
\r
2675 \begin_inset Formula $\mathrm{72\, bp=1\, inch}$
\r
2678 ), that the index should be moved to the left or top, resp..
\r
2679 The commands are written to the index.
\r
2680 This way the command
\r
2681 \begin_inset Newline newline
\r
2691 \begin_inset Formula $\to$
\r
2697 \begin_inset Formula $\to$
\r
2706 \begin_layout Plain Layout
\r
2716 \begin_inset Formula $\to$
\r
2720 \begin_inset Newline newline
\r
2725 produces a correct typeset formula:
\r
2726 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
\r
2732 \begin_layout Subsection
\r
2733 Binomial Coefficients
\r
2734 \begin_inset Index idx
\r
2737 \begin_layout Plain Layout
\r
2738 Binomial coefficients
\r
2746 \begin_layout Standard
\r
2747 Binomial coefficients are inserted with the command
\r
2754 \begin_inset Index idx
\r
2757 \begin_layout Plain Layout
\r
2765 or with the submenu of the math toolbar button
\r
2766 \begin_inset Graphics
\r
2767 filename ../images/math/frac-square.png
\r
2773 As with fractions (
\r
2785 there are the commands
\r
2792 \begin_inset Index idx
\r
2795 \begin_layout Plain Layout
\r
2810 \begin_inset Index idx
\r
2813 \begin_layout Plain Layout
\r
2822 For other brackets around binomial coeficients there are the commands
\r
2829 \begin_inset Index idx
\r
2832 \begin_layout Plain Layout
\r
2847 \begin_inset Index idx
\r
2850 \begin_layout Plain Layout
\r
2861 \begin_layout Standard
\r
2863 \begin_inset Tabular
\r
2864 <lyxtabular version="3" rows="6" columns="2">
\r
2865 <features rotate="0" tabularvalignment="middle">
\r
2866 <column alignment="center" valignment="top" width="0pt">
\r
2867 <column alignment="center" valignment="top" width="0pt">
\r
2869 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
2872 \begin_layout Plain Layout
\r
2878 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
2881 \begin_layout Plain Layout
\r
2883 \begin_inset Note Note
\r
2886 \begin_layout Plain Layout
\r
2893 is only used as spacer.
\r
2905 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
2908 \begin_layout Plain Layout
\r
2915 \begin_layout Plain Layout
\r
2925 \begin_inset Formula $\downarrow$
\r
2933 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
2936 \begin_layout Plain Layout
\r
2937 \begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$
\r
2947 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
2950 \begin_layout Plain Layout
\r
2957 \begin_layout Plain Layout
\r
2967 \begin_inset Formula $\downarrow$
\r
2975 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
2978 \begin_layout Plain Layout
\r
2979 \begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$
\r
2989 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
2992 \begin_layout Plain Layout
\r
2999 \begin_layout Plain Layout
\r
3009 \begin_inset Formula $\downarrow$
\r
3017 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
3020 \begin_layout Plain Layout
\r
3021 \begin_inset Formula $\raisebox{5mm}{}\tbinom{A}{B}\raisebox{-2.5mm}{}$
\r
3031 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
3034 \begin_layout Plain Layout
\r
3041 \begin_layout Plain Layout
\r
3051 \begin_inset Formula $\downarrow$
\r
3059 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
3062 \begin_layout Plain Layout
\r
3063 \begin_inset Formula $\raisebox{5mm}{}{A \brack B}\raisebox{-2.5mm}{}$
\r
3073 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
3076 \begin_layout Plain Layout
\r
3083 \begin_layout Plain Layout
\r
3093 \begin_inset Formula $\downarrow$
\r
3101 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
3104 \begin_layout Plain Layout
\r
3105 \begin_inset Formula $\raisebox{5mm}{}{A \brace B}\raisebox{-2.5mm}{}$
\r
3121 \begin_layout Subsection
\r
3122 Case Differentiations
\r
3123 \begin_inset Index idx
\r
3126 \begin_layout Plain Layout
\r
3127 Case differentiations
\r
3135 \begin_layout Standard
\r
3137 \begin_inset Tabular
\r
3138 <lyxtabular version="3" rows="3" columns="2">
\r
3139 <features rotate="0" tabularvalignment="middle">
\r
3140 <column alignment="center" valignment="top" width="0pt">
\r
3141 <column alignment="center" valignment="top" width="0pt">
\r
3143 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
3146 \begin_layout Plain Layout
\r
3152 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
3155 \begin_layout Plain Layout
\r
3163 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
3166 \begin_layout Plain Layout
\r
3173 \begin_layout Plain Layout
\r
3183 \begin_inset Formula $\to$
\r
3187 \begin_inset Index idx
\r
3190 \begin_layout Plain Layout
\r
3203 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
3206 \begin_layout Plain Layout
\r
3207 \begin_inset Formula $\begin{cases}
\r
3208 A & B>0\end{cases}$
\r
3218 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
3221 \begin_layout Plain Layout
\r
3228 \begin_layout Plain Layout
\r
3240 arg "newline-insert newline"
\r
3248 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
3251 \begin_layout Plain Layout
\r
3252 \begin_inset Formula $\begin{cases}
\r
3253 A & \textrm{for }x>0\\
\r
3254 B & \textrm{for }x=0
\r
3271 \begin_layout Standard
\r
3278 or pressing the math toolbar button
\r
3279 \begin_inset Graphics
\r
3280 filename ../images/math/cases.png
\r
3285 you can create new lines with the shortcut
\r
3288 arg "newline-insert newline"
\r
3291 or the table toolbar button
\r
3292 \begin_inset Graphics
\r
3293 filename ../images/tabular-feature_append-row.png
\r
3301 \begin_layout Standard
\r
3308 is also available via the menu
\r
3310 Insert\SpecialChar \menuseparator
\r
3311 Math\SpecialChar \menuseparator
\r
3317 \begin_layout Subsection
\r
3319 \begin_inset Index idx
\r
3322 \begin_layout Plain Layout
\r
3331 \begin_layout Standard
\r
3339 \begin_inset Index idx
\r
3342 \begin_layout Plain Layout
\r
3350 every character can be displayed canceled.
\r
3351 The characters are quasi accentuated by a slash.
\r
3354 \begin_layout Standard
\r
3356 \begin_inset Tabular
\r
3357 <lyxtabular version="3" rows="4" columns="2">
\r
3358 <features rotate="0" tabularvalignment="middle">
\r
3359 <column alignment="center" valignment="top" width="0pt">
\r
3360 <column alignment="center" valignment="top" width="0pt">
\r
3362 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
3365 \begin_layout Plain Layout
\r
3371 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
3374 \begin_layout Plain Layout
\r
3382 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
3385 \begin_layout Plain Layout
\r
3393 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
3396 \begin_layout Plain Layout
\r
3397 \begin_inset Formula $\not=$
\r
3407 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
3410 \begin_layout Plain Layout
\r
3420 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
3423 \begin_layout Plain Layout
\r
3424 \begin_inset Formula $\not\le$
\r
3434 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
3437 \begin_layout Plain Layout
\r
3447 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
3450 \begin_layout Plain Layout
\r
3451 \begin_inset Formula $\not\parallel$
\r
3467 \begin_layout Standard
\r
3468 The last example shows that not all negations look good.
\r
3469 Therefore there are special commands for some negations (see
\r
3470 \begin_inset CommandInset ref
\r
3472 reference "sub:Mathematical-Symbols"
\r
3477 \begin_inset CommandInset ref
\r
3479 reference "sec:Relations"
\r
3486 \begin_layout Subsection
\r
3488 \begin_inset CommandInset label
\r
3489 LatexCommand label
\r
3490 name "sub:Placeholders"
\r
3495 \begin_inset Index idx
\r
3498 \begin_layout Plain Layout
\r
3505 \begin_inset Index idx
\r
3508 \begin_layout Plain Layout
\r
3509 Chemical characters ! Isotopes
\r
3515 \begin_inset Index idx
\r
3518 \begin_layout Plain Layout
\r
3523 \begin_layout Plain Layout
\r
3530 Chemical characters
\r
3534 \begin_layout Plain Layout
\r
3549 \begin_layout Standard
\r
3550 When displaying e.
\r
3551 \begin_inset space \thinspace{}
\r
3555 \begin_inset space \space{}
\r
3562 \begin_layout Plain Layout
\r
3563 Typesetting isotopes and chemical symbols is described in
\r
3564 \begin_inset CommandInset ref
\r
3566 reference "sub:Chemical-Symbols-and"
\r
3575 the following problem occurs:
\r
3578 \begin_layout Standard
\r
3580 \begin_inset Tabular
\r
3581 <lyxtabular version="3" rows="2" columns="2">
\r
3582 <features rotate="0" tabularvalignment="middle">
\r
3583 <column alignment="center" valignment="top" width="0pt">
\r
3584 <column alignment="center" valignment="top" width="0pt">
\r
3586 <cell alignment="center" valignment="top" usebox="none">
\r
3589 \begin_layout Plain Layout
\r
3590 Indices created with sub- and superscripts:
\r
3595 <cell alignment="center" valignment="top" usebox="none">
\r
3598 \begin_layout Plain Layout
\r
3599 \begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
\r
3609 <cell alignment="center" valignment="top" usebox="none">
\r
3612 \begin_layout Plain Layout
\r
3618 <cell alignment="center" valignment="top" usebox="none">
\r
3621 \begin_layout Plain Layout
\r
3622 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
\r
3636 \begin_inset Note Note
\r
3639 \begin_layout Plain Layout
\r
3646 is only used as spacer.
\r
3654 \begin_layout Standard
\r
3655 The shorter index is by default placed below or above the first character
\r
3656 of the longer index.
\r
3657 To avoid this there is the command
\r
3664 \begin_inset Index idx
\r
3667 \begin_layout Plain Layout
\r
3675 or the math toolbar button
\r
3676 \begin_inset space \thinspace{}
\r
3683 \begin_layout Plain Layout
\r
3684 can be found in the submenu of the toolbar button
\r
3685 \begin_inset Graphics
\r
3686 filename ../images/math/space.png
\r
3697 \begin_inset Graphics
\r
3698 filename ../images/math/phantom.png
\r
3703 that creates one or more phantom characters.
\r
3710 a small blue box appears that is superposed with two red arrows.
\r
3711 The arrows indicate that the complete width and height of the box content
\r
3712 will be created as placeholder.
\r
3713 Phantom characters are accordingly placeholders with the size of the characters.
\r
3716 \begin_layout Standard
\r
3718 \begin_inset Tabular
\r
3719 <lyxtabular version="3" rows="4" columns="2">
\r
3720 <features rotate="0" tabularvalignment="middle">
\r
3721 <column alignment="center" valignment="top">
\r
3722 <column alignment="center" valignment="top">
\r
3724 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
3727 \begin_layout Plain Layout
\r
3733 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
3736 \begin_layout Plain Layout
\r
3738 \begin_inset Note Note
\r
3741 \begin_layout Plain Layout
\r
3748 is only used as spacer.
\r
3760 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
3763 \begin_layout Plain Layout
\r
3768 \begin_layout Plain Layout
\r
3783 \begin_layout Plain Layout
\r
3793 \begin_inset Formula $\to$
\r
3800 \begin_layout Plain Layout
\r
3814 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
3817 \begin_layout Plain Layout
\r
3818 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
\r
3828 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
3831 \begin_layout Plain Layout
\r
3836 \begin_layout Plain Layout
\r
3851 \begin_layout Plain Layout
\r
3861 \begin_inset Formula $\to$
\r
3868 \begin_layout Plain Layout
\r
3882 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
3885 \begin_layout Plain Layout
\r
3886 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
\r
3896 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
3899 \begin_layout Plain Layout
\r
3906 \begin_layout Plain Layout
\r
3921 \begin_layout Plain Layout
\r
3931 \begin_inset Formula $\to$
\r
3938 \begin_layout Plain Layout
\r
3952 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
3955 \begin_layout Plain Layout
\r
3956 \begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
\r
3972 \begin_layout Standard
\r
3973 Furthermore there are the commands
\r
3980 \begin_inset Index idx
\r
3983 \begin_layout Plain Layout
\r
3992 \begin_inset space ~
\r
3996 \begin_inset Graphics
\r
3997 filename ../images/math/vphantom.png
\r
4009 \begin_inset Index idx
\r
4012 \begin_layout Plain Layout
\r
4021 \begin_inset space ~
\r
4025 \begin_inset Graphics
\r
4026 filename ../images/math/hphantom.png
\r
4038 creates only space for the maximal height of the characters in the box
\r
4039 but not for its width.
\r
4046 creates only space for the width of the box content.
\r
4047 Therefore the boxes of both commands have only one red arrow.
\r
4050 \begin_layout Standard
\r
4051 For example the command
\r
4061 \begin_layout Plain Layout
\r
4076 creates space for the height of the integral sign,
\r
4080 \begin_layout Plain Layout
\r
4087 creates an integral sign, see
\r
4088 \begin_inset CommandInset ref
\r
4090 reference "sub:Big-Operators"
\r
4099 because this is the larger character.
\r
4100 An example application is in
\r
4101 \begin_inset CommandInset ref
\r
4103 reference "sub:Multiline-Brackets"
\r
4110 \begin_layout Standard
\r
4111 Placeholders can also be used for text when they are inserted via the menu
\r
4114 Insert\SpecialChar \menuseparator
\r
4115 Formatting\SpecialChar \menuseparator
\r
4121 \begin_layout Standard
\r
4122 This is a sentence.
\r
4123 \begin_inset Newline newline
\r
4127 \begin_inset Phantom Phantom
\r
4130 \begin_layout Plain Layout
\r
4139 \begin_layout Subsection
\r
4141 \begin_inset Index idx
\r
4144 \begin_layout Plain Layout
\r
4151 \begin_inset Index idx
\r
4154 \begin_layout Plain Layout
\r
4155 Formula ! underlined
\r
4163 \begin_layout Standard
\r
4165 \begin_inset Tabular
\r
4166 <lyxtabular version="3" rows="4" columns="2">
\r
4167 <features rotate="0" tabularvalignment="middle">
\r
4168 <column alignment="center" valignment="top" width="0pt">
\r
4169 <column alignment="center" valignment="top" width="0pt">
\r
4171 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
4174 \begin_layout Plain Layout
\r
4180 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
4183 \begin_layout Plain Layout
\r
4185 \begin_inset Note Note
\r
4188 \begin_layout Plain Layout
\r
4195 is only used as spacer.
\r
4207 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
4210 \begin_layout Plain Layout
\r
4217 \begin_layout Plain Layout
\r
4227 \begin_inset Index idx
\r
4230 \begin_layout Plain Layout
\r
4243 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
4246 \begin_layout Plain Layout
\r
4247 \begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
\r
4257 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
4260 \begin_layout Plain Layout
\r
4267 \begin_layout Plain Layout
\r
4277 \begin_inset Index idx
\r
4280 \begin_layout Plain Layout
\r
4293 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
4296 \begin_layout Plain Layout
\r
4297 \begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
\r
4307 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
4310 \begin_layout Plain Layout
\r
4317 \begin_layout Plain Layout
\r
4332 \begin_layout Plain Layout
\r
4346 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
4349 \begin_layout Plain Layout
\r
4350 \begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
\r
4366 \begin_layout Standard
\r
4367 In the last example it doesn't matter if first
\r
4382 \begin_layout Standard
\r
4383 To double underline use
\r
4392 \begin_layout Standard
\r
4393 It is possible to place up to 6 lines above or below characters.
\r
4396 \begin_layout Standard
\r
4397 \begin_inset VSpace bigskip
\r
4400 Custom lines can be created using the command
\r
4407 \begin_inset Index idx
\r
4410 \begin_layout Plain Layout
\r
4418 which has the following scheme:
\r
4421 \begin_layout Standard
\r
4426 rule[vertical offset]{length}{thickness}
\r
4429 \begin_layout Standard
\r
4430 The optional vertical offset shifts the line upwards (or downwards, when
\r
4431 the value is negative).
\r
4432 The units listed in
\r
4433 \begin_inset CommandInset ref
\r
4435 reference "tab:Available-units"
\r
4439 can be used for the values.
\r
4440 Here are two example lines created with the commands
\r
4441 \begin_inset Newline newline
\r
4448 rule[-2ex]{3cm}{2pt}
\r
4459 \begin_layout Standard
\r
4460 This is a sentence
\r
4461 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
\r
4467 \begin_layout Standard
\r
4474 can also be used for text when a line is inserted via the menu
\r
4476 Insert\SpecialChar \menuseparator
\r
4477 Formatting\SpecialChar \menuseparator
\r
4479 \begin_inset space ~
\r
4487 \begin_layout Standard
\r
4488 This is a sentence
\r
4489 \begin_inset CommandInset line
\r
4500 \begin_layout Subsection
\r
4502 \begin_inset CommandInset label
\r
4503 LatexCommand label
\r
4504 name "sub:Ellipses"
\r
4509 \begin_inset Index idx
\r
4512 \begin_layout Plain Layout
\r
4521 \begin_layout Standard
\r
4522 There are different types of ellipses available.
\r
4526 \begin_layout Plain Layout
\r
4527 In the math toolbar in the submenu of the button
\r
4528 \begin_inset Graphics
\r
4529 filename ../images/math/ldots.png
\r
4539 For listings dots at the baseline are used (
\r
4546 \begin_inset Index idx
\r
4549 \begin_layout Plain Layout
\r
4557 ), while for operations dots are needed that are on the same height as the
\r
4565 \begin_inset Index idx
\r
4568 \begin_layout Plain Layout
\r
4577 When using the command
\r
4584 \begin_inset Index idx
\r
4587 \begin_layout Plain Layout
\r
4595 , LaTeX decides on the basis of the next character what type is used.
\r
4598 \begin_layout Standard
\r
4600 \begin_inset Tabular
\r
4601 <lyxtabular version="3" rows="9" columns="2">
\r
4602 <features rotate="0" tabularvalignment="middle">
\r
4603 <column alignment="center" valignment="top" width="0pt">
\r
4604 <column alignment="center" valignment="top" width="0pt">
\r
4606 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
4609 \begin_layout Plain Layout
\r
4615 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
4618 \begin_layout Plain Layout
\r
4626 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
4629 \begin_layout Plain Layout
\r
4634 \begin_layout Plain Layout
\r
4649 \begin_layout Plain Layout
\r
4663 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
4666 \begin_layout Plain Layout
\r
4667 \begin_inset Formula $A_{1},\dots,A_{n}$
\r
4677 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
4680 \begin_layout Plain Layout
\r
4685 \begin_layout Plain Layout
\r
4700 \begin_layout Plain Layout
\r
4714 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
4717 \begin_layout Plain Layout
\r
4718 \begin_inset Formula $A_{1}+\dots+A_{n}$
\r
4728 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
4731 \begin_layout Plain Layout
\r
4736 \begin_layout Plain Layout
\r
4751 \begin_layout Plain Layout
\r
4765 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
4768 \begin_layout Plain Layout
\r
4769 \begin_inset Formula $A_{1},\ldots,A_{n}$
\r
4779 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
4782 \begin_layout Plain Layout
\r
4787 \begin_layout Plain Layout
\r
4802 \begin_layout Plain Layout
\r
4816 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
4819 \begin_layout Plain Layout
\r
4820 \begin_inset Formula $A_{1}+\cdots+A_{n}$
\r
4830 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
4833 \begin_layout Plain Layout
\r
4841 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
4844 \begin_layout Plain Layout
\r
4845 \begin_inset Formula $\vdots$
\r
4855 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
4858 \begin_layout Plain Layout
\r
4866 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
4869 \begin_layout Plain Layout
\r
4870 \begin_inset Formula $\ddots$
\r
4880 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
4883 \begin_layout Plain Layout
\r
4891 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
4894 \begin_layout Plain Layout
\r
4895 \begin_inset Formula $\iddots$
\r
4905 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
4908 \begin_layout Plain Layout
\r
4910 \begin_inset space \thinspace{}
\r
4913 matrix with the different dots
\r
4918 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
4921 \begin_layout Plain Layout
\r
4922 \begin_inset Formula $\begin{array}{ccc}
\r
4923 A_{11} & \cdots & A_{1m}\\
\r
4924 \vdots & \ddots & \vdots\\
\r
4925 A_{n1} & \cdots & A_{nm}
\r
4942 \begin_layout Standard
\r
4943 The ellipses available in menu
\r
4945 Insert\SpecialChar \menuseparator
\r
4947 \begin_inset space ~
\r
4961 \begin_layout Standard
\r
4962 \begin_inset VSpace medskip
\r
4971 , one of the options
\r
4973 Use mathdots package (automatically)
\r
4975 must be set in the document settings under
\r
4978 \begin_inset space ~
\r
4984 \begin_inset Newline newline
\r
4989 Use mathdots package
\r
4991 will improve the appearance of all dots in the documents if their font
\r
4992 style or size is not the default.
\r
4995 \begin_layout Standard
\r
4996 \begin_inset VSpace medskip
\r
4999 Specially for matrices there are ellipses that span over several columns.
\r
5000 They are created with the command
\r
5007 \begin_inset Index idx
\r
5010 \begin_layout Plain Layout
\r
5018 , that has the following scheme:
\r
5021 \begin_layout Standard
\r
5026 hdotsfor[distance]{number of columns}
\r
5029 \begin_layout Standard
\r
5030 The number of columns specifies how many columns should be spanned.
\r
5031 Distance is a factor for the distance between the dots.
\r
5034 \begin_layout Standard
\r
5035 In the following matrix the command
\r
5041 was inserted in the first box of the second line, to get an ellipsis with
\r
5042 a dot distance twice as long as with the command
\r
5049 \begin_inset Formula
\r
5051 \left(\begin{array}{cccc}
\r
5055 \end{array}\right)
\r
5060 Note that the matrix fields that should be spanned must be empty, otherwise
\r
5061 you get LaTeX-errors.
\r
5064 \begin_layout Standard
\r
5065 \begin_inset VSpace bigskip
\r
5068 Furthermore you can fill with the command
\r
5075 \begin_inset Index idx
\r
5078 \begin_layout Plain Layout
\r
5086 the rest of a line with dots.
\r
5087 The effect of these commands is the same as with
\r
5094 \begin_inset CommandInset ref
\r
5096 reference "sub:Variable-Space"
\r
5103 \begin_layout Standard
\r
5104 For example the command
\r
5112 \begin_layout Plain Layout
\r
5126 \begin_layout Standard
\r
5127 \begin_inset Formula $A\dotfill B$
\r
5133 \begin_layout Standard
\r
5140 there is for a line the command
\r
5147 \begin_inset Index idx
\r
5150 \begin_layout Plain Layout
\r
5161 \begin_layout Standard
\r
5162 \begin_inset Formula $A\hrulefill B$
\r
5168 \begin_layout Standard
\r
5169 To use the commands for text, they have to be inserted in TeX-mode.
\r
5172 \begin_layout Section
\r
5174 \begin_inset CommandInset label
\r
5175 LatexCommand label
\r
5176 name "sec:Matrices"
\r
5181 \begin_inset Index idx
\r
5184 \begin_layout Plain Layout
\r
5193 \begin_layout Standard
\r
5194 Matrices can be inserted via the math toolbar button
\r
5195 \begin_inset Graphics
\r
5196 filename ../images/dialog-show_mathmatrix.png
\r
5203 Insert\SpecialChar \menuseparator
\r
5204 Math\SpecialChar \menuseparator
\r
5208 In the matrix dialog you can specify the number of columns and rows, the
\r
5209 alignment and the decoration.
\r
5210 The vertical alignment is only of importance for matrices in inline formulas:
\r
5213 \begin_layout Standard
\r
5214 The first matrix is top
\r
5215 \begin_inset Formula $\begin{array}[t]{cccc}
\r
5222 , the second middle
\r
5223 \begin_inset Formula $\begin{array}{cccc}
\r
5230 and the third bottom
\r
5231 \begin_inset Formula $\begin{array}[b]{cccc}
\r
5241 \begin_layout Standard
\r
5242 The horizontal alignment specifies how the column entries should be aligned.
\r
5243 It is set by entering a letter for every column.
\r
5248 denotes left aligned,
\r
5257 To create for example a 4
\r
5262 \begin_inset space ~
\r
5265 matrix where the first column is left aligned, the second and third are
\r
5266 centered and the last one is right aligned, one enters for the horizontal
\r
5272 Normally in a matrix all columns are centered, therefore the default for
\r
5273 every column is a
\r
5280 \begin_layout Standard
\r
5281 Horizontal alignment:
\r
5284 \begin_layout Standard
\r
5290 \begin_inset Formula $\begin{array}{lll}
\r
5302 \begin_inset Formula $\begin{array}{ccc}
\r
5314 \begin_inset Formula $\begin{array}{rrr}
\r
5324 \begin_layout Standard
\r
5325 To add or delete rows and columns subsequently, the math toolbar buttons
\r
5327 \begin_inset Graphics
\r
5328 filename ../images/tabular-feature_append-row.png
\r
5334 \begin_inset Graphics
\r
5335 filename ../images/tabular-feature_delete-row.png
\r
5341 \begin_inset space \thinspace{}
\r
5346 Edit\SpecialChar \menuseparator
\r
5350 New rows can also be created with
\r
5353 arg "newline-insert newline"
\r
5359 \begin_layout Standard
\r
5360 \begin_inset VSpace bigskip
\r
5367 adds parentheses in the selected style around the matrix.
\r
5368 Alternatively, parentheses can can either be created with the commands
\r
5376 \begin_inset Index idx
\r
5379 \begin_layout Plain Layout
\r
5394 \begin_inset Index idx
\r
5397 \begin_layout Plain Layout
\r
5408 \begin_inset space ~
\r
5414 \begin_inset CommandInset ref
\r
5416 reference "sub:Automatic-Bracket-Size"
\r
5420 , or by using the following commands:
\r
5421 \begin_inset VSpace medskip
\r
5427 \begin_layout Standard
\r
5428 \begin_inset space \hfill{}
\r
5432 \begin_inset Tabular
\r
5433 <lyxtabular version="3" rows="4" columns="2">
\r
5434 <features rotate="0" tabularvalignment="middle">
\r
5435 <column alignment="center" valignment="top">
\r
5436 <column alignment="center" valignment="top">
\r
5438 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
5441 \begin_layout Plain Layout
\r
5447 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
5450 \begin_layout Plain Layout
\r
5452 \begin_inset Note Note
\r
5455 \begin_layout Plain Layout
\r
5462 is only used as spacer.
\r
5474 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
5477 \begin_layout Plain Layout
\r
5484 \begin_layout Plain Layout
\r
5498 \begin_inset space \thinspace{}
\r
5506 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
5509 \begin_layout Plain Layout
\r
5510 \begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
\r
5511 0 & \textrm{-}\mathrm{i}\\
\r
5513 \end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
\r
5523 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
5526 \begin_layout Plain Layout
\r
5533 \begin_layout Plain Layout
\r
5547 \begin_inset space \thinspace{}
\r
5555 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
5558 \begin_layout Plain Layout
\r
5559 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
\r
5560 0 & \textrm{-}\mathrm{i}\\
\r
5562 \end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
\r
5572 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
5575 \begin_layout Plain Layout
\r
5582 \begin_layout Plain Layout
\r
5596 \begin_inset space \thinspace{}
\r
5604 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
5607 \begin_layout Plain Layout
\r
5608 \begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
\r
5609 0 & \textrm{-}\mathrm{i}\\
\r
5611 \end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
\r
5625 \begin_inset space \hfill{}
\r
5629 \begin_inset Tabular
\r
5630 <lyxtabular version="3" rows="4" columns="2">
\r
5631 <features rotate="0" tabularvalignment="middle">
\r
5632 <column alignment="center" valignment="top">
\r
5633 <column alignment="center" valignment="top">
\r
5635 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
5638 \begin_layout Plain Layout
\r
5644 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
5647 \begin_layout Plain Layout
\r
5655 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
5658 \begin_layout Plain Layout
\r
5665 \begin_layout Plain Layout
\r
5679 \begin_inset space \thinspace{}
\r
5687 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
5690 \begin_layout Plain Layout
\r
5691 \begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
\r
5692 0 & \textrm{-}\mathrm{i}\\
\r
5694 \end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
\r
5704 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
5707 \begin_layout Plain Layout
\r
5714 \begin_layout Plain Layout
\r
5728 \begin_inset space \thinspace{}
\r
5736 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
5739 \begin_layout Plain Layout
\r
5740 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
\r
5741 0 & \textrm{-}\mathrm{i}\\
\r
5743 \end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
\r
5753 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
5756 \begin_layout Plain Layout
\r
5763 \begin_layout Plain Layout
\r
5777 \begin_inset space \thinspace{}
\r
5785 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
5788 \begin_layout Plain Layout
\r
5789 \begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
\r
5790 0 & \textrm{-}\mathrm{i}\\
\r
5792 \end{array}\end{matrix}\raisebox{-5.3mm}{}$
\r
5806 \begin_inset space \hfill{}
\r
5812 \begin_layout Standard
\r
5813 \begin_inset VSpace medskip
\r
5817 \begin_inset space \thinspace{}
\r
5821 \begin_inset space \space{}
\r
5830 is inserted, a blue box appears between two vertical lines where the matrix
\r
5832 \begin_inset Newline newline
\r
5835 Note that decorated matrices ignore the vertical alignment.
\r
5838 \begin_layout Standard
\r
5839 \begin_inset VSpace bigskip
\r
5842 As all multiline formulas are matrices, the length
\r
5849 \begin_inset Index idx
\r
5852 \begin_layout Plain Layout
\r
5860 that is described in
\r
5861 \begin_inset CommandInset ref
\r
5863 reference "sub:Column-Separation"
\r
5867 can also be used to change the column separation of matrices.
\r
5870 \begin_layout Standard
\r
5871 To change the row separation, the command
\r
5878 \begin_inset Index idx
\r
5881 \begin_layout Plain Layout
\r
5890 It is used as follows:
\r
5893 \begin_layout Standard
\r
5900 arraystretch}{stretch factor}
\r
5901 \begin_inset Index idx
\r
5904 \begin_layout Plain Layout
\r
5915 \begin_layout Standard
\r
5922 assigns the stretch factor to the predefined command
\r
5930 \begin_inset space \thinspace{}
\r
5934 \begin_inset space \space{}
\r
5937 the row separation, use the factor 2.
\r
5938 This is then used for all following matrices.
\r
5939 To go back to the original separation, assign the factor 1 to
\r
5948 \begin_layout Standard
\r
5949 To set matrices into a text line, the command
\r
5956 \begin_inset Index idx
\r
5959 \begin_layout Plain Layout
\r
5968 When it is inserted a blue box with two dashed lines appears.
\r
5969 In this box the matrix is inserted.
\r
5972 \begin_layout Standard
\r
5974 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
\r
5976 \end{smallmatrix}\right)$
\r
5982 \begin_layout Section
\r
5983 Brackets and Delimiters
\r
5984 \begin_inset Index idx
\r
5987 \begin_layout Plain Layout
\r
5994 \begin_inset Index idx
\r
5997 \begin_layout Plain Layout
\r
6006 \begin_layout Subsection
\r
6007 Vertical Brackets and Delimiters
\r
6008 \begin_inset Index idx
\r
6011 \begin_layout Plain Layout
\r
6012 Brackets ! vertical
\r
6020 \begin_layout Standard
\r
6021 \begin_inset space \hfill{}
\r
6025 \begin_inset Tabular
\r
6026 <lyxtabular version="3" rows="9" columns="2">
\r
6027 <features rotate="0" tabularvalignment="middle">
\r
6028 <column alignment="center" valignment="top" width="0pt">
\r
6029 <column alignment="center" valignment="top" width="0pt">
\r
6031 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
6034 \begin_layout Plain Layout
\r
6040 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
6043 \begin_layout Plain Layout
\r
6051 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
6054 \begin_layout Plain Layout
\r
6060 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
6063 \begin_layout Plain Layout
\r
6064 \begin_inset Formula $($
\r
6074 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
6077 \begin_layout Plain Layout
\r
6083 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
6086 \begin_layout Plain Layout
\r
6087 \begin_inset Formula $\{$
\r
6097 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
6100 \begin_layout Plain Layout
\r
6106 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
6109 \begin_layout Plain Layout
\r
6110 \begin_inset Formula $[$
\r
6120 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
6123 \begin_layout Plain Layout
\r
6131 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
6134 \begin_layout Plain Layout
\r
6135 \begin_inset Formula $\langle$
\r
6145 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
6148 \begin_layout Plain Layout
\r
6156 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
6159 \begin_layout Plain Layout
\r
6160 \begin_inset Formula $\lceil$
\r
6170 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
6173 \begin_layout Plain Layout
\r
6181 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
6184 \begin_layout Plain Layout
\r
6185 \begin_inset Formula $\lfloor$
\r
6195 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
6198 \begin_layout Plain Layout
\r
6204 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
6207 \begin_layout Plain Layout
\r
6208 \begin_inset Formula $/$
\r
6218 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
6221 \begin_layout Plain Layout
\r
6227 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
6230 \begin_layout Plain Layout
\r
6231 \begin_inset Formula $|$
\r
6245 \begin_inset space \hfill{}
\r
6249 \begin_inset Tabular
\r
6250 <lyxtabular version="3" rows="9" columns="2">
\r
6251 <features rotate="0" tabularvalignment="middle">
\r
6252 <column alignment="center" valignment="top" width="0pt">
\r
6253 <column alignment="center" valignment="top" width="0pt">
\r
6255 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
6258 \begin_layout Plain Layout
\r
6264 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
6267 \begin_layout Plain Layout
\r
6275 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
6278 \begin_layout Plain Layout
\r
6284 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
6287 \begin_layout Plain Layout
\r
6288 \begin_inset Formula $)$
\r
6298 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
6301 \begin_layout Plain Layout
\r
6307 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
6310 \begin_layout Plain Layout
\r
6311 \begin_inset Formula $\}$
\r
6321 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
6324 \begin_layout Plain Layout
\r
6330 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
6333 \begin_layout Plain Layout
\r
6334 \begin_inset Formula $]$
\r
6344 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
6347 \begin_layout Plain Layout
\r
6355 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
6358 \begin_layout Plain Layout
\r
6359 \begin_inset Formula $\rangle$
\r
6369 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
6372 \begin_layout Plain Layout
\r
6380 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
6383 \begin_layout Plain Layout
\r
6384 \begin_inset Formula $\rceil$
\r
6394 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
6397 \begin_layout Plain Layout
\r
6405 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
6408 \begin_layout Plain Layout
\r
6409 \begin_inset Formula $\rfloor$
\r
6419 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
6422 \begin_layout Plain Layout
\r
6432 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
6435 \begin_layout Plain Layout
\r
6436 \begin_inset Formula $\backslash$
\r
6446 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
6449 \begin_layout Plain Layout
\r
6457 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
6460 \begin_layout Plain Layout
\r
6461 \begin_inset Formula $\|$
\r
6475 \begin_inset space \hfill{}
\r
6481 \begin_layout Standard
\r
6484 \begin_inset Note Greyedout
\r
6487 \begin_layout Plain Layout
\r
6492 In TeX-mode the command
\r
6499 \begin_inset Index idx
\r
6502 \begin_layout Plain Layout
\r
6510 must be used for the backslash, because the command
\r
6518 produces a line break there.
\r
6526 \begin_layout Standard
\r
6527 For all characters listed above the size can be adjusted with the commands
\r
6528 described in the following two subsections.
\r
6529 When using these commands, the characters < and > can directly be used
\r
6530 instead of the commands
\r
6545 \begin_layout Subsubsection
\r
6546 Manual Bracket Size
\r
6547 \begin_inset CommandInset label
\r
6548 LatexCommand label
\r
6549 name "sub:Manual-Bracket-Size"
\r
6554 \begin_inset Index idx
\r
6557 \begin_layout Plain Layout
\r
6558 Bracket size ! manual
\r
6566 \begin_layout Standard
\r
6567 The bracket size can be specified manually by the LaTeX-commands
\r
6574 \begin_inset Index idx
\r
6577 \begin_layout Plain Layout
\r
6610 denotes the smallest and
\r
6616 the largest bracket size.
\r
6619 \begin_layout Standard
\r
6620 These commands are used to emphasize levels of brackets:
\r
6623 \begin_layout Standard
\r
6625 \begin_inset Tabular
\r
6626 <lyxtabular version="3" rows="2" columns="2">
\r
6627 <features rotate="0" tabularvalignment="middle">
\r
6628 <column alignment="center" valignment="top" width="0pt">
\r
6629 <column alignment="center" valignment="top" width="0pt">
\r
6631 <cell alignment="center" valignment="top" usebox="none">
\r
6634 \begin_layout Plain Layout
\r
6635 all brackets in the same size:
\r
6640 <cell alignment="center" valignment="top" usebox="none">
\r
6643 \begin_layout Plain Layout
\r
6644 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
\r
6654 <cell alignment="center" valignment="top" usebox="none">
\r
6657 \begin_layout Plain Layout
\r
6658 this looks better:
\r
6663 <cell alignment="center" valignment="top" usebox="none">
\r
6666 \begin_layout Plain Layout
\r
6667 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
\r
6681 \begin_inset Note Note
\r
6684 \begin_layout Plain Layout
\r
6691 is only used as spacer.
\r
6699 \begin_layout Standard
\r
6700 For the second formula the command
\r
6710 \begin_layout Plain Layout
\r
6724 \begin_layout Standard
\r
6725 Here is an overview about all bracket sizes:
\r
6728 \begin_layout Standard
\r
6748 \begin_layout Plain Layout
\r
6765 \begin_layout Plain Layout
\r
6778 \begin_layout Plain Layout
\r
6794 \begin_layout Standard
\r
6796 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
\r
6802 \begin_layout Standard
\r
6809 -commands there is the variant
\r
6816 \begin_inset Index idx
\r
6819 \begin_layout Plain Layout
\r
6827 that adds a bit more space between the bracket and its content, and the
\r
6841 \begin_inset Index idx
\r
6844 \begin_layout Plain Layout
\r
6854 , that don't add additional space.
\r
6859 at the end of the command
\r
6865 is for a left bracket; for a right bracket this will be replaced by an
\r
6871 A left or right bracket can each be an opening or closing bracket.
\r
6874 \begin_layout Standard
\r
6875 In the following table is a comparison of the variants:
\r
6878 \begin_layout Standard
\r
6880 \begin_inset Tabular
\r
6881 <lyxtabular version="3" rows="5" columns="2">
\r
6882 <features rotate="0" tabularvalignment="middle">
\r
6883 <column alignment="center" valignment="middle">
\r
6884 <column alignment="center" valignment="middle">
\r
6886 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
6889 \begin_layout Plain Layout
\r
6895 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
6898 \begin_layout Plain Layout
\r
6900 \begin_inset Note Note
\r
6903 \begin_layout Plain Layout
\r
6910 is only used as spacer.
\r
6922 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
6925 \begin_layout Plain Layout
\r
6940 \begin_layout Plain Layout
\r
6958 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
6961 \begin_layout Plain Layout
\r
6962 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
\r
6972 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
6975 \begin_layout Plain Layout
\r
6990 \begin_layout Plain Layout
\r
7008 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
7011 \begin_layout Plain Layout
\r
7012 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
\r
7022 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
7025 \begin_layout Plain Layout
\r
7040 \begin_layout Plain Layout
\r
7058 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
7061 \begin_layout Plain Layout
\r
7062 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
\r
7072 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
7075 \begin_layout Plain Layout
\r
7087 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
7090 \begin_layout Plain Layout
\r
7091 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
\r
7107 \begin_layout Subsubsection
\r
7108 Automatic Bracket Size
\r
7109 \begin_inset CommandInset label
\r
7110 LatexCommand label
\r
7111 name "sub:Automatic-Bracket-Size"
\r
7116 \begin_inset Index idx
\r
7119 \begin_layout Plain Layout
\r
7120 Bracket size ! automatic
\r
7128 \begin_layout Standard
\r
7129 Brackets with variable size can be inserted with the commands
\r
7136 \begin_inset Index idx
\r
7139 \begin_layout Plain Layout
\r
7154 \begin_inset Index idx
\r
7157 \begin_layout Plain Layout
\r
7165 or via the math toolbar button
\r
7166 \begin_inset Graphics
\r
7167 filename ../images/dialog-show_mathdelimiter.png
\r
7185 the wanted bracket must be inserted.
\r
7186 The bracket size will then automatically be calculated for the output.
\r
7189 \begin_layout Standard
\r
7191 normal bracket: The command
\r
7201 \begin_layout Plain Layout
\r
7211 \begin_inset Formula $\downarrow$
\r
7218 \begin_layout Plain Layout
\r
7230 \begin_inset Formula
\r
7240 \begin_layout Standard
\r
7242 multiline bracket: The command
\r
7254 \begin_layout Plain Layout
\r
7264 \begin_inset Formula $\downarrow$
\r
7271 \begin_layout Plain Layout
\r
7285 \begin_inset Formula
\r
7287 \ln\left(\frac{A}{C}\right)
\r
7295 \begin_layout Standard
\r
7311 \begin_inset space ~
\r
7317 This has the advantage that you can see in LyX immediately the real bracket
\r
7318 size and that the matching right bracket will be created too.
\r
7319 \begin_inset Newline newline
\r
7322 The command for the last example would then be:
\r
7336 \begin_layout Plain Layout
\r
7346 \begin_inset Formula $\downarrow$
\r
7352 \begin_layout Standard
\r
7353 To omit a left or right bracket, a dot is inserted for the omitted bracket.
\r
7354 For example the command
\r
7364 \begin_layout Plain Layout
\r
7374 \begin_inset Formula $\downarrow$
\r
7381 \begin_layout Plain Layout
\r
7397 \begin_inset Formula
\r
7399 \left.\frac{A}{B}\right\}
\r
7418 will be converted by LyX to brackets in the right size when the document
\r
7419 is reloaded and an omitted bracket will appear as dashed line.
\r
7422 \begin_layout Standard
\r
7423 \begin_inset VSpace bigskip
\r
7426 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
\r
7434 \begin_inset Index idx
\r
7437 \begin_layout Plain Layout
\r
7445 is additionally available for all brackets and limits.
\r
7446 With this command the height of the following character is adapted to the
\r
7447 one of the surrounding brackets, what is e.
\r
7448 \begin_inset space \thinspace{}
\r
7452 \begin_inset space \space{}
\r
7455 needed for physical vectors:
\r
7456 \begin_inset Formula
\r
7458 \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle
\r
7463 For physical vectors there is a special LaTeX-package, described in
\r
7464 \begin_inset CommandInset ref
\r
7466 reference "sub:Physical-Vectors"
\r
7473 \begin_layout Subsection
\r
7474 Horizontal Brackets
\r
7475 \begin_inset Index idx
\r
7478 \begin_layout Plain Layout
\r
7479 Brackets ! horizontal
\r
7487 \begin_layout Standard
\r
7489 \begin_inset Tabular
\r
7490 <lyxtabular version="3" rows="4" columns="2">
\r
7491 <features rotate="0" tabularvalignment="middle">
\r
7492 <column alignment="center" valignment="top" width="0pt">
\r
7493 <column alignment="center" valignment="top" width="0pt">
\r
7495 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
7498 \begin_layout Plain Layout
\r
7500 \begin_inset Note Note
\r
7503 \begin_layout Plain Layout
\r
7510 is only used as spacer.
\r
7520 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
7523 \begin_layout Plain Layout
\r
7531 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
7534 \begin_layout Plain Layout
\r
7538 \begin_layout Plain Layout
\r
7553 \begin_layout Plain Layout
\r
7566 \begin_layout Plain Layout
\r
7579 \begin_layout Plain Layout
\r
7592 \begin_layout Plain Layout
\r
7600 \begin_inset Index idx
\r
7603 \begin_layout Plain Layout
\r
7616 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
7619 \begin_layout Plain Layout
\r
7620 \begin_inset Formula $\overbrace{A+B}^{3}$
\r
7630 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
7633 \begin_layout Plain Layout
\r
7637 \begin_layout Plain Layout
\r
7652 \begin_layout Plain Layout
\r
7665 \begin_layout Plain Layout
\r
7678 \begin_layout Plain Layout
\r
7686 \begin_inset Index idx
\r
7689 \begin_layout Plain Layout
\r
7702 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
7705 \begin_layout Plain Layout
\r
7706 \begin_inset Formula $\underbrace{A+B}_{5}$
\r
7716 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
7719 \begin_layout Plain Layout
\r
7726 \begin_layout Plain Layout
\r
7741 \begin_layout Plain Layout
\r
7754 \begin_layout Plain Layout
\r
7767 \begin_layout Plain Layout
\r
7780 \begin_layout Plain Layout
\r
7793 \begin_layout Plain Layout
\r
7806 \begin_layout Plain Layout
\r
7820 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
7823 \begin_layout Plain Layout
\r
7824 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
\r
7840 \begin_layout Standard
\r
7841 In the last example it doesn't matter if
\r
7853 is inserted at first.
\r
7856 \begin_layout Standard
\r
7857 \begin_inset VSpace bigskip
\r
7860 When brackets are needed that overlap each other, multiline formulas, as
\r
7862 \begin_inset CommandInset ref
\r
7864 reference "sec:Multiline-Formulas"
\r
7869 \begin_inset Formula
\r
7871 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
\r
7872 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
\r
7877 In the first row the formula is inserted together with the first brace.
\r
7878 It is hereby important that the space command
\r
7882 \begin_layout Plain Layout
\r
7883 Space commands are explained in
\r
7884 \begin_inset CommandInset ref
\r
7886 reference "sub:Predefined-Space"
\r
7901 is inserted before the first
\r
7902 \begin_inset Formula $d$
\r
7905 , because the brace that ends behind the
\r
7906 \begin_inset Formula $q$
\r
7909 prevents that the following
\r
7910 \begin_inset Quotes eld
\r
7914 \begin_inset Quotes erd
\r
7917 is surrounded by space.
\r
7921 \begin_layout Plain Layout
\r
7922 because a bracket is not handled as a character, see
\r
7923 \begin_inset CommandInset ref
\r
7925 reference "sub:Binary-Operators"
\r
7934 In the second row the second brace is inserted.
\r
7935 As it should begin before the
\r
7936 \begin_inset Formula $b$
\r
7939 , first the command
\r
7951 \begin_layout Plain Layout
\r
7959 \begin_inset CommandInset ref
\r
7961 reference "sub:Placeholders"
\r
7970 This space is needed because the
\r
7971 \begin_inset Quotes eld
\r
7975 \begin_inset Quotes erd
\r
7978 is also surrounded by space in the formula.
\r
7979 The brace is placed under the command
\r
7983 hphantom{bbqq+dddd}
\r
7988 \begin_layout Standard
\r
7989 It gets more complicated when brackets overlap each other, like in the following
\r
7994 \begin_layout Plain Layout
\r
8006 \begin_inset Formula
\r
8008 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
\r
8009 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd
\r
8018 \begin_layout Plain Layout
\r
8029 The first formula row is the same as the second row of the previous example,
\r
8030 with the difference that the brace is above.
\r
8031 The second row contains the formula together with the second brace.
\r
8032 To avoid that there is space between the upper brace in the first row and
\r
8033 the formula, the row spacing needs to be reduced.
\r
8034 This is not easily possible due to a bug in LyX
\r
8038 \begin_layout Plain Layout
\r
8039 \begin_inset CommandInset href
\r
8041 name "LyX-bug #1505"
\r
8042 target "http://www.lyx.org/trac/ticket/1505"
\r
8052 As a solution for the problem, the global formula row separation
\r
8059 \begin_inset Index idx
\r
8062 \begin_layout Plain Layout
\r
8070 must be changed to -6
\r
8071 \begin_inset space \thinspace{}
\r
8074 pt before the formula with the command
\r
8089 is set back after the formula to the standard value of 3
\r
8090 \begin_inset space \thinspace{}
\r
8093 pt using the same command.
\r
8094 More about the row separation in formulas is explained in
\r
8095 \begin_inset CommandInset ref
\r
8097 reference "sub:Line-Separation"
\r
8104 \begin_layout Section
\r
8106 \begin_inset Index idx
\r
8109 \begin_layout Plain Layout
\r
8118 \begin_layout Standard
\r
8119 Arrows can be inserted via the math toolbar button
\r
8120 \begin_inset Graphics
\r
8121 filename ../images/math/leftarrow.png
\r
8126 or the commands listed in the following subsections.
\r
8129 \begin_layout Subsection
\r
8131 \begin_inset Index idx
\r
8134 \begin_layout Plain Layout
\r
8135 Arrows ! horizontal
\r
8143 \begin_layout Standard
\r
8144 \begin_inset space \hfill{}
\r
8148 \begin_inset Tabular
\r
8149 <lyxtabular version="3" rows="8" columns="2">
\r
8150 <features rotate="0" tabularvalignment="middle">
\r
8151 <column alignment="center" valignment="top" width="0pt">
\r
8152 <column alignment="center" valignment="top" width="0pt">
\r
8154 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
8157 \begin_layout Plain Layout
\r
8163 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
8166 \begin_layout Plain Layout
\r
8174 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
8177 \begin_layout Plain Layout
\r
8185 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
8188 \begin_layout Plain Layout
\r
8189 \begin_inset Formula $\gets$
\r
8199 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
8202 \begin_layout Plain Layout
\r
8210 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
8213 \begin_layout Plain Layout
\r
8214 \begin_inset Formula $\Leftarrow$
\r
8224 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
8227 \begin_layout Plain Layout
\r
8235 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
8238 \begin_layout Plain Layout
\r
8239 \begin_inset Formula $\longleftarrow$
\r
8249 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
8252 \begin_layout Plain Layout
\r
8260 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
8263 \begin_layout Plain Layout
\r
8264 \begin_inset Formula $\Longleftarrow$
\r
8274 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
8277 \begin_layout Plain Layout
\r
8285 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
8288 \begin_layout Plain Layout
\r
8289 \begin_inset Formula $\leftharpoonup$
\r
8299 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
8302 \begin_layout Plain Layout
\r
8310 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
8313 \begin_layout Plain Layout
\r
8314 \begin_inset Formula $\leftharpoondown$
\r
8324 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
8327 \begin_layout Plain Layout
\r
8335 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
8338 \begin_layout Plain Layout
\r
8339 \begin_inset Formula $\hookleftarrow$
\r
8353 \begin_inset space \hfill{}
\r
8357 \begin_inset Tabular
\r
8358 <lyxtabular version="3" rows="8" columns="2">
\r
8359 <features rotate="0" tabularvalignment="middle">
\r
8360 <column alignment="center" valignment="top" width="0pt">
\r
8361 <column alignment="center" valignment="top" width="0pt">
\r
8363 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
8366 \begin_layout Plain Layout
\r
8372 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
8375 \begin_layout Plain Layout
\r
8383 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
8386 \begin_layout Plain Layout
\r
8394 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
8397 \begin_layout Plain Layout
\r
8398 \begin_inset Formula $\to$
\r
8408 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
8411 \begin_layout Plain Layout
\r
8419 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
8422 \begin_layout Plain Layout
\r
8423 \begin_inset Formula $\Rightarrow$
\r
8433 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
8436 \begin_layout Plain Layout
\r
8444 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
8447 \begin_layout Plain Layout
\r
8448 \begin_inset Formula $\longrightarrow$
\r
8458 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
8461 \begin_layout Plain Layout
\r
8469 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
8472 \begin_layout Plain Layout
\r
8473 \begin_inset Formula $\Longrightarrow$
\r
8483 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
8486 \begin_layout Plain Layout
\r
8494 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
8497 \begin_layout Plain Layout
\r
8498 \begin_inset Formula $\rightharpoonup$
\r
8508 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
8511 \begin_layout Plain Layout
\r
8519 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
8522 \begin_layout Plain Layout
\r
8523 \begin_inset Formula $\rightharpoondown$
\r
8533 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
8536 \begin_layout Plain Layout
\r
8544 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
8547 \begin_layout Plain Layout
\r
8548 \begin_inset Formula $\hookrightarrow$
\r
8562 \begin_inset space \hfill{}
\r
8568 \begin_layout Standard
\r
8569 \begin_inset space \hfill{}
\r
8573 \begin_inset Tabular
\r
8574 <lyxtabular version="3" rows="6" columns="2">
\r
8575 <features rotate="0" tabularvalignment="middle">
\r
8576 <column alignment="center" valignment="top" width="0pt">
\r
8577 <column alignment="center" valignment="top" width="0pt">
\r
8579 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
8582 \begin_layout Plain Layout
\r
8588 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
8591 \begin_layout Plain Layout
\r
8599 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
8602 \begin_layout Plain Layout
\r
8610 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
8613 \begin_layout Plain Layout
\r
8614 \begin_inset Formula $\leftrightarrow$
\r
8624 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
8627 \begin_layout Plain Layout
\r
8635 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
8638 \begin_layout Plain Layout
\r
8639 \begin_inset Formula $\Leftrightarrow$
\r
8649 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
8652 \begin_layout Plain Layout
\r
8655 longleftrightarrow
\r
8660 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
8663 \begin_layout Plain Layout
\r
8664 \begin_inset Formula $\longleftrightarrow$
\r
8674 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
8677 \begin_layout Plain Layout
\r
8680 Longleftrightarrow
\r
8685 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
8688 \begin_layout Plain Layout
\r
8689 \begin_inset Formula $\Longleftrightarrow$
\r
8699 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
8702 \begin_layout Plain Layout
\r
8710 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
8713 \begin_layout Plain Layout
\r
8714 \begin_inset Formula $\rightleftharpoons$
\r
8728 \begin_inset space \hspace{}
\r
8733 \begin_inset space \hfill{}
\r
8737 \begin_inset Tabular
\r
8738 <lyxtabular version="3" rows="5" columns="2">
\r
8739 <features rotate="0" tabularvalignment="middle">
\r
8740 <column alignment="center" valignment="top" width="0pt">
\r
8741 <column alignment="center" valignment="top" width="0pt">
\r
8743 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
8746 \begin_layout Plain Layout
\r
8752 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
8755 \begin_layout Plain Layout
\r
8763 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
8766 \begin_layout Plain Layout
\r
8774 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
8777 \begin_layout Plain Layout
\r
8778 \begin_inset Formula $\mapsto$
\r
8788 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
8791 \begin_layout Plain Layout
\r
8799 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
8802 \begin_layout Plain Layout
\r
8803 \begin_inset Formula $\longmapsto$
\r
8813 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
8816 \begin_layout Plain Layout
\r
8824 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
8827 \begin_layout Plain Layout
\r
8828 \begin_inset Formula $\leadsto$
\r
8838 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
8841 \begin_layout Plain Layout
\r
8849 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
8852 \begin_layout Plain Layout
\r
8853 \begin_inset Formula $\dasharrow$
\r
8867 \begin_inset space \hfill{}
\r
8873 \begin_layout Standard
\r
8874 \begin_inset VSpace medskip
\r
8877 Arrows used as accents like e.
\r
8878 \begin_inset space \thinspace{}
\r
8882 \begin_inset space \space{}
\r
8885 vector arrows are listed in
\r
8886 \begin_inset CommandInset ref
\r
8888 reference "sec:Accents"
\r
8895 \begin_layout Standard
\r
8896 \begin_inset VSpace bigskip
\r
8899 Furthermore there are the labeled arrows
\r
8900 \begin_inset Index idx
\r
8903 \begin_layout Plain Layout
\r
8916 \begin_inset Index idx
\r
8919 \begin_layout Plain Layout
\r
8934 \begin_inset Index idx
\r
8937 \begin_layout Plain Layout
\r
8944 \begin_layout Plain Layout
\r
8959 When inserting one of these commands in a formula, an arrow with two blue
\r
8960 boxes appear where the label can be inserted.
\r
8961 The length of the arrow adapts to the label width.
\r
8964 \begin_layout Standard
\r
8966 \begin_inset Tabular
\r
8967 <lyxtabular version="3" rows="3" columns="2">
\r
8968 <features rotate="0" tabularvalignment="middle">
\r
8969 <column alignment="center" valignment="top" width="0pt">
\r
8970 <column alignment="center" valignment="top" width="0pt">
\r
8972 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
8975 \begin_layout Plain Layout
\r
8981 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
8984 \begin_layout Plain Layout
\r
8986 \begin_inset Note Note
\r
8989 \begin_layout Plain Layout
\r
8996 is only used as spacer.
\r
9008 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
9011 \begin_layout Plain Layout
\r
9018 \begin_layout Plain Layout
\r
9028 \begin_inset Formula $\downarrow$
\r
9032 \begin_inset Formula $\to$
\r
9040 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
9043 \begin_layout Plain Layout
\r
9044 \begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
\r
9054 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
9057 \begin_layout Plain Layout
\r
9064 \begin_layout Plain Layout
\r
9074 \begin_inset Formula $\downarrow$
\r
9078 \begin_inset Formula $\to$
\r
9086 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
9089 \begin_layout Plain Layout
\r
9090 \begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
\r
9106 \begin_layout Subsection
\r
9107 Vertical and diagonal Arrows
\r
9108 \begin_inset Index idx
\r
9111 \begin_layout Plain Layout
\r
9118 \begin_inset Index idx
\r
9121 \begin_layout Plain Layout
\r
9130 \begin_layout Standard
\r
9131 \begin_inset space \hfill{}
\r
9135 \begin_inset Tabular
\r
9136 <lyxtabular version="3" rows="7" columns="2">
\r
9137 <features rotate="0" tabularvalignment="middle">
\r
9138 <column alignment="center" valignment="top" width="0pt">
\r
9139 <column alignment="center" valignment="top" width="0pt">
\r
9141 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
9144 \begin_layout Plain Layout
\r
9150 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
9153 \begin_layout Plain Layout
\r
9161 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
9164 \begin_layout Plain Layout
\r
9172 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
9175 \begin_layout Plain Layout
\r
9176 \begin_inset Formula $\uparrow$
\r
9186 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
9189 \begin_layout Plain Layout
\r
9197 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
9200 \begin_layout Plain Layout
\r
9201 \begin_inset Formula $\Uparrow$
\r
9211 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
9214 \begin_layout Plain Layout
\r
9222 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
9225 \begin_layout Plain Layout
\r
9226 \begin_inset Formula $\updownarrow$
\r
9236 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
9239 \begin_layout Plain Layout
\r
9247 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
9250 \begin_layout Plain Layout
\r
9251 \begin_inset Formula $\Updownarrow$
\r
9261 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
9264 \begin_layout Plain Layout
\r
9272 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
9275 \begin_layout Plain Layout
\r
9276 \begin_inset Formula $\Downarrow$
\r
9286 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
9289 \begin_layout Plain Layout
\r
9297 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
9300 \begin_layout Plain Layout
\r
9301 \begin_inset Formula $\downarrow$
\r
9315 \begin_inset space \hfill{}
\r
9319 \begin_inset Tabular
\r
9320 <lyxtabular version="3" rows="5" columns="2">
\r
9321 <features rotate="0" tabularvalignment="middle">
\r
9322 <column alignment="center" valignment="top" width="0pt">
\r
9323 <column alignment="center" valignment="top" width="0pt">
\r
9325 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
9328 \begin_layout Plain Layout
\r
9334 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
9337 \begin_layout Plain Layout
\r
9345 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
9348 \begin_layout Plain Layout
\r
9356 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
9359 \begin_layout Plain Layout
\r
9360 \begin_inset Formula $\nearrow$
\r
9370 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
9373 \begin_layout Plain Layout
\r
9381 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
9384 \begin_layout Plain Layout
\r
9385 \begin_inset Formula $\searrow$
\r
9395 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
9398 \begin_layout Plain Layout
\r
9406 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
9409 \begin_layout Plain Layout
\r
9410 \begin_inset Formula $\swarrow$
\r
9420 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
9423 \begin_layout Plain Layout
\r
9431 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
9434 \begin_layout Plain Layout
\r
9435 \begin_inset Formula $\nwarrow$
\r
9449 \begin_inset space \hfill{}
\r
9455 \begin_layout Standard
\r
9456 \begin_inset VSpace medskip
\r
9459 Vertical arrows can be used also as delimiters together with the commands
\r
9461 \begin_inset CommandInset ref
\r
9463 reference "sub:Manual-Bracket-Size"
\r
9468 \begin_inset CommandInset ref
\r
9470 reference "sub:Automatic-Bracket-Size"
\r
9477 \begin_layout Section
\r
9479 \begin_inset CommandInset label
\r
9480 LatexCommand label
\r
9481 name "sec:Accents"
\r
9486 \begin_inset Index idx
\r
9489 \begin_layout Plain Layout
\r
9498 \begin_layout Standard
\r
9499 Accents can be inserted via the math toolbar button
\r
9500 \begin_inset Graphics
\r
9501 filename ../images/math/hat.png
\r
9506 or the commands listed in the following subsections.
\r
9509 \begin_layout Subsection
\r
9510 Accents for one Character
\r
9514 \begin_layout Plain Layout
\r
9527 \begin_layout Plain Layout
\r
9528 accents in text see
\r
9529 \begin_inset CommandInset ref
\r
9531 reference "sub:Accents-in-Text"
\r
9544 \begin_layout Plain Layout
\r
9552 \begin_inset Note Note
\r
9555 \begin_layout Plain Layout
\r
9562 is used to avoid that the footnote appears in the PDF-bookmark.
\r
9565 \begin_layout Plain Layout
\r
9573 \begin_inset CommandInset ref
\r
9575 reference "sub:Formulas-in-Section"
\r
9585 \begin_inset CommandInset label
\r
9586 LatexCommand label
\r
9587 name "sub:Accents-for-one"
\r
9592 \begin_inset Index idx
\r
9595 \begin_layout Plain Layout
\r
9596 Accents ! for one character
\r
9604 \begin_layout Standard
\r
9605 \begin_inset space \hfill{}
\r
9609 \begin_inset Tabular
\r
9610 <lyxtabular version="3" rows="8" columns="2">
\r
9611 <features rotate="0" tabularvalignment="middle">
\r
9612 <column alignment="center" valignment="top" width="0pt">
\r
9613 <column alignment="center" valignment="top" width="0pt">
\r
9615 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
9618 \begin_layout Plain Layout
\r
9624 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
9627 \begin_layout Plain Layout
\r
9629 \begin_inset Note Note
\r
9632 \begin_layout Plain Layout
\r
9639 is only used as spacer.
\r
9651 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
9654 \begin_layout Plain Layout
\r
9661 \begin_layout Plain Layout
\r
9675 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
9678 \begin_layout Plain Layout
\r
9679 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
\r
9689 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
9692 \begin_layout Plain Layout
\r
9699 \begin_layout Plain Layout
\r
9713 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
9716 \begin_layout Plain Layout
\r
9717 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
\r
9727 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
9730 \begin_layout Plain Layout
\r
9737 \begin_layout Plain Layout
\r
9751 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
9754 \begin_layout Plain Layout
\r
9755 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
\r
9765 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
9768 \begin_layout Plain Layout
\r
9775 \begin_layout Plain Layout
\r
9789 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
9792 \begin_layout Plain Layout
\r
9793 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
\r
9803 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
9806 \begin_layout Plain Layout
\r
9813 \begin_layout Plain Layout
\r
9823 \begin_inset Index idx
\r
9826 \begin_layout Plain Layout
\r
9837 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
9840 \begin_layout Plain Layout
\r
9841 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
\r
9851 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
9854 \begin_layout Plain Layout
\r
9861 \begin_layout Plain Layout
\r
9875 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
9878 \begin_layout Plain Layout
\r
9879 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
\r
9889 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
9892 \begin_layout Plain Layout
\r
9899 \begin_layout Plain Layout
\r
9913 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
9916 \begin_layout Plain Layout
\r
9917 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
\r
9931 \begin_inset space \hfill{}
\r
9935 \begin_inset Tabular
\r
9936 <lyxtabular version="3" rows="7" columns="2">
\r
9937 <features rotate="0" tabularvalignment="middle">
\r
9938 <column alignment="center" valignment="top" width="0pt">
\r
9939 <column alignment="center" valignment="top" width="0pt">
\r
9941 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
9944 \begin_layout Plain Layout
\r
9950 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
9953 \begin_layout Plain Layout
\r
9961 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
9964 \begin_layout Plain Layout
\r
9971 \begin_layout Plain Layout
\r
9985 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
9988 \begin_layout Plain Layout
\r
9989 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
\r
9999 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
10000 \begin_inset Text
\r
10002 \begin_layout Plain Layout
\r
10009 \begin_layout Plain Layout
\r
10023 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
10024 \begin_inset Text
\r
10026 \begin_layout Plain Layout
\r
10027 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
\r
10037 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
10038 \begin_inset Text
\r
10040 \begin_layout Plain Layout
\r
10047 \begin_layout Plain Layout
\r
10061 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
10062 \begin_inset Text
\r
10064 \begin_layout Plain Layout
\r
10065 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
\r
10075 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
10076 \begin_inset Text
\r
10078 \begin_layout Plain Layout
\r
10085 \begin_layout Plain Layout
\r
10099 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
10100 \begin_inset Text
\r
10102 \begin_layout Plain Layout
\r
10103 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
\r
10113 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
10114 \begin_inset Text
\r
10116 \begin_layout Plain Layout
\r
10123 \begin_layout Plain Layout
\r
10137 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
10138 \begin_inset Text
\r
10140 \begin_layout Plain Layout
\r
10141 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
\r
10151 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
10152 \begin_inset Text
\r
10154 \begin_layout Plain Layout
\r
10161 \begin_layout Plain Layout
\r
10175 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
10176 \begin_inset Text
\r
10178 \begin_layout Plain Layout
\r
10179 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
\r
10193 \begin_inset space \hfill{}
\r
10199 \begin_layout Standard
\r
10200 \begin_inset VSpace bigskip
\r
10206 \begin_layout Standard
\r
10207 You can directly insert accents like é to formulas.
\r
10208 LyX will transform them to the corresponding accent command.
\r
10210 \begin_inset Index idx
\r
10213 \begin_layout Plain Layout
\r
10219 it is better to insert a quotation mark before the vowel.
\r
10220 These two characters are then treated by LaTeX as
\r
10224 character when the formula part with the umlaut is marked as German.
\r
10231 , with this method
\r
10232 \begin_inset Quotes eld
\r
10236 \begin_inset Quotes erd
\r
10239 umlauts are created as demonstrated in the following example:
\r
10242 \begin_layout Standard
\r
10243 \begin_inset VSpace -2mm
\r
10249 \begin_layout Standard
\r
10251 \begin_inset Tabular
\r
10252 <lyxtabular version="3" rows="3" columns="2">
\r
10253 <features rotate="0" tabularvalignment="middle">
\r
10254 <column alignment="center" valignment="top">
\r
10255 <column alignment="center" valignment="top">
\r
10257 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
10258 \begin_inset Text
\r
10260 \begin_layout Plain Layout
\r
10266 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
10267 \begin_inset Text
\r
10269 \begin_layout Plain Layout
\r
10271 \begin_inset Note Note
\r
10274 \begin_layout Plain Layout
\r
10282 \begin_inset space \thinspace{}
\r
10285 pt space are only used as spacer.
\r
10297 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
10298 \begin_inset Text
\r
10300 \begin_layout Plain Layout
\r
10303 \begin_inset Quotes grd
\r
10311 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
10312 \begin_inset Text
\r
10314 \begin_layout Plain Layout
\r
10315 \begin_inset space \hspace{}
\r
10322 \begin_inset Formula $"i$
\r
10332 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
10333 \begin_inset Text
\r
10335 \begin_layout Plain Layout
\r
10342 \begin_layout Plain Layout
\r
10356 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
10357 \begin_inset Text
\r
10359 \begin_layout Plain Layout
\r
10360 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
\r
10376 \begin_layout Standard
\r
10377 Another advantage to
\r
10383 is that umlauts can directly be converted to mathematical text because
\r
10384 the accent commands above are
\r
10390 in mathematical text
\r
10393 To convert an accented character to mathematical text, only the character
\r
10394 under the accent may be converted.
\r
10395 This applies also for all other conversions, e.
\r
10396 \begin_inset space \thinspace{}
\r
10400 \begin_inset space \space{}
\r
10403 to italic or bold.
\r
10406 \begin_layout Standard
\r
10407 In mathematical text, umlauts and other accented characters can directly
\r
10411 \begin_layout Subsection
\r
10412 Accents for several Characters
\r
10413 \begin_inset Index idx
\r
10416 \begin_layout Plain Layout
\r
10417 Accents ! for several characters
\r
10425 \begin_layout Standard
\r
10426 \begin_inset space \hfill{}
\r
10430 \begin_inset Tabular
\r
10431 <lyxtabular version="3" rows="5" columns="2">
\r
10432 <features rotate="0" tabularvalignment="middle">
\r
10433 <column alignment="center" valignment="top" width="0pt">
\r
10434 <column alignment="center" valignment="top" width="0pt">
\r
10436 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
10437 \begin_inset Text
\r
10439 \begin_layout Plain Layout
\r
10445 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
10446 \begin_inset Text
\r
10448 \begin_layout Plain Layout
\r
10450 \begin_inset Note Note
\r
10453 \begin_layout Plain Layout
\r
10460 is only used as spacer.
\r
10472 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
10473 \begin_inset Text
\r
10475 \begin_layout Plain Layout
\r
10482 \begin_layout Plain Layout
\r
10496 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
10497 \begin_inset Text
\r
10499 \begin_layout Plain Layout
\r
10500 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
\r
10510 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
10511 \begin_inset Text
\r
10513 \begin_layout Plain Layout
\r
10520 \begin_layout Plain Layout
\r
10534 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
10535 \begin_inset Text
\r
10537 \begin_layout Plain Layout
\r
10538 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
\r
10548 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
10549 \begin_inset Text
\r
10551 \begin_layout Plain Layout
\r
10554 overleftrightarrow
\r
10558 \begin_layout Plain Layout
\r
10572 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
10573 \begin_inset Text
\r
10575 \begin_layout Plain Layout
\r
10576 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
\r
10586 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
10587 \begin_inset Text
\r
10589 \begin_layout Plain Layout
\r
10592 underleftrightarrow
\r
10596 \begin_layout Plain Layout
\r
10610 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
10611 \begin_inset Text
\r
10613 \begin_layout Plain Layout
\r
10614 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
\r
10628 \begin_inset space \hfill{}
\r
10632 \begin_inset Tabular
\r
10633 <lyxtabular version="3" rows="5" columns="2">
\r
10634 <features rotate="0" tabularvalignment="middle">
\r
10635 <column alignment="center" valignment="top" width="0pt">
\r
10636 <column alignment="center" valignment="top" width="0pt">
\r
10638 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
10639 \begin_inset Text
\r
10641 \begin_layout Plain Layout
\r
10647 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
10648 \begin_inset Text
\r
10650 \begin_layout Plain Layout
\r
10658 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
10659 \begin_inset Text
\r
10661 \begin_layout Plain Layout
\r
10668 \begin_layout Plain Layout
\r
10682 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
10683 \begin_inset Text
\r
10685 \begin_layout Plain Layout
\r
10686 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
\r
10696 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
10697 \begin_inset Text
\r
10699 \begin_layout Plain Layout
\r
10706 \begin_layout Plain Layout
\r
10720 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
10721 \begin_inset Text
\r
10723 \begin_layout Plain Layout
\r
10724 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
\r
10734 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
10735 \begin_inset Text
\r
10737 \begin_layout Plain Layout
\r
10744 \begin_layout Plain Layout
\r
10758 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
10759 \begin_inset Text
\r
10761 \begin_layout Plain Layout
\r
10762 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
\r
10772 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
10773 \begin_inset Text
\r
10775 \begin_layout Plain Layout
\r
10782 \begin_layout Plain Layout
\r
10796 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
10797 \begin_inset Text
\r
10799 \begin_layout Plain Layout
\r
10800 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
\r
10814 \begin_inset space \hfill{}
\r
10820 \begin_layout Standard
\r
10821 \begin_inset VSpace medskip
\r
10824 With these commands as many characters as you like can be accented.
\r
10837 will only be set in the output with a length of three characters, as shown
\r
10838 in the following example:
\r
10839 \begin_inset Formula
\r
10841 \widetilde{A+B=C-D}
\r
10849 \begin_layout Standard
\r
10850 With the commands
\r
10857 \begin_inset Index idx
\r
10860 \begin_layout Plain Layout
\r
10875 \begin_inset Index idx
\r
10878 \begin_layout Plain Layout
\r
10886 described in the previous subsection it is also possible to accent several
\r
10896 \begin_layout Plain Layout
\r
10906 \begin_inset Formula $\downarrow$
\r
10912 \begin_inset Formula
\r
10914 \underset{***}{A=B}
\r
10922 \begin_layout Standard
\r
10923 \begin_inset Newpage newpage
\r
10929 \begin_layout Section
\r
10931 \begin_inset CommandInset label
\r
10932 LatexCommand label
\r
10938 \begin_inset Index idx
\r
10941 \begin_layout Plain Layout
\r
10942 Space ! horizontal
\r
10950 \begin_layout Subsection
\r
10952 \begin_inset CommandInset label
\r
10953 LatexCommand label
\r
10954 name "sub:Predefined-Space"
\r
10959 \begin_inset Index idx
\r
10962 \begin_layout Plain Layout
\r
10963 Space ! horizontal ! predefined
\r
10971 \begin_layout Standard
\r
10972 Sometimes it is necessary to insert horizontal space into a formula.
\r
10973 This is done by inserting a protected space (shortcut
\r
10974 \begin_inset Info
\r
10976 arg "command-alternatives space-insert protected ; math-space"
\r
10981 \begin_inset Quotes eld
\r
10990 \begin_layout Plain Layout
\r
11002 \begin_inset Quotes erd
\r
11005 appears and by pressing
\r
11009 several times one can select one of eight different space sizes.
\r
11010 The spaces can also be inserted using the math toolbar button
\r
11011 \begin_inset Graphics
\r
11012 filename ../images/math/space.png
\r
11017 or special commands.
\r
11018 Independent from the inserted command, one can select the size again by
\r
11026 \begin_layout Standard
\r
11029 \begin_inset VSpace -5mm
\r
11033 \begin_inset Tabular
\r
11034 <lyxtabular version="3" rows="3" columns="7">
\r
11035 <features rotate="0" tabularvalignment="middle">
\r
11036 <column alignment="center" valignment="middle" width="6.8cm">
\r
11037 <column alignment="center" valignment="top">
\r
11038 <column alignment="center" valignment="top">
\r
11039 <column alignment="center" valignment="top">
\r
11040 <column alignment="center" valignment="top">
\r
11041 <column alignment="center" valignment="top">
\r
11042 <column alignment="center" valignment="top">
\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
11053 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
11054 \begin_inset Text
\r
11056 \begin_layout Plain Layout
\r
11064 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
11065 \begin_inset Text
\r
11067 \begin_layout Plain Layout
\r
11075 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
11076 \begin_inset Text
\r
11078 \begin_layout Plain Layout
\r
11086 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
11087 \begin_inset Text
\r
11089 \begin_layout Plain Layout
\r
11097 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
11098 \begin_inset Text
\r
11100 \begin_layout Plain Layout
\r
11108 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
11109 \begin_inset Text
\r
11111 \begin_layout Plain Layout
\r
11121 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
11122 \begin_inset Text
\r
11124 \begin_layout Plain Layout
\r
11129 keystrokes after inserting the protected space
\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" usebox="none">
\r
11171 \begin_inset Text
\r
11173 \begin_layout Plain Layout
\r
11179 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
11180 \begin_inset Text
\r
11182 \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
11199 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
11200 \begin_inset Text
\r
11202 \begin_layout Plain Layout
\r
11203 \begin_inset Formula $A\, B$
\r
11211 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
11212 \begin_inset Text
\r
11214 \begin_layout Plain Layout
\r
11215 \begin_inset Formula $A\: B$
\r
11223 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
11224 \begin_inset Text
\r
11226 \begin_layout Plain Layout
\r
11227 \begin_inset Formula $A\; B$
\r
11235 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
11236 \begin_inset Text
\r
11238 \begin_layout Plain Layout
\r
11239 \begin_inset Formula $A\quad B$
\r
11247 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
11248 \begin_inset Text
\r
11250 \begin_layout Plain Layout
\r
11251 \begin_inset Formula $A\qquad B$
\r
11259 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
11260 \begin_inset Text
\r
11262 \begin_layout Plain Layout
\r
11263 \begin_inset Formula $A\! B$
\r
11279 \begin_layout Standard
\r
11280 The last size seem to produce no space.
\r
11281 It is displayed red in LyX contrary to the other sizes, because it is a
\r
11283 There are two more negative spaces:
\r
11286 \begin_layout Standard
\r
11288 \begin_inset Tabular
\r
11289 <lyxtabular version="3" rows="3" columns="3">
\r
11290 <features rotate="0" tabularvalignment="middle">
\r
11291 <column alignment="center" valignment="middle" width="6.8cm">
\r
11292 <column alignment="center" valignment="top" width="0pt">
\r
11293 <column alignment="center" valignment="top" width="0pt">
\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
11304 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
11305 \begin_inset Text
\r
11307 \begin_layout Plain Layout
\r
11315 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
11316 \begin_inset Text
\r
11318 \begin_layout Plain Layout
\r
11328 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
11329 \begin_inset Text
\r
11331 \begin_layout Plain Layout
\r
11336 keystrokes after inserting the protected space
\r
11341 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
11342 \begin_inset Text
\r
11344 \begin_layout Plain Layout
\r
11350 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
11351 \begin_inset Text
\r
11353 \begin_layout Plain Layout
\r
11361 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
11362 \begin_inset Text
\r
11364 \begin_layout Plain Layout
\r
11370 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
11371 \begin_inset Text
\r
11373 \begin_layout Plain Layout
\r
11374 \begin_inset Formula $A\negmedspace B$
\r
11382 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
11383 \begin_inset Text
\r
11385 \begin_layout Plain Layout
\r
11386 \begin_inset Formula $A\negthickspace B$
\r
11402 \begin_layout Standard
\r
11403 Negative spaces can lead to characters overlapping each other.
\r
11404 Thus they can be used to enforce ligatures, which are e.
\r
11405 \begin_inset space \thinspace{}
\r
11409 \begin_inset space \space{}
\r
11412 useful for summation operators:
\r
11415 \begin_layout Standard
\r
11417 \begin_inset Tabular
\r
11418 <lyxtabular version="3" rows="3" columns="2">
\r
11419 <features rotate="0" tabularvalignment="middle">
\r
11420 <column alignment="center" valignment="top">
\r
11421 <column alignment="center" valignment="top">
\r
11423 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
11424 \begin_inset Text
\r
11426 \begin_layout Plain Layout
\r
11432 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
11433 \begin_inset Text
\r
11435 \begin_layout Plain Layout
\r
11437 \begin_inset Note Note
\r
11440 \begin_layout Plain Layout
\r
11447 is only used as spacer.
\r
11459 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
11460 \begin_inset Text
\r
11462 \begin_layout Plain Layout
\r
11471 \begin_layout Plain Layout
\r
11485 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
11486 \begin_inset Text
\r
11488 \begin_layout Plain Layout
\r
11489 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
\r
11499 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
11500 \begin_inset Text
\r
11502 \begin_layout Plain Layout
\r
11513 \begin_layout Plain Layout
\r
11527 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
11528 \begin_inset Text
\r
11530 \begin_layout Plain Layout
\r
11531 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
\r
11547 \begin_layout Standard
\r
11548 Relations like for example equal signs, are always surrounded by space.
\r
11549 To suppress this, the equal sign is placed into a TeX-brace.
\r
11550 The following example demonstrates this:
\r
11553 \begin_layout Standard
\r
11555 \begin_inset Tabular
\r
11556 <lyxtabular version="3" rows="2" columns="2">
\r
11557 <features rotate="0" tabularvalignment="middle">
\r
11558 <column alignment="center" valignment="top" width="0pt">
\r
11559 <column alignment="center" valignment="top" width="0pt">
\r
11561 <cell alignment="center" valignment="top" usebox="none">
\r
11562 \begin_inset Text
\r
11564 \begin_layout Plain Layout
\r
11570 <cell alignment="center" valignment="top" usebox="none">
\r
11571 \begin_inset Text
\r
11573 \begin_layout Plain Layout
\r
11574 \begin_inset Formula $A=B$
\r
11584 <cell alignment="center" valignment="top" usebox="none">
\r
11585 \begin_inset Text
\r
11587 \begin_layout Plain Layout
\r
11588 \begin_inset Note Note
\r
11591 \begin_layout Plain Layout
\r
11598 is only used as spacer.
\r
11604 \begin_inset Formula $\raisebox{5mm}{}$
\r
11607 equation without space
\r
11612 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
\r
11613 \begin_inset Text
\r
11615 \begin_layout Plain Layout
\r
11616 \begin_inset Formula $A{=}B$
\r
11632 \begin_layout Standard
\r
11634 The command for the last formula is:
\r
11639 \begin_inset Formula $\to$
\r
11645 \begin_layout Standard
\r
11646 \begin_inset VSpace bigskip
\r
11649 Spaces are needed for physical units, because the space between the value
\r
11650 and the unit is the smallest one and not a normal space.
\r
11651 For units in text, the smallest space is inserted via the menu
\r
11653 Insert\SpecialChar \menuseparator
\r
11654 Formatting\SpecialChar \menuseparator
\r
11656 \begin_inset space ~
\r
11662 \begin_inset Info
\r
11664 arg "space-insert thin"
\r
11670 \begin_layout Standard
\r
11671 An example to visualize the difference:
\r
11674 \begin_layout Standard
\r
11675 \begin_inset Tabular
\r
11676 <lyxtabular version="3" rows="2" columns="2">
\r
11677 <features rotate="0" tabularvalignment="middle">
\r
11678 <column alignment="left" valignment="top">
\r
11679 <column alignment="left" valignment="top">
\r
11681 <cell alignment="center" valignment="top" usebox="none">
\r
11682 \begin_inset Text
\r
11684 \begin_layout Plain Layout
\r
11686 \begin_inset Formula $\cdot$
\r
11694 <cell alignment="center" valignment="top" usebox="none">
\r
11695 \begin_inset Text
\r
11697 \begin_layout Plain Layout
\r
11698 space between value and unit
\r
11705 <cell alignment="center" valignment="top" usebox="none">
\r
11706 \begin_inset Text
\r
11708 \begin_layout Plain Layout
\r
11710 \begin_inset space \thinspace{}
\r
11714 \begin_inset Formula $\cdot$
\r
11722 <cell alignment="center" valignment="top" usebox="none">
\r
11723 \begin_inset Text
\r
11725 \begin_layout Plain Layout
\r
11726 smallest space between value and unit
\r
11739 \begin_layout Subsection
\r
11744 \begin_layout Plain Layout
\r
11754 \begin_inset Foot
\r
11757 \begin_layout Plain Layout
\r
11758 for vertical space in formulas see
\r
11759 \begin_inset CommandInset ref
\r
11761 reference "sub:Line-Separation"
\r
11774 \begin_layout Plain Layout
\r
11782 \begin_inset Note Note
\r
11785 \begin_layout Plain Layout
\r
11788 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
\r
11791 \begin_layout Plain Layout
\r
11794 texorpdfstring is in section
\r
11795 \begin_inset CommandInset ref
\r
11797 reference "sub:Formulas-in-Section"
\r
11807 \begin_inset CommandInset label
\r
11808 LatexCommand label
\r
11809 name "sub:Variable-Space"
\r
11814 \begin_inset Index idx
\r
11817 \begin_layout Plain Layout
\r
11818 Space ! horizontal ! variable
\r
11826 \begin_layout Standard
\r
11827 Space with a defined length can be inserted with the command
\r
11834 \begin_inset Index idx
\r
11837 \begin_layout Plain Layout
\r
11847 \begin_inset Quotes eld
\r
11856 \begin_layout Plain Layout
\r
11868 \begin_inset Quotes erd
\r
11872 The length can be specified by left-clicking on the
\r
11873 \begin_inset Quotes eld
\r
11882 \begin_layout Plain Layout
\r
11894 \begin_inset Quotes erd
\r
11898 The length may also be negative.
\r
11899 To insert as much space as is available, the command
\r
11906 \begin_inset Index idx
\r
11909 \begin_layout Plain Layout
\r
11920 \begin_layout Standard
\r
11921 \begin_inset VSpace -1mm
\r
11927 \begin_layout Standard
\r
11929 \begin_inset Tabular
\r
11930 <lyxtabular version="3" rows="4" columns="2">
\r
11931 <features rotate="0" tabularvalignment="middle">
\r
11932 <column alignment="center" valignment="top">
\r
11933 <column alignment="center" valignment="top">
\r
11935 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
11936 \begin_inset Text
\r
11938 \begin_layout Plain Layout
\r
11946 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
11947 \begin_inset Text
\r
11949 \begin_layout Plain Layout
\r
11957 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
11958 \begin_inset Text
\r
11960 \begin_layout Plain Layout
\r
11967 \begin_layout Plain Layout
\r
11977 \begin_inset Formula $\to$
\r
11983 \begin_inset space \thinspace{}
\r
11991 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
11992 \begin_inset Text
\r
11994 \begin_layout Plain Layout
\r
11995 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
\r
12005 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
12006 \begin_inset Text
\r
12008 \begin_layout Plain Layout
\r
12015 \begin_layout Plain Layout
\r
12025 \begin_inset Formula $\to$
\r
12031 \begin_inset space \thinspace{}
\r
12039 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
12040 \begin_inset Text
\r
12042 \begin_layout Plain Layout
\r
12043 \begin_inset Formula $A\hspace{-1mm}A\not=A$
\r
12053 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
12054 \begin_inset Text
\r
12056 \begin_layout Plain Layout
\r
12063 \begin_layout Plain Layout
\r
12077 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
12078 \begin_inset Text
\r
12080 \begin_layout Plain Layout
\r
12081 \begin_inset Formula $A=A\hfill B=B$
\r
12097 \begin_layout Standard
\r
12098 In the last example the available space is given by the longest column entry
\r
12100 In an inline formula the space depends on the length of the line in which
\r
12108 Thus, when the line uses the full width, no space will be created.
\r
12115 only has an effect on displayed formulas when the formula style
\r
12120 (Formula styles are explained in
\r
12121 \begin_inset CommandInset ref
\r
12123 reference "sec:Formula-Styles"
\r
12130 \begin_layout Standard
\r
12137 , there are the commands
\r
12149 that fill the space with a pattern, see
\r
12150 \begin_inset CommandInset ref
\r
12152 reference "sub:Ellipses"
\r
12159 \begin_layout Standard
\r
12160 For text, variable space can be inserted via the menu
\r
12162 Insert\SpecialChar \menuseparator
\r
12163 Formatting\SpecialChar \menuseparator
\r
12165 \begin_inset space ~
\r
12173 \begin_layout Standard
\r
12174 This is a line with
\r
12175 \begin_inset space \hspace{}
\r
12180 \begin_inset space \thinspace{}
\r
12186 \begin_layout Standard
\r
12187 This is a line with
\r
12188 \begin_inset space \hfill{}
\r
12194 \begin_layout Subsection
\r
12195 Space besides inline Formulas
\r
12196 \begin_inset Index idx
\r
12199 \begin_layout Plain Layout
\r
12200 Space ! besides inline formulas
\r
12208 \begin_layout Standard
\r
12209 The space that surrounds inline formulas can be adjusted with the length
\r
12217 \begin_inset Index idx
\r
12220 \begin_layout Plain Layout
\r
12229 The value of a length is set with the command
\r
12236 \begin_inset Index idx
\r
12239 \begin_layout Plain Layout
\r
12247 which has the following scheme:
\r
12250 \begin_layout Standard
\r
12255 setlength{length name}{value}
\r
12258 \begin_layout Standard
\r
12266 \begin_inset space \thinspace{}
\r
12272 \begin_layout Standard
\r
12279 mathsurround}{5mm}
\r
12282 \begin_layout Standard
\r
12283 is inserted in TeX-mode.
\r
12285 \begin_inset space \thinspace{}
\r
12288 mm space will now be set around all inline formulas:
\r
12292 \begin_layout Plain Layout
\r
12298 mathsurround}{5mm}
\r
12306 \begin_layout Standard
\r
12307 This is a line with an inline formula
\r
12308 \begin_inset Formula $A=B$
\r
12312 \begin_inset space \thinspace{}
\r
12315 mm surrounding space.
\r
12319 \begin_layout Plain Layout
\r
12325 mathsurround}{0pt}
\r
12333 \begin_layout Standard
\r
12334 To return to the predefined value,
\r
12340 is set to the value 0
\r
12341 \begin_inset space \thinspace{}
\r
12347 \begin_layout Section
\r
12349 \begin_inset Index idx
\r
12352 \begin_layout Plain Layout
\r
12359 \begin_inset Index idx
\r
12362 \begin_layout Plain Layout
\r
12367 \begin_layout Plain Layout
\r
12378 \begin_layout Plain Layout
\r
12393 \begin_layout Standard
\r
12394 Boxes for text are described in chapter
\r
12395 \family typewriter
\r
12399 \family typewriter
\r
12401 \begin_inset space ~
\r
12409 \begin_layout Subsection
\r
12411 \begin_inset CommandInset label
\r
12412 LatexCommand label
\r
12413 name "sub:Boxes-with-Frame"
\r
12418 \begin_inset Index idx
\r
12421 \begin_layout Plain Layout
\r
12422 Boxes ! with frame
\r
12430 \begin_layout Standard
\r
12431 It is possible to frame a formula or part of one with the commands
\r
12438 \begin_inset Index idx
\r
12441 \begin_layout Plain Layout
\r
12456 \begin_inset Index idx
\r
12459 \begin_layout Plain Layout
\r
12470 \begin_layout Standard
\r
12471 When one of these commands is inserted in a formula, a blue box appears
\r
12472 within a frame to enter formula parts.
\r
12479 an additional formula has to be created by
\r
12483 within this box, because the box content will otherwise be treated as mathemati
\r
12491 is used, a new formula is automatically created inside the frame.
\r
12494 \begin_layout Standard
\r
12501 is not suitable to frame displayed formulas because the formula will always
\r
12502 be set in the size of the text.
\r
12509 is in contrary not suitable to frame inline formulas, because the formula
\r
12510 will always be set in the size of a displayed formula.
\r
12513 \begin_layout Standard
\r
12527 \begin_inset Index idx
\r
12530 \begin_layout Plain Layout
\r
12538 where additionally the frame width and the alignment can be specified.
\r
12545 is used in the following scheme:
\r
12548 \begin_layout Standard
\r
12553 framebox[frame width][position]{box content}
\r
12556 \begin_layout Standard
\r
12557 The position can either be
\r
12574 right aligns the formula in the box.
\r
12575 When no position is given, the formula will be centered.
\r
12576 \begin_inset Newline newline
\r
12579 If no width is given, also no position can be given.
\r
12580 In this case the frame width is adjusted to the box content like for
\r
12589 \begin_layout Standard
\r
12590 When the command
\r
12596 is inserted, a box appears containing three blue boxes.
\r
12597 The first two boxes are surrounded by brackets and denote the two optional
\r
12599 The third box is for formula parts like for
\r
12608 \begin_layout Standard
\r
12609 \begin_inset Newpage newpage
\r
12615 \begin_layout Standard
\r
12617 \begin_inset Tabular
\r
12618 <lyxtabular version="3" rows="5" columns="2">
\r
12619 <features rotate="0" tabularvalignment="middle">
\r
12620 <column alignment="center" valignment="top">
\r
12621 <column alignment="center" valignment="top">
\r
12623 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
12624 \begin_inset Text
\r
12626 \begin_layout Plain Layout
\r
12632 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
12633 \begin_inset Text
\r
12635 \begin_layout Plain Layout
\r
12637 \begin_inset Note Note
\r
12640 \begin_layout Plain Layout
\r
12647 is only used as spacer.
\r
12659 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
12660 \begin_inset Text
\r
12662 \begin_layout Plain Layout
\r
12669 \begin_layout Plain Layout
\r
12688 \begin_layout Plain Layout
\r
12702 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
12703 \begin_inset Text
\r
12705 \begin_layout Plain Layout
\r
12706 \begin_inset Formula $\raisebox{6mm}{}\fbox{\ensuremath{\int A=B}}\raisebox{-4mm}{}$
\r
12716 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
12717 \begin_inset Text
\r
12719 \begin_layout Plain Layout
\r
12726 \begin_layout Plain Layout
\r
12741 \begin_layout Plain Layout
\r
12755 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
12756 \begin_inset Text
\r
12758 \begin_layout Plain Layout
\r
12759 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
\r
12769 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
12770 \begin_inset Text
\r
12772 \begin_layout Plain Layout
\r
12779 \begin_layout Plain Layout
\r
12793 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
12794 \begin_inset Text
\r
12796 \begin_layout Plain Layout
\r
12797 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
\r
12807 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
12808 \begin_inset Text
\r
12810 \begin_layout Plain Layout
\r
12817 \begin_layout Plain Layout
\r
12827 \begin_inset Formula $\to$
\r
12831 \begin_inset Formula $\to$
\r
12844 \begin_layout Plain Layout
\r
12854 \begin_inset Formula $\downarrow$
\r
12862 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
12863 \begin_inset Text
\r
12865 \begin_layout Plain Layout
\r
12866 \begin_inset Formula $\raisebox{6mm}{}$
\r
12870 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
\r
12874 \begin_inset Formula $\raisebox{-4mm}{}$
\r
12890 \begin_layout Standard
\r
12891 The frame thickness can also be adjusted.
\r
12892 To do this the following commands have to be inserted in TeX-mode before
\r
12896 \begin_layout Standard
\r
12906 \begin_inset Quotes eld
\r
12910 \begin_inset Quotes erd
\r
12924 \begin_inset Quotes eld
\r
12928 \begin_inset Quotes erd
\r
12934 \begin_layout Standard
\r
12935 \begin_inset Quotes eld
\r
12939 \begin_inset Quotes erd
\r
12942 specifies the minimal distance between the frame and the first character
\r
12944 An example for this is the following framed formula:
\r
12948 \begin_layout Plain Layout
\r
12960 \begin_inset Formula
\r
12967 Before this formula the commands
\r
12970 \begin_layout Standard
\r
12992 \begin_layout Standard
\r
12993 were inserted in TeX-mode.
\r
12994 The given values are used for all following boxes.
\r
12997 \begin_layout Standard
\r
12998 To return to the standard frame size, the command
\r
13001 \begin_layout Standard
\r
13026 \begin_layout Plain Layout
\r
13040 \begin_layout Standard
\r
13041 is inserted in TeX-mode before the next formula.
\r
13044 \begin_layout Subsection
\r
13045 Boxes without Frame
\r
13046 \begin_inset CommandInset label
\r
13047 LatexCommand label
\r
13048 name "sub:Boxes-without-Frame"
\r
13053 \begin_inset Index idx
\r
13056 \begin_layout Plain Layout
\r
13057 Boxes ! without frame
\r
13065 \begin_layout Standard
\r
13066 For boxes without a frame there are the following box commands:
\r
13073 \begin_inset Index idx
\r
13076 \begin_layout Plain Layout
\r
13091 \begin_inset Index idx
\r
13094 \begin_layout Plain Layout
\r
13109 \begin_inset Index idx
\r
13112 \begin_layout Plain Layout
\r
13123 \begin_layout Standard
\r
13130 a box can be super- or subscripted.
\r
13131 But in contrary to normal super- and subscripting, the characters in the
\r
13132 box keep their font size.
\r
13139 is used in the following scheme:
\r
13142 \begin_layout Standard
\r
13147 raisebox{height}{box content}
\r
13150 \begin_layout Standard
\r
13151 When the box should contain a formula, an extra formula is needed like for
\r
13162 \begin_inset Note Greyedout
\r
13165 \begin_layout Plain Layout
\r
13176 this extra formula is created by pressing
\r
13180 twice instead of once because LyX doesn't yet support
\r
13194 \begin_layout Standard
\r
13196 \begin_inset Tabular
\r
13197 <lyxtabular version="3" rows="4" columns="2">
\r
13198 <features rotate="0" tabularvalignment="middle">
\r
13199 <column alignment="center" valignment="top">
\r
13200 <column alignment="center" valignment="top">
\r
13202 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
13203 \begin_inset Text
\r
13205 \begin_layout Plain Layout
\r
13211 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
13212 \begin_inset Text
\r
13214 \begin_layout Plain Layout
\r
13222 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
13223 \begin_inset Text
\r
13225 \begin_layout Plain Layout
\r
13229 \begin_inset Formula $\to$
\r
13235 \begin_inset Formula $\to$
\r
13243 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
13244 \begin_inset Text
\r
13246 \begin_layout Plain Layout
\r
13247 \begin_inset Formula $H\raisebox{2mm}{al}lo$
\r
13257 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
13258 \begin_inset Text
\r
13260 \begin_layout Plain Layout
\r
13264 \begin_inset Formula $\to$
\r
13270 \begin_inset Formula $\to$
\r
13278 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
13279 \begin_inset Text
\r
13281 \begin_layout Plain Layout
\r
13282 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
\r
13292 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
13293 \begin_inset Text
\r
13295 \begin_layout Plain Layout
\r
13299 \begin_inset Formula $\to$
\r
13318 \begin_layout Plain Layout
\r
13332 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
13333 \begin_inset Text
\r
13335 \begin_layout Plain Layout
\r
13336 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
\r
13352 \begin_layout Standard
\r
13359 is equivalent to
\r
13371 is equivalent to
\r
13377 , with the difference that there is no frame.
\r
13380 \begin_layout Subsection
\r
13382 \begin_inset CommandInset label
\r
13383 LatexCommand label
\r
13384 name "sub:Colored-Boxes"
\r
13389 \begin_inset Index idx
\r
13392 \begin_layout Plain Layout
\r
13401 \begin_layout Standard
\r
13402 To be able to use all commands explained in this section, the LaTeX-package
\r
13408 \begin_inset Foot
\r
13411 \begin_layout Plain Layout
\r
13412 The LaTeX-package
\r
13416 is part of every LaTeX standard installation.
\r
13422 \begin_inset Index idx
\r
13425 \begin_layout Plain Layout
\r
13431 has to be loaded in the LaTeX-preamble with the line
\r
13432 \begin_inset Foot
\r
13435 \begin_layout Plain Layout
\r
13436 When text is colored somewhere in the document with a predefined color,
\r
13437 LyX loads the LaTeX-package
\r
13442 Thus it is possible that the package is loaded twice, but this does not
\r
13449 \begin_inset Note Note
\r
13452 \begin_layout Plain Layout
\r
13453 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
\r
13462 \begin_layout Standard
\r
13467 usepackage{color}
\r
13470 \begin_layout Standard
\r
13471 \begin_inset VSpace medskip
\r
13474 To color boxes, the command
\r
13481 \begin_inset Index idx
\r
13484 \begin_layout Plain Layout
\r
13492 is used in the following scheme:
\r
13495 \begin_layout Standard
\r
13500 colorbox{color}{box content}
\r
13503 \begin_layout Standard
\r
13504 The box content can also be a box and a
\r
13510 can also be part of another box (see the 2nd and 3rd example).
\r
13511 When the box should contain a formula, an extra formula has to be created,
\r
13512 the same way as for
\r
13519 \begin_inset Foot
\r
13522 \begin_layout Plain Layout
\r
13523 This also applies for the command
\r
13537 \begin_layout Standard
\r
13538 One of the following predefined colors can be chosen:
\r
13541 \begin_layout Standard
\r
13575 \begin_layout Standard
\r
13577 \begin_inset Tabular
\r
13578 <lyxtabular version="3" rows="4" columns="2">
\r
13579 <features rotate="0" tabularvalignment="middle">
\r
13580 <column alignment="center" valignment="top">
\r
13581 <column alignment="center" valignment="top">
\r
13583 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
13584 \begin_inset Text
\r
13586 \begin_layout Plain Layout
\r
13592 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
13593 \begin_inset Text
\r
13595 \begin_layout Plain Layout
\r
13597 \begin_inset Note Note
\r
13600 \begin_layout Plain Layout
\r
13607 is only used as spacer.
\r
13619 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
13620 \begin_inset Text
\r
13622 \begin_layout Plain Layout
\r
13626 \begin_inset Formula $\to$
\r
13636 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
13637 \begin_inset Text
\r
13639 \begin_layout Plain Layout
\r
13640 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
\r
13650 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
13651 \begin_inset Text
\r
13653 \begin_layout Plain Layout
\r
13657 \begin_inset Formula $\to$
\r
13668 \begin_layout Plain Layout
\r
13682 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
13683 \begin_inset Text
\r
13685 \begin_layout Plain Layout
\r
13686 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
\r
13696 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
13697 \begin_inset Text
\r
13699 \begin_layout Plain Layout
\r
13706 \begin_layout Plain Layout
\r
13718 \begin_inset Formula $\to$
\r
13737 \begin_layout Plain Layout
\r
13751 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
13752 \begin_inset Text
\r
13754 \begin_layout Plain Layout
\r
13755 \begin_inset Formula $\raisebox{7mm}{}\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}\raisebox{-5mm}{}$
\r
13771 \begin_layout Standard
\r
13778 only colors the box but not the characters in the box.
\r
13779 To color all characters, the whole formula is highlighted and the desired
\r
13780 color is chosen in the
\r
13783 \begin_inset space ~
\r
13789 The dialog can be called with the toolbar button
\r
13790 \begin_inset Graphics
\r
13791 filename ../images/dialog-show_character.png
\r
13798 Edit\SpecialChar \menuseparator
\r
13800 \begin_inset space ~
\r
13803 Style\SpecialChar \menuseparator
\r
13807 The formula number then has the same color as the formula.
\r
13808 When the formula number should get another color than the formula characters,
\r
13809 the color must be changed within the formula.
\r
13812 \begin_layout Standard
\r
13816 \begin_layout Standard
\r
13819 \begin_inset Formula
\r
13821 \int A=B\label{eq:red}
\r
13829 \begin_inset Formula
\r
13831 \textcolor{red}{\int A=B}\label{eq:redgreen}
\r
13839 \begin_layout Standard
\r
13841 \begin_inset CommandInset ref
\r
13842 LatexCommand eqref
\r
13843 reference "eq:red"
\r
13847 is completely colored red.
\r
13848 \begin_inset Newline newline
\r
13852 \begin_inset CommandInset ref
\r
13853 LatexCommand eqref
\r
13854 reference "eq:redgreen"
\r
13858 was first completely colored green to set the color for the formula number.
\r
13859 Subsequently the formula characters were colored red.
\r
13862 \begin_layout Standard
\r
13863 \begin_inset VSpace bigskip
\r
13866 To color the frame different than the rest of the box, the command
\r
13873 \begin_inset Index idx
\r
13876 \begin_layout Plain Layout
\r
13884 is used in the following scheme:
\r
13887 \begin_layout Standard
\r
13892 fcolorbox{frame color}{color}{box content}
\r
13895 \begin_layout Standard
\r
13902 is an extension of the command
\r
13909 The frame width is set, like for
\r
13932 \begin_layout Plain Layout
\r
13944 \begin_inset Formula
\r
13946 \fcolorbox{cyan}{magenta}{A=B}
\r
13955 \begin_layout Plain Layout
\r
13969 \begin_layout Standard
\r
13970 This formula was created with the command
\r
13971 \begin_inset Newline newline
\r
13979 \begin_inset Formula $\to$
\r
13985 \begin_inset Formula $\to$
\r
13995 \begin_layout Standard
\r
13996 \begin_inset VSpace bigskip
\r
13999 To use other colors than the predefined ones, they have to be defined first.
\r
14002 \begin_layout Standard
\r
14003 One can for example define the color
\r
14004 \begin_inset Quotes eld
\r
14012 \begin_inset Quotes erd
\r
14015 with the LaTeX-preamble line:
\r
14018 \begin_layout Standard
\r
14023 definecolor{darkgreen}{cmyk}{0.5,
\r
14038 \begin_inset Index idx
\r
14041 \begin_layout Plain Layout
\r
14052 \begin_layout Standard
\r
14057 is the color space that denotes the colors
\r
14074 The four comma separated numbers are the portion factor for the corresponding
\r
14075 colors of the color space.
\r
14076 The factors can be in the range of 0
\r
14077 \begin_inset space \thinspace{}
\r
14081 \begin_inset space \thinspace{}
\r
14089 also the color space
\r
14093 can be used for definitions.
\r
14110 , so that there are in this case three portion factors for the corresponding
\r
14112 Furthermore there is the color space
\r
14116 with one portion factor for the gray value.
\r
14119 \begin_layout Standard
\r
14120 As example a framed box with the new defined color
\r
14124 where the characters have been colored
\r
14129 \begin_inset Formula
\r
14131 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}
\r
14139 \begin_layout Standard
\r
14140 Self-defined colors can also be used for text with the help of the command
\r
14148 \begin_inset Index idx
\r
14151 \begin_layout Plain Layout
\r
14160 \begin_layout Standard
\r
14164 \begin_layout Plain Layout
\r
14168 textcolor{darkgreen}{
\r
14173 This sentence is
\r
14174 \begin_inset Quotes eld
\r
14178 \begin_inset Quotes erd
\r
14185 \begin_layout Plain Layout
\r
14195 \begin_layout Standard
\r
14203 \begin_inset Index idx
\r
14206 \begin_layout Plain Layout
\r
14214 is used in the scheme
\r
14218 textcolor{color}{characters to color}
\r
14223 \begin_layout Subsection
\r
14225 \begin_inset CommandInset label
\r
14226 LatexCommand label
\r
14227 name "sub:Paragraph-Boxes"
\r
14232 \begin_inset Index idx
\r
14235 \begin_layout Plain Layout
\r
14236 Boxes ! as paragraph
\r
14244 \begin_layout Standard
\r
14245 A box that can contain several lines and paragraphs, a so-called paragraph
\r
14246 box (parbox), can be created with the menu
\r
14248 Insert\SpecialChar \menuseparator
\r
14251 or the toolbar button
\r
14252 \begin_inset Graphics
\r
14253 filename ../images/box-insert.png
\r
14261 \begin_layout Standard
\r
14262 The following example shows a framed parbox in a line:
\r
14265 \begin_layout Standard
\r
14266 \begin_inset VSpace medskip
\r
14270 \begin_inset Box Boxed
\r
14280 height_special "totalheight"
\r
14283 \begin_layout Plain Layout
\r
14284 This is a paragraph box.
\r
14286 \begin_inset space \thinspace{}
\r
14289 cm long and can also contain formulas:
\r
14290 \begin_inset Formula $\int A\,\mathrm{d}s=C$
\r
14301 \begin_layout Standard
\r
14302 \begin_inset VSpace medskip
\r
14308 \begin_layout Standard
\r
14309 Such a box is created by right-clicking on the gray box inset.
\r
14310 A dialog pops up showing the box properties.
\r
14311 In our case set:
\r
14315 : Rectangular box,
\r
14324 \begin_inset space \thinspace{}
\r
14329 Vertical Box Alignment
\r
14334 \begin_layout Standard
\r
14335 \begin_inset VSpace medskip
\r
14338 In LaTeX a parbox is created with the command
\r
14345 \begin_inset Index idx
\r
14348 \begin_layout Plain Layout
\r
14356 which has the following scheme:
\r
14359 \begin_layout Standard
\r
14364 parbox[position]{width}{box content}
\r
14367 \begin_layout Standard
\r
14382 \begin_inset Quotes eld
\r
14386 \begin_inset Quotes erd
\r
14389 means that the box is aligned within the surrounding text with its last
\r
14396 \begin_inset Quotes eld
\r
14400 \begin_inset Quotes erd
\r
14403 this is done with the first line.
\r
14404 When no position is given, the box will be vertically centered, see section
\r
14412 \begin_inset space ~
\r
14417 manual for examples.
\r
14420 \begin_layout Standard
\r
14421 \begin_inset VSpace bigskip
\r
14424 To frame formulas completely, including the formula number, the formula
\r
14425 must be set into a parbox.
\r
14426 To do this, the command
\r
14440 is inserted in TeX-mode before the formula.
\r
14448 \begin_inset Index idx
\r
14451 \begin_layout Plain Layout
\r
14459 is hereby the line width set for the document.
\r
14460 Because the frame is outside the parbox, 2
\r
14461 \begin_inset space \thinspace{}
\r
14464 times the frame separation and the frame thickness must be subtracted from
\r
14466 As this is not automatically done by LyX due to a bug
\r
14467 \begin_inset Foot
\r
14470 \begin_layout Plain Layout
\r
14471 \begin_inset CommandInset href
\r
14472 LatexCommand href
\r
14473 name "LyX-bug #4483"
\r
14474 target "http://www.lyx.org/trac/ticket/4483"
\r
14483 , TeX-mode has to be used.
\r
14484 To be able to multiply and subtract in arguments, the LaTeX-package
\r
14489 \begin_inset Foot
\r
14492 \begin_layout Plain Layout
\r
14497 is part of every LaTeX standard installation.
\r
14503 \begin_inset Index idx
\r
14506 \begin_layout Plain Layout
\r
14512 must be loaded in the LaTeX-preamble with the line
\r
14515 \begin_layout Standard
\r
14523 \begin_layout Standard
\r
14524 Behind the formula both boxes are closed by entering
\r
14529 Here is an example:
\r
14533 \begin_layout Plain Layout
\r
14547 \begin_layout Standard
\r
14551 \begin_layout Plain Layout
\r
14569 \begin_inset Formula
\r
14571 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}
\r
14580 \begin_layout Plain Layout
\r
14591 \begin_layout Plain Layout
\r
14605 \begin_layout Standard
\r
14606 \begin_inset VSpace medskip
\r
14609 As a parbox is used as the argument of
\r
14615 , there is in this case no difference between
\r
14630 \begin_layout Standard
\r
14631 \begin_inset VSpace bigskip
\r
14634 Paragraph boxes are very useful to comment formulas directly.
\r
14641 is used in combination with the command
\r
14655 \begin_inset CommandInset ref
\r
14657 reference "sub:User-defined-Numbering"
\r
14664 \begin_layout Standard
\r
14665 An example of a formula commented with
\r
14674 \begin_layout Standard
\r
14678 \begin_layout Plain Layout
\r
14691 This is a description.
\r
14692 It is distinctly separated from the formula and multiline.
\r
14696 \begin_layout Plain Layout
\r
14708 \begin_layout Standard
\r
14709 Such a formula must be inserted completely in TeX-mode because LyX does
\r
14710 not yet support the command
\r
14717 The formula is created with the following command sequence:
\r
14720 \begin_layout Standard
\r
14733 is inserted in TeX-mode.
\r
14734 \begin_inset Foot
\r
14737 \begin_layout Plain Layout
\r
14738 When the formula style
\r
14750 can also be replaced by
\r
14757 (formula styles see
\r
14758 \begin_inset CommandInset ref
\r
14760 reference "sec:Formula-Styles"
\r
14769 Then the description follows as normal text and finally
\r
14775 is inserted in TeX-mode.
\r
14788 hereby create a displayed formula.
\r
14791 \begin_layout Standard
\r
14792 The advantages of
\r
14798 can be seen in this example that was
\r
14799 \begin_inset Quotes eld
\r
14803 \begin_inset Quotes erd
\r
14806 using the mathematical textmode:
\r
14807 \begin_inset Formula
\r
14809 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}
\r
14817 \begin_layout Section
\r
14819 \begin_inset Index idx
\r
14822 \begin_layout Plain Layout
\r
14831 \begin_layout Subsection
\r
14833 \begin_inset CommandInset label
\r
14834 LatexCommand label
\r
14835 name "sub:Big-Operators"
\r
14840 \begin_inset Index idx
\r
14843 \begin_layout Plain Layout
\r
14850 \begin_inset Index idx
\r
14853 \begin_layout Plain Layout
\r
14860 \begin_inset Index idx
\r
14863 \begin_layout Plain Layout
\r
14872 \begin_layout Standard
\r
14873 To be able to use all integral operators listed here, the option
\r
14875 Use esint package automatically
\r
14877 must be set in the document settings under
\r
14880 \begin_inset space ~
\r
14888 \begin_layout Standard
\r
14889 \begin_inset space \hfill{}
\r
14893 \begin_inset Tabular
\r
14894 <lyxtabular version="3" rows="11" columns="2">
\r
14895 <features rotate="0" tabularvalignment="middle">
\r
14896 <column alignment="center" valignment="top" width="0pt">
\r
14897 <column alignment="center" valignment="top" width="0pt">
\r
14899 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
14900 \begin_inset Text
\r
14902 \begin_layout Plain Layout
\r
14908 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
14909 \begin_inset Text
\r
14911 \begin_layout Plain Layout
\r
14919 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
14920 \begin_inset Text
\r
14922 \begin_layout Plain Layout
\r
14926 \begin_inset Index idx
\r
14929 \begin_layout Plain Layout
\r
14942 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
14943 \begin_inset Text
\r
14945 \begin_layout Plain Layout
\r
14946 \begin_inset Formula $\int$
\r
14956 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
14957 \begin_inset Text
\r
14959 \begin_layout Plain Layout
\r
14967 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
14968 \begin_inset Text
\r
14970 \begin_layout Plain Layout
\r
14971 \begin_inset Formula $\oint$
\r
14981 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
14982 \begin_inset Text
\r
14984 \begin_layout Plain Layout
\r
14992 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
14993 \begin_inset Text
\r
14995 \begin_layout Plain Layout
\r
14996 \begin_inset Formula $\ointctrclockwise$
\r
15006 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
15007 \begin_inset Text
\r
15009 \begin_layout Plain Layout
\r
15017 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
15018 \begin_inset Text
\r
15020 \begin_layout Plain Layout
\r
15021 \begin_inset Formula $\ointclockwise$
\r
15031 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
15032 \begin_inset Text
\r
15034 \begin_layout Plain Layout
\r
15042 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
15043 \begin_inset Text
\r
15045 \begin_layout Plain Layout
\r
15046 \begin_inset Formula $\sqint$
\r
15056 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
15057 \begin_inset Text
\r
15059 \begin_layout Plain Layout
\r
15067 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
15068 \begin_inset Text
\r
15070 \begin_layout Plain Layout
\r
15072 \begin_inset Formula $\fint$
\r
15082 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
15083 \begin_inset Text
\r
15085 \begin_layout Plain Layout
\r
15093 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
15094 \begin_inset Text
\r
15096 \begin_layout Plain Layout
\r
15098 \begin_inset Formula $\landupint$
\r
15108 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
15109 \begin_inset Text
\r
15111 \begin_layout Plain Layout
\r
15119 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
15120 \begin_inset Text
\r
15122 \begin_layout Plain Layout
\r
15124 \begin_inset Formula $\landdownint$
\r
15134 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
15135 \begin_inset Text
\r
15137 \begin_layout Plain Layout
\r
15145 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
15146 \begin_inset Text
\r
15148 \begin_layout Plain Layout
\r
15149 \begin_inset Formula $\bigcap$
\r
15159 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
15160 \begin_inset Text
\r
15162 \begin_layout Plain Layout
\r
15170 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
15171 \begin_inset Text
\r
15173 \begin_layout Plain Layout
\r
15174 \begin_inset Formula $\bigcup$
\r
15188 \begin_inset space \hfill{}
\r
15192 \begin_inset Tabular
\r
15193 <lyxtabular version="3" rows="11" columns="2">
\r
15194 <features rotate="0" tabularvalignment="middle">
\r
15195 <column alignment="center" valignment="top" width="0pt">
\r
15196 <column alignment="center" valignment="top" width="0pt">
\r
15198 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
15199 \begin_inset Text
\r
15201 \begin_layout Plain Layout
\r
15207 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
15208 \begin_inset Text
\r
15210 \begin_layout Plain Layout
\r
15218 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
15219 \begin_inset Text
\r
15221 \begin_layout Plain Layout
\r
15225 \begin_inset Index idx
\r
15228 \begin_layout Plain Layout
\r
15241 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
15242 \begin_inset Text
\r
15244 \begin_layout Plain Layout
\r
15245 \begin_inset Formula $\sum$
\r
15255 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
15256 \begin_inset Text
\r
15258 \begin_layout Plain Layout
\r
15262 \begin_inset Index idx
\r
15265 \begin_layout Plain Layout
\r
15272 \begin_layout Plain Layout
\r
15291 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
15292 \begin_inset Text
\r
15294 \begin_layout Plain Layout
\r
15295 \begin_inset Formula $\prod$
\r
15305 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
15306 \begin_inset Text
\r
15308 \begin_layout Plain Layout
\r
15316 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
15317 \begin_inset Text
\r
15319 \begin_layout Plain Layout
\r
15320 \begin_inset Formula $\coprod$
\r
15330 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
15331 \begin_inset Text
\r
15333 \begin_layout Plain Layout
\r
15341 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
15342 \begin_inset Text
\r
15344 \begin_layout Plain Layout
\r
15345 \begin_inset Formula $\bigodot$
\r
15355 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
15356 \begin_inset Text
\r
15358 \begin_layout Plain Layout
\r
15366 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
15367 \begin_inset Text
\r
15369 \begin_layout Plain Layout
\r
15370 \begin_inset Formula $\bigotimes$
\r
15380 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
15381 \begin_inset Text
\r
15383 \begin_layout Plain Layout
\r
15391 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
15392 \begin_inset Text
\r
15394 \begin_layout Plain Layout
\r
15395 \begin_inset Formula $\bigoplus$
\r
15405 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
15406 \begin_inset Text
\r
15408 \begin_layout Plain Layout
\r
15416 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
15417 \begin_inset Text
\r
15419 \begin_layout Plain Layout
\r
15420 \begin_inset Formula $\bigwedge$
\r
15430 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
15431 \begin_inset Text
\r
15433 \begin_layout Plain Layout
\r
15441 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
15442 \begin_inset Text
\r
15444 \begin_layout Plain Layout
\r
15445 \begin_inset Formula $\bigvee$
\r
15455 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
15456 \begin_inset Text
\r
15458 \begin_layout Plain Layout
\r
15466 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
15467 \begin_inset Text
\r
15469 \begin_layout Plain Layout
\r
15470 \begin_inset Formula $\bigsqcup$
\r
15480 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
15481 \begin_inset Text
\r
15483 \begin_layout Plain Layout
\r
15491 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
15492 \begin_inset Text
\r
15494 \begin_layout Plain Layout
\r
15495 \begin_inset Formula $\biguplus$
\r
15509 \begin_inset space \hfill{}
\r
15515 \begin_layout Standard
\r
15516 All big operators can also be inserted via the math toolbar button
\r
15517 \begin_inset Graphics
\r
15518 filename ../images/math/intop.png
\r
15526 \begin_layout Standard
\r
15527 The operators are called big because they are bigger than the sometimes
\r
15528 equal looking binary operators.
\r
15529 All big operators can have limits as described in the next subsection.
\r
15532 \begin_layout Standard
\r
15533 For all integral operators there is a second version available, ending in
\r
15551 These operators are different from
\r
15558 \begin_inset space \space{}
\r
15561 in the style the operator limits are displayed, see
\r
15562 \begin_inset CommandInset ref
\r
15564 reference "sub:Operator-Limits"
\r
15572 \begin_layout Subsubsection*
\r
15573 Advice for Integrals
\r
15576 \begin_layout Standard
\r
15581 in an integral is an operator, that therefore has to be set upright.
\r
15582 This is done by highlighting the
\r
15586 and using the keyboard shortcut
\r
15587 \begin_inset Info
\r
15593 \begin_inset Foot
\r
15596 \begin_layout Plain Layout
\r
15602 \begin_inset CommandInset ref
\r
15604 reference "sub:Font-Styles"
\r
15614 Finally the smallest space is inserted before the
\r
15618 , as this is usual for operators.
\r
15622 \begin_layout Standard
\r
15624 \begin_inset Formula $\int A(x)dx$
\r
15628 \begin_inset Newline newline
\r
15632 \begin_inset Phantom HPhantom
\r
15635 \begin_layout Plain Layout
\r
15642 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
\r
15648 \begin_layout Standard
\r
15649 For multiple integrals there are the following commands:
\r
15650 \begin_inset VSpace medskip
\r
15656 \begin_layout Standard
\r
15657 \begin_inset space \hfill{}
\r
15661 \begin_inset Tabular
\r
15662 <lyxtabular version="3" rows="4" columns="2">
\r
15663 <features rotate="0" tabularvalignment="middle">
\r
15664 <column alignment="center" valignment="top">
\r
15665 <column alignment="center" valignment="top">
\r
15667 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
15668 \begin_inset Text
\r
15670 \begin_layout Plain Layout
\r
15676 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
15677 \begin_inset Text
\r
15679 \begin_layout Plain Layout
\r
15681 \begin_inset Note Note
\r
15684 \begin_layout Plain Layout
\r
15691 is only used as spacer.
\r
15703 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
15704 \begin_inset Text
\r
15706 \begin_layout Plain Layout
\r
15714 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
15715 \begin_inset Text
\r
15717 \begin_layout Plain Layout
\r
15718 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
\r
15728 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
15729 \begin_inset Text
\r
15731 \begin_layout Plain Layout
\r
15739 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
15740 \begin_inset Text
\r
15742 \begin_layout Plain Layout
\r
15743 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
\r
15753 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
15754 \begin_inset Text
\r
15756 \begin_layout Plain Layout
\r
15764 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
15765 \begin_inset Text
\r
15767 \begin_layout Plain Layout
\r
15768 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
\r
15782 \begin_inset space \hfill{}
\r
15786 \begin_inset Tabular
\r
15787 <lyxtabular version="3" rows="4" columns="2">
\r
15788 <features rotate="0" tabularvalignment="middle">
\r
15789 <column alignment="center" valignment="top">
\r
15790 <column alignment="center" valignment="top">
\r
15792 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
15793 \begin_inset Text
\r
15795 \begin_layout Plain Layout
\r
15801 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
15802 \begin_inset Text
\r
15804 \begin_layout Plain Layout
\r
15812 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
15813 \begin_inset Text
\r
15815 \begin_layout Plain Layout
\r
15823 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
15824 \begin_inset Text
\r
15826 \begin_layout Plain Layout
\r
15827 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
\r
15837 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
15838 \begin_inset Text
\r
15840 \begin_layout Plain Layout
\r
15848 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
15849 \begin_inset Text
\r
15851 \begin_layout Plain Layout
\r
15852 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
\r
15862 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
15863 \begin_inset Text
\r
15865 \begin_layout Plain Layout
\r
15873 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
15874 \begin_inset Text
\r
15876 \begin_layout Plain Layout
\r
15877 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
\r
15891 \begin_inset space \hfill{}
\r
15897 \begin_layout Standard
\r
15898 \begin_inset Newpage newpage
\r
15904 \begin_layout Subsection
\r
15906 \begin_inset CommandInset label
\r
15907 LatexCommand label
\r
15908 name "sub:Operator-Limits"
\r
15913 \begin_inset Index idx
\r
15916 \begin_layout Plain Layout
\r
15917 Operators ! Limits
\r
15925 \begin_layout Standard
\r
15926 Limits are created by super- and subscripts:
\r
15929 \begin_layout Standard
\r
15931 \begin_inset Tabular
\r
15932 <lyxtabular version="3" rows="2" columns="2">
\r
15933 <features rotate="0" tabularvalignment="middle">
\r
15934 <column alignment="center" valignment="top" width="0pt">
\r
15935 <column alignment="center" valignment="top" width="0pt">
\r
15937 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
15938 \begin_inset Text
\r
15940 \begin_layout Plain Layout
\r
15946 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
15947 \begin_inset Text
\r
15949 \begin_layout Plain Layout
\r
15951 \begin_inset Note Note
\r
15954 \begin_layout Plain Layout
\r
15961 is only used as spacer.
\r
15973 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
15974 \begin_inset Text
\r
15976 \begin_layout Plain Layout
\r
15985 \begin_layout Plain Layout
\r
15995 \begin_inset Formula $\to$
\r
15999 \begin_inset Formula $\to$
\r
16007 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
16008 \begin_inset Text
\r
16010 \begin_layout Plain Layout
\r
16011 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
\r
16027 \begin_layout Standard
\r
16028 Limits of inline formulas are set right beside the operator.
\r
16029 Limits in displayed formulas are set above or below the operator, except
\r
16030 for integral limits.
\r
16033 \begin_layout Standard
\r
16034 To force that the limits are set beside the operator, the cursor is set
\r
16035 directly behind the operator and the limits type is changed with the menu
\r
16038 Edit\SpecialChar \menuseparator
\r
16039 Math\SpecialChar \menuseparator
\r
16040 Change Limits Type
\r
16049 \begin_inset Info
\r
16051 arg "math-limits"
\r
16058 \begin_layout Standard
\r
16059 The default limits type is this:
\r
16060 \begin_inset Formula
\r
16062 \sum_{x=0}^{\infty}\frac{1}{x^{2}}
\r
16067 This is how it looks when the limits type was changed to
\r
16074 \begin_inset Formula
\r
16076 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}
\r
16081 For integrals, except those ending with
\r
16097 etc., the limits are by default set beside the operator.
\r
16098 But for multiple integrals the limits are often set below the operator.
\r
16099 In the following example the limits type was therefore set to
\r
16103 and so set below the integrals:
\r
16104 \begin_inset Formula
\r
16106 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}
\r
16114 \begin_layout Standard
\r
16115 \begin_inset VSpace medskip
\r
16118 To specify conditions for limits, the commands
\r
16125 \begin_inset Index idx
\r
16128 \begin_layout Plain Layout
\r
16143 \begin_inset Index idx
\r
16146 \begin_layout Plain Layout
\r
16155 To create for example this expression
\r
16156 \begin_inset Formula
\r
16158 \sum_{\begin{subarray}{c}
\r
16161 k\,\in\,\mathbb{N}
\r
16162 \end{subarray}}^{n}k^{-2}\label{eq:substack}
\r
16170 \begin_layout Standard
\r
16171 the following has to be done:
\r
16172 \begin_inset Newline newline
\r
16175 First the command
\r
16187 \begin_layout Plain Layout
\r
16199 One is now in a blue box under the summation operator and insert there
\r
16208 \begin_layout Plain Layout
\r
16220 The blue box is now within a purple box and now several lines can be written
\r
16221 among each other.
\r
16222 A new line is created by inserting a line break (
\r
16223 \begin_inset Info
\r
16225 arg "newline-insert newline"
\r
16230 \begin_inset Newline newline
\r
16235 0<k<1000 Ctrl+Return
\r
16236 \begin_inset Newline newline
\r
16241 is typed in, a new box appears below for the new line.
\r
16244 \begin_layout Standard
\r
16245 The alignment of the lines can be changed to left aligned with the
\r
16255 Edit\SpecialChar \menuseparator
\r
16259 To get right alignment,
\r
16267 \begin_layout Plain Layout
\r
16278 is inserted at the beginning of the line.
\r
16281 \begin_layout Standard
\r
16288 is equivalent to
\r
16294 with the difference that the lines are always centered.
\r
16297 \begin_layout Standard
\r
16298 \begin_inset VSpace bigskip
\r
16302 \begin_inset CommandInset ref
\r
16303 LatexCommand eqref
\r
16304 reference "eq:substack"
\r
16308 there can be too much space beside an operator, because the characters
\r
16309 following the operator are set beside the limits.
\r
16312 \begin_layout Standard
\r
16313 To avoid this, the following macro can be used in the LaTeX-preamble:
\r
16316 \begin_layout Standard
\r
16330 \begin_inset Newline newline
\r
16341 mathclapinternal}
\r
16342 \begin_inset Newline newline
\r
16349 mathclapinternal #1#2{
\r
16353 mathsurround =0pt #1{#2}$}}
\r
16356 \begin_layout Standard
\r
16357 This defines the command
\r
16364 \begin_inset Index idx
\r
16367 \begin_layout Plain Layout
\r
16375 that sets the width of the limit to 0
\r
16376 \begin_inset space \thinspace{}
\r
16380 The command scheme is
\r
16383 \begin_layout Standard
\r
16391 \begin_layout Standard
\r
16392 where the limit can consist of several conditions.
\r
16395 \begin_layout Standard
\r
16396 Applied on formula
\r
16397 \begin_inset CommandInset ref
\r
16398 LatexCommand eqref
\r
16399 reference "eq:substack"
\r
16403 , one uses the command
\r
16406 \begin_layout Standard
\r
16419 \begin_layout Plain Layout
\r
16428 0<k<1000 Ctrl+Return
\r
16431 \begin_layout Standard
\r
16432 to create the lower limit.
\r
16433 The summand is now directly behind the summation operator:
\r
16434 \begin_inset Formula
\r
16436 \sum_{\mathclap{\substack{0<k<1000\\
\r
16438 k\,\in\,\mathbb{N}
\r
16448 \begin_layout Standard
\r
16449 \begin_inset VSpace bigskip
\r
16452 How to use one limit for several operators is described in
\r
16453 \begin_inset CommandInset ref
\r
16455 reference "sub:Self-defined-Operators"
\r
16462 \begin_layout Subsection
\r
16463 Decoration for Operators
\r
16464 \begin_inset Index idx
\r
16467 \begin_layout Plain Layout
\r
16468 Operators ! Decoration
\r
16476 \begin_layout Standard
\r
16477 With the commands
\r
16484 \begin_inset Index idx
\r
16487 \begin_layout Plain Layout
\r
16502 \begin_inset Index idx
\r
16505 \begin_layout Plain Layout
\r
16513 characters can be placed above or below an operator, respectively.
\r
16514 With the command
\r
16521 \begin_inset Index idx
\r
16524 \begin_layout Plain Layout
\r
16532 characters can be set before and behind a big operator.
\r
16533 The command scheme is:
\r
16536 \begin_layout Standard
\r
16541 sideset{character
\r
16545 before}{character
\r
16552 \begin_layout Standard
\r
16559 must always be before the operator.
\r
16560 You can decorate with several characters and even with other operators
\r
16562 To place for example only characters behind a big operator, write nothing
\r
16563 between the first braces but don't omit the braces.
\r
16566 \begin_layout Standard
\r
16567 For example the command
\r
16572 \begin_inset Formula $\to$
\r
16582 \begin_inset Formula $\to$
\r
16591 \begin_layout Plain Layout
\r
16607 \begin_inset Formula
\r
16609 \sideset{}{'}\sum_{k=1}^{n}
\r
16617 \begin_layout Standard
\r
16618 \begin_inset Note Greyedout
\r
16621 \begin_layout Plain Layout
\r
16628 can only be used to decorate big operators, binary operators are not allowed.
\r
16636 \begin_layout Standard
\r
16649 can also be used to decorate symbols and characters.
\r
16650 For example, the command
\r
16658 \begin_layout Plain Layout
\r
16673 \begin_layout Plain Layout
\r
16685 \begin_inset Formula $\uparrow$
\r
16693 \begin_inset Formula
\r
16695 \overset{a}{\maltese}
\r
16703 \begin_layout Subsection
\r
16705 \begin_inset CommandInset label
\r
16706 LatexCommand label
\r
16707 name "sub:Binary-Operators"
\r
16712 \begin_inset Index idx
\r
16715 \begin_layout Plain Layout
\r
16716 Operators ! binary
\r
16724 \begin_layout Standard
\r
16725 Binary operators are surrounded by space when there is a character before
\r
16727 \begin_inset VSpace medskip
\r
16733 \begin_layout Standard
\r
16734 \begin_inset space \hfill{}
\r
16738 \begin_inset Tabular
\r
16739 <lyxtabular version="3" rows="13" columns="2">
\r
16740 <features rotate="0" tabularvalignment="middle">
\r
16741 <column alignment="center" valignment="top" width="0pt">
\r
16742 <column alignment="center" valignment="top" width="0pt">
\r
16744 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
16745 \begin_inset Text
\r
16747 \begin_layout Plain Layout
\r
16749 \begin_inset Note Note
\r
16752 \begin_layout Plain Layout
\r
16759 is only used as spacer.
\r
16769 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
16770 \begin_inset Text
\r
16772 \begin_layout Plain Layout
\r
16780 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
16781 \begin_inset Text
\r
16783 \begin_layout Plain Layout
\r
16789 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
16790 \begin_inset Text
\r
16792 \begin_layout Plain Layout
\r
16793 \begin_inset Formula $+$
\r
16803 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
16804 \begin_inset Text
\r
16806 \begin_layout Plain Layout
\r
16812 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
16813 \begin_inset Text
\r
16815 \begin_layout Plain Layout
\r
16816 \begin_inset Formula $-$
\r
16826 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
16827 \begin_inset Text
\r
16829 \begin_layout Plain Layout
\r
16837 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
16838 \begin_inset Text
\r
16840 \begin_layout Plain Layout
\r
16841 \begin_inset Formula $\pm$
\r
16851 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
16852 \begin_inset Text
\r
16854 \begin_layout Plain Layout
\r
16862 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
16863 \begin_inset Text
\r
16865 \begin_layout Plain Layout
\r
16866 \begin_inset Formula $\mp$
\r
16876 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
16877 \begin_inset Text
\r
16879 \begin_layout Plain Layout
\r
16887 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
16888 \begin_inset Text
\r
16890 \begin_layout Plain Layout
\r
16891 \begin_inset Formula $\cdot$
\r
16901 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
16902 \begin_inset Text
\r
16904 \begin_layout Plain Layout
\r
16912 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
16913 \begin_inset Text
\r
16915 \begin_layout Plain Layout
\r
16916 \begin_inset Formula $\times$
\r
16926 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
16927 \begin_inset Text
\r
16929 \begin_layout Plain Layout
\r
16937 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
16938 \begin_inset Text
\r
16940 \begin_layout Plain Layout
\r
16941 \begin_inset Formula $\div$
\r
16951 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
16952 \begin_inset Text
\r
16954 \begin_layout Plain Layout
\r
16958 \begin_layout Plain Layout
\r
16962 raisebox{-1.2mm}{
\r
16971 \begin_layout Plain Layout
\r
16983 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
16984 \begin_inset Text
\r
16986 \begin_layout Plain Layout
\r
16987 \begin_inset Formula $*$
\r
16997 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
16998 \begin_inset Text
\r
17000 \begin_layout Plain Layout
\r
17008 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
17009 \begin_inset Text
\r
17011 \begin_layout Plain Layout
\r
17012 \begin_inset Formula $\star$
\r
17022 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
17023 \begin_inset Text
\r
17025 \begin_layout Plain Layout
\r
17033 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
17034 \begin_inset Text
\r
17036 \begin_layout Plain Layout
\r
17037 \begin_inset Formula $\circ$
\r
17047 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
17048 \begin_inset Text
\r
17050 \begin_layout Plain Layout
\r
17058 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
17059 \begin_inset Text
\r
17061 \begin_layout Plain Layout
\r
17062 \begin_inset Formula $\diamond$
\r
17072 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
17073 \begin_inset Text
\r
17075 \begin_layout Plain Layout
\r
17083 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
17084 \begin_inset Text
\r
17086 \begin_layout Plain Layout
\r
17087 \begin_inset Formula $\bullet$
\r
17101 \begin_inset space \hfill{}
\r
17105 \begin_inset Tabular
\r
17106 <lyxtabular version="3" rows="13" columns="2">
\r
17107 <features rotate="0" tabularvalignment="middle">
\r
17108 <column alignment="center" valignment="top" width="0pt">
\r
17109 <column alignment="center" valignment="top" width="0pt">
\r
17111 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
17112 \begin_inset Text
\r
17114 \begin_layout Plain Layout
\r
17120 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
17121 \begin_inset Text
\r
17123 \begin_layout Plain Layout
\r
17131 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
17132 \begin_inset Text
\r
17134 \begin_layout Plain Layout
\r
17142 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
17143 \begin_inset Text
\r
17145 \begin_layout Plain Layout
\r
17146 \begin_inset Formula $\nabla$
\r
17156 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
17157 \begin_inset Text
\r
17159 \begin_layout Plain Layout
\r
17167 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
17168 \begin_inset Text
\r
17170 \begin_layout Plain Layout
\r
17171 \begin_inset Formula $\bigtriangledown$
\r
17181 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
17182 \begin_inset Text
\r
17184 \begin_layout Plain Layout
\r
17192 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
17193 \begin_inset Text
\r
17195 \begin_layout Plain Layout
\r
17196 \begin_inset Formula $\bigtriangleup$
\r
17206 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
17207 \begin_inset Text
\r
17209 \begin_layout Plain Layout
\r
17217 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
17218 \begin_inset Text
\r
17220 \begin_layout Plain Layout
\r
17221 \begin_inset Formula $\Box$
\r
17231 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
17232 \begin_inset Text
\r
17234 \begin_layout Plain Layout
\r
17242 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
17243 \begin_inset Text
\r
17245 \begin_layout Plain Layout
\r
17246 \begin_inset Formula $\cap$
\r
17256 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
17257 \begin_inset Text
\r
17259 \begin_layout Plain Layout
\r
17267 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
17268 \begin_inset Text
\r
17270 \begin_layout Plain Layout
\r
17271 \begin_inset Formula $\cup$
\r
17281 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
17282 \begin_inset Text
\r
17284 \begin_layout Plain Layout
\r
17292 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
17293 \begin_inset Text
\r
17295 \begin_layout Plain Layout
\r
17296 \begin_inset Formula $\dagger$
\r
17306 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
17307 \begin_inset Text
\r
17309 \begin_layout Plain Layout
\r
17317 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
17318 \begin_inset Text
\r
17320 \begin_layout Plain Layout
\r
17321 \begin_inset Formula $\ddagger$
\r
17331 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
17332 \begin_inset Text
\r
17334 \begin_layout Plain Layout
\r
17342 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
17343 \begin_inset Text
\r
17345 \begin_layout Plain Layout
\r
17346 \begin_inset Formula $\wr$
\r
17356 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
17357 \begin_inset Text
\r
17359 \begin_layout Plain Layout
\r
17367 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
17368 \begin_inset Text
\r
17370 \begin_layout Plain Layout
\r
17371 \begin_inset Formula $\bigcirc$
\r
17381 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
17382 \begin_inset Text
\r
17384 \begin_layout Plain Layout
\r
17392 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
17393 \begin_inset Text
\r
17395 \begin_layout Plain Layout
\r
17396 \begin_inset Formula $\wedge$
\r
17406 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
17407 \begin_inset Text
\r
17409 \begin_layout Plain Layout
\r
17417 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
17418 \begin_inset Text
\r
17420 \begin_layout Plain Layout
\r
17421 \begin_inset Formula $\vee$
\r
17435 \begin_inset space \hfill{}
\r
17439 \begin_inset Tabular
\r
17440 <lyxtabular version="3" rows="13" columns="2">
\r
17441 <features rotate="0" tabularvalignment="middle">
\r
17442 <column alignment="center" valignment="top" width="0pt">
\r
17443 <column alignment="center" valignment="top" width="0pt">
\r
17445 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
17446 \begin_inset Text
\r
17448 \begin_layout Plain Layout
\r
17454 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
17455 \begin_inset Text
\r
17457 \begin_layout Plain Layout
\r
17465 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
17466 \begin_inset Text
\r
17468 \begin_layout Plain Layout
\r
17476 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
17477 \begin_inset Text
\r
17479 \begin_layout Plain Layout
\r
17480 \begin_inset Formula $\oplus$
\r
17490 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
17491 \begin_inset Text
\r
17493 \begin_layout Plain Layout
\r
17501 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
17502 \begin_inset Text
\r
17504 \begin_layout Plain Layout
\r
17505 \begin_inset Formula $\ominus$
\r
17515 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
17516 \begin_inset Text
\r
17518 \begin_layout Plain Layout
\r
17526 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
17527 \begin_inset Text
\r
17529 \begin_layout Plain Layout
\r
17530 \begin_inset Formula $\otimes$
\r
17540 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
17541 \begin_inset Text
\r
17543 \begin_layout Plain Layout
\r
17551 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
17552 \begin_inset Text
\r
17554 \begin_layout Plain Layout
\r
17555 \begin_inset Formula $\oslash$
\r
17565 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
17566 \begin_inset Text
\r
17568 \begin_layout Plain Layout
\r
17576 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
17577 \begin_inset Text
\r
17579 \begin_layout Plain Layout
\r
17580 \begin_inset Formula $\odot$
\r
17590 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
17591 \begin_inset Text
\r
17593 \begin_layout Plain Layout
\r
17601 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
17602 \begin_inset Text
\r
17604 \begin_layout Plain Layout
\r
17605 \begin_inset Formula $\amalg$
\r
17615 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
17616 \begin_inset Text
\r
17618 \begin_layout Plain Layout
\r
17626 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
17627 \begin_inset Text
\r
17629 \begin_layout Plain Layout
\r
17630 \begin_inset Formula $\uplus$
\r
17640 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
17641 \begin_inset Text
\r
17643 \begin_layout Plain Layout
\r
17651 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
17652 \begin_inset Text
\r
17654 \begin_layout Plain Layout
\r
17655 \begin_inset Formula $\setminus$
\r
17665 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
17666 \begin_inset Text
\r
17668 \begin_layout Plain Layout
\r
17676 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
17677 \begin_inset Text
\r
17679 \begin_layout Plain Layout
\r
17680 \begin_inset Formula $\sqcap$
\r
17690 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
17691 \begin_inset Text
\r
17693 \begin_layout Plain Layout
\r
17701 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
17702 \begin_inset Text
\r
17704 \begin_layout Plain Layout
\r
17705 \begin_inset Formula $\sqcup$
\r
17715 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
17716 \begin_inset Text
\r
17718 \begin_layout Plain Layout
\r
17726 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
17727 \begin_inset Text
\r
17729 \begin_layout Plain Layout
\r
17730 \begin_inset Formula $\triangleleft$
\r
17740 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
17741 \begin_inset Text
\r
17743 \begin_layout Plain Layout
\r
17751 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
17752 \begin_inset Text
\r
17754 \begin_layout Plain Layout
\r
17755 \begin_inset Formula $\triangleright$
\r
17769 \begin_inset space \hfill{}
\r
17775 \begin_layout Standard
\r
17776 All binary operators can also be inserted via the math toolbar button
\r
17777 \begin_inset Graphics
\r
17778 filename ../images/math/pm.png
\r
17786 \begin_layout Standard
\r
17787 To typeset the Laplace operator also
\r
17804 \begin_inset Formula $\nabla^{2}$
\r
17807 ) can be used instead of
\r
17816 \begin_layout Standard
\r
17823 Insert\SpecialChar \menuseparator
\r
17824 Special Character
\r
17835 \begin_layout Subsection
\r
17836 Self-defined Operators
\r
17837 \begin_inset CommandInset label
\r
17838 LatexCommand label
\r
17839 name "sub:Self-defined-Operators"
\r
17844 \begin_inset Index idx
\r
17847 \begin_layout Plain Layout
\r
17848 Operators ! self-defined
\r
17856 \begin_layout Standard
\r
17857 With the help of the command
\r
17861 DeclareMathOperator
\r
17864 \begin_inset Index idx
\r
17867 \begin_layout Plain Layout
\r
17872 DeclareMathOperator
\r
17877 custom operators can be defined in the LaTeX-preamble.
\r
17878 Its command scheme is:
\r
17881 \begin_layout Standard
\r
17886 DeclareMathOperator{new command}{display}
\r
17889 \begin_layout Standard
\r
17890 Display can be characters or symbols that define how the operator looks
\r
17892 To define a big operator a * is set behind the command.
\r
17893 All self-defined big operators can have limits as described in
\r
17894 \begin_inset CommandInset ref
\r
17896 reference "sub:Operator-Limits"
\r
17903 \begin_layout Standard
\r
17904 For example the LaTeX-preamble line
\r
17907 \begin_layout Standard
\r
17912 DeclareMathOperator*{
\r
17919 \begin_layout Standard
\r
17920 defines the command
\r
17926 , that inserts a big operator consisting of the lozenge symbol from
\r
17927 \begin_inset CommandInset ref
\r
17929 reference "sub:Miscellaneous-Symbols"
\r
17934 \begin_inset Formula
\r
17936 \Lozenge_{n=1}^{\infty}
\r
17941 The command for this formula is:
\r
17952 \begin_inset Formula $\to$
\r
17958 \begin_layout Standard
\r
17959 \begin_inset VSpace bigskip
\r
17962 When self-defined operators are not used several times in the document,
\r
17963 they can also be defined with the commands
\r
17970 \begin_inset Index idx
\r
17973 \begin_layout Plain Layout
\r
17988 \begin_inset Index idx
\r
17991 \begin_layout Plain Layout
\r
17999 , which have the following scheme:
\r
18002 \begin_layout Standard
\r
18016 \begin_layout Standard
\r
18023 defines big operators,
\r
18029 binary operators.
\r
18032 \begin_layout Standard
\r
18040 \begin_inset space \thinspace{}
\r
18044 \begin_inset space \space{}
\r
18047 be used to use one limit for several operators:
\r
18050 \begin_layout Standard
\r
18051 \begin_inset Formula
\r
18053 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
\r
18061 \begin_layout Standard
\r
18062 The command for the formula above is:
\r
18063 \begin_inset Newline newline
\r
18082 \begin_layout Plain Layout
\r
18094 \begin_inset Formula $\to$
\r
18103 \begin_layout Plain Layout
\r
18117 \begin_layout Section
\r
18119 \begin_inset Index idx
\r
18122 \begin_layout Plain Layout
\r
18131 \begin_layout Subsection
\r
18133 \begin_inset CommandInset label
\r
18134 LatexCommand label
\r
18135 name "sub:Font-Styles"
\r
18140 \begin_inset Index idx
\r
18143 \begin_layout Plain Layout
\r
18152 \begin_layout Standard
\r
18153 Latin letters in formulas can be set in one of the following font styles:
\r
18154 \begin_inset VSpace -2mm
\r
18160 \begin_layout Standard
\r
18162 \begin_inset Tabular
\r
18163 <lyxtabular version="3" rows="7" columns="3">
\r
18164 <features rotate="0" tabularvalignment="middle">
\r
18165 <column alignment="center" valignment="top">
\r
18166 <column alignment="center" valignment="top">
\r
18167 <column alignment="center" valignment="top">
\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" usebox="none">
\r
18179 \begin_inset Text
\r
18181 \begin_layout Plain Layout
\r
18187 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
18188 \begin_inset Text
\r
18190 \begin_layout Plain Layout
\r
18198 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
18199 \begin_inset Text
\r
18201 \begin_layout Plain Layout
\r
18210 \begin_layout Plain Layout
\r
18226 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
18227 \begin_inset Text
\r
18229 \begin_layout Plain Layout
\r
18230 \begin_inset Formula $\mathbb{ABC}$
\r
18238 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
18239 \begin_inset Text
\r
18241 \begin_layout Plain Layout
\r
18242 \begin_inset Info
\r
18254 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
18255 \begin_inset Text
\r
18257 \begin_layout Plain Layout
\r
18266 \begin_layout Plain Layout
\r
18282 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
18283 \begin_inset Text
\r
18285 \begin_layout Plain Layout
\r
18286 \begin_inset Formula $\mathbf{AbC}$
\r
18294 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
18295 \begin_inset Text
\r
18297 \begin_layout Plain Layout
\r
18298 \begin_inset Info
\r
18310 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
18311 \begin_inset Text
\r
18313 \begin_layout Plain Layout
\r
18322 \begin_layout Plain Layout
\r
18338 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
18339 \begin_inset Text
\r
18341 \begin_layout Plain Layout
\r
18342 \begin_inset Formula $\boldsymbol{AbC}$
\r
18350 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
18351 \begin_inset Text
\r
18353 \begin_layout Plain Layout
\r
18354 \begin_inset Info
\r
18356 arg "font-boldsymbol"
\r
18366 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
18367 \begin_inset Text
\r
18369 \begin_layout Plain Layout
\r
18378 \begin_layout Plain Layout
\r
18394 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
18395 \begin_inset Text
\r
18397 \begin_layout Plain Layout
\r
18398 \begin_inset Formula $\mathcal{ABC}$
\r
18406 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
18407 \begin_inset Text
\r
18409 \begin_layout Plain Layout
\r
18410 \begin_inset Info
\r
18422 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
18423 \begin_inset Text
\r
18425 \begin_layout Plain Layout
\r
18434 \begin_layout Plain Layout
\r
18450 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
18451 \begin_inset Text
\r
18453 \begin_layout Plain Layout
\r
18454 \begin_inset Formula $\mathfrak{AbC}$
\r
18462 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
18463 \begin_inset Text
\r
18465 \begin_layout Plain Layout
\r
18473 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
18474 \begin_inset Text
\r
18476 \begin_layout Plain Layout
\r
18485 \begin_layout Plain Layout
\r
18501 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
18502 \begin_inset Text
\r
18504 \begin_layout Plain Layout
\r
18505 \begin_inset Formula $\mathscr{AbC}$
\r
18513 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
18514 \begin_inset Text
\r
18516 \begin_layout Plain Layout
\r
18530 \begin_layout Standard
\r
18532 \begin_inset Tabular
\r
18533 <lyxtabular version="3" rows="5" columns="3">
\r
18534 <features rotate="0" tabularvalignment="middle">
\r
18535 <column alignment="center" valignment="top">
\r
18536 <column alignment="center" valignment="top">
\r
18537 <column alignment="center" valignment="top">
\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" usebox="none">
\r
18549 \begin_inset Text
\r
18551 \begin_layout Plain Layout
\r
18557 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
18558 \begin_inset Text
\r
18560 \begin_layout Plain Layout
\r
18568 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
18569 \begin_inset Text
\r
18571 \begin_layout Plain Layout
\r
18580 \begin_layout Plain Layout
\r
18596 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
18597 \begin_inset Text
\r
18599 \begin_layout Plain Layout
\r
18600 \begin_inset Formula $\mathit{AbC}$
\r
18608 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
18609 \begin_inset Text
\r
18611 \begin_layout Plain Layout
\r
18619 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
18620 \begin_inset Text
\r
18622 \begin_layout Plain Layout
\r
18631 \begin_layout Plain Layout
\r
18647 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
18648 \begin_inset Text
\r
18650 \begin_layout Plain Layout
\r
18651 \begin_inset Formula $\mathrm{AbC}$
\r
18659 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
18660 \begin_inset Text
\r
18662 \begin_layout Plain Layout
\r
18663 \begin_inset Info
\r
18675 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
18676 \begin_inset Text
\r
18678 \begin_layout Plain Layout
\r
18687 \begin_layout Plain Layout
\r
18703 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
18704 \begin_inset Text
\r
18706 \begin_layout Plain Layout
\r
18707 \begin_inset Formula $\mathsf{AbC}$
\r
18715 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
18716 \begin_inset Text
\r
18718 \begin_layout Plain Layout
\r
18719 \begin_inset Info
\r
18731 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
18732 \begin_inset Text
\r
18734 \begin_layout Plain Layout
\r
18743 \begin_layout Plain Layout
\r
18759 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
18760 \begin_inset Text
\r
18762 \begin_layout Plain Layout
\r
18763 \begin_inset Formula $\mathtt{AbC}$
\r
18771 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
18772 \begin_inset Text
\r
18774 \begin_layout Plain Layout
\r
18775 \begin_inset Info
\r
18777 arg "font-typewriter"
\r
18793 \begin_layout Standard
\r
18794 \begin_inset Note Greyedout
\r
18797 \begin_layout Plain Layout
\r
18814 can only be used for big letters.
\r
18822 \begin_layout Standard
\r
18823 Predefined is the style
\r
18832 \begin_layout Standard
\r
18833 The style commands work also for letters in mathematical constructs:
\r
18834 \begin_inset Formula
\r
18836 \mathfrak{A=\frac{b}{C}}
\r
18844 \begin_layout Standard
\r
18845 Characters in mathematical text don't appear in a math font style but in
\r
18846 the text font style
\r
18853 That their style can't be set correctly via the text style dialog is a
\r
18855 \begin_inset Foot
\r
18858 \begin_layout Plain Layout
\r
18859 \begin_inset CommandInset href
\r
18860 LatexCommand href
\r
18861 name "LyX-bug #4629"
\r
18862 target "http://www.lyx.org/trac/ticket/4629"
\r
18874 \begin_layout Standard
\r
18875 Instead of the style commands the dialog
\r
18877 Edit\SpecialChar \menuseparator
\r
18878 Math\SpecialChar \menuseparator
\r
18881 or the toolbar button
\r
18882 \begin_inset Graphics
\r
18883 filename ../images/math/font.png
\r
18891 \begin_layout Subsection
\r
18893 \begin_inset CommandInset label
\r
18894 LatexCommand label
\r
18895 name "sub:Bold-Formulas"
\r
18900 \begin_inset Index idx
\r
18903 \begin_layout Plain Layout
\r
18912 \begin_layout Standard
\r
18913 To make a complete formula bold, the command
\r
18919 from the previous subsection cannot be used, because it doesn't work for
\r
18920 small Greek letters.
\r
18921 Furthermore it prints Latin letters always upright, like in the following
\r
18925 \begin_layout Standard
\r
18926 \begin_inset Formula
\r
18928 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
\r
18936 \begin_layout Standard
\r
18937 To display the formula correctly, the command
\r
18944 \begin_inset Formula
\r
18946 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
\r
18951 It is also possible to set the formula in a
\r
18953 boldmath environment
\r
18956 This environment is created by inserting the command
\r
18963 \begin_inset Index idx
\r
18966 \begin_layout Plain Layout
\r
18975 To end the environment, the command
\r
18982 \begin_inset Index idx
\r
18985 \begin_layout Plain Layout
\r
18993 is inserted in TeX-mode.
\r
18997 \begin_layout Plain Layout
\r
19007 \begin_inset Formula
\r
19009 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
\r
19018 \begin_layout Plain Layout
\r
19030 \begin_layout Subsection
\r
19032 \begin_inset Index idx
\r
19035 \begin_layout Plain Layout
\r
19036 Formula ! colored
\r
19044 \begin_layout Standard
\r
19045 Formulas can be colored like normal text: Highlight a formula or a formula
\r
19046 part and use the
\r
19051 Here is a formula in magenta:
\r
19052 \begin_inset Formula
\r
19054 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
\r
19062 \begin_layout Standard
\r
19063 You can also define your own colors as described in
\r
19064 \begin_inset CommandInset ref
\r
19066 reference "sub:Colored-Boxes"
\r
19071 They can be used with the TeX code command
\r
19078 \begin_inset Index idx
\r
19081 \begin_layout Plain Layout
\r
19092 \begin_layout Standard
\r
19097 textcolor{color}{characters or formula}
\r
19100 \begin_layout Standard
\r
19101 The following example was colored completely dark green and partly red:
\r
19104 \begin_layout Standard
\r
19108 \begin_layout Plain Layout
\r
19112 textcolor{darkgreen}{
\r
19118 \begin_inset Formula
\r
19120 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
\r
19129 \begin_layout Plain Layout
\r
19139 \begin_layout Standard
\r
19140 Due to a bug in LyX only complete formulas can be colored with self-defined
\r
19142 \begin_inset Foot
\r
19145 \begin_layout Plain Layout
\r
19146 \begin_inset CommandInset href
\r
19147 LatexCommand href
\r
19148 name "LyX-bug #5269"
\r
19149 target "http://www.lyx.org/trac/ticket/5269"
\r
19161 \begin_layout Subsection
\r
19163 \begin_inset CommandInset label
\r
19164 LatexCommand label
\r
19165 name "sub:Font-Sizes"
\r
19170 \begin_inset Index idx
\r
19173 \begin_layout Plain Layout
\r
19182 \begin_layout Standard
\r
19183 For characters in formulas there are, analog to characters in text, the
\r
19184 following size commands:
\r
19187 \begin_layout Standard
\r
19231 \begin_inset Newline newline
\r
19253 \begin_layout Standard
\r
19254 The size produced by the commands depends on the document font size, which
\r
19255 corresponds to the command
\r
19262 The other commands produce smaller or larger sizes than
\r
19269 The font size can however not exceed a certain value.
\r
19270 Is for example the document font size 12
\r
19271 \begin_inset space \thinspace{}
\r
19280 switches to the same size as
\r
19290 \begin_layout Standard
\r
19291 A size command is inserted in TeX-mode before the formula and sets the size
\r
19292 for all following formula and text characters.
\r
19293 To switch back to the initial size, the command
\r
19299 is inserted behind the formula in TeX-mode.
\r
19302 \begin_layout Standard
\r
19303 Within a formula the size can be changed using the following size commands:
\r
19306 \begin_layout Standard
\r
19309 \begin_inset Tabular
\r
19310 <lyxtabular version="3" rows="5" columns="2">
\r
19311 <features rotate="0" tabularvalignment="middle">
\r
19312 <column alignment="center" valignment="top">
\r
19313 <column alignment="center" valignment="top">
\r
19315 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
19316 \begin_inset Text
\r
19318 \begin_layout Plain Layout
\r
19324 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
19325 \begin_inset Text
\r
19327 \begin_layout Plain Layout
\r
19329 \begin_inset Note Note
\r
19332 \begin_layout Plain Layout
\r
19339 is only used as spacer.
\r
19351 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
19352 \begin_inset Text
\r
19354 \begin_layout Plain Layout
\r
19358 \begin_inset Index idx
\r
19361 \begin_layout Plain Layout
\r
19374 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
19375 \begin_inset Text
\r
19377 \begin_layout Plain Layout
\r
19378 \begin_inset Formula $\raisebox{6.5mm}{}{\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-5.5mm}{}$
\r
19388 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
19389 \begin_inset Text
\r
19391 \begin_layout Plain Layout
\r
19399 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
19400 \begin_inset Text
\r
19402 \begin_layout Plain Layout
\r
19403 \begin_inset Formula $\raisebox{4.5mm}{}{\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-4mm}{}$
\r
19413 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
19414 \begin_inset Text
\r
19416 \begin_layout Plain Layout
\r
19424 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
19425 \begin_inset Text
\r
19427 \begin_layout Plain Layout
\r
19428 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
\r
19438 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
19439 \begin_inset Text
\r
19441 \begin_layout Plain Layout
\r
19444 scriptscriptstyle
\r
19449 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
19450 \begin_inset Text
\r
19452 \begin_layout Plain Layout
\r
19453 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
\r
19469 \begin_layout Standard
\r
19470 After entering these commands, a blue box appears in which the formula parts
\r
19474 \begin_layout Standard
\r
19475 There is a further method to change the font size, that though only works
\r
19476 for symbols or letters in mathematical text.
\r
19477 To use it, one of the above text size commands is inserted in mathematical
\r
19479 All following characters until the end of the mathematical text or until
\r
19480 another size command will have the selected size.
\r
19482 \begin_inset VSpace -2mm
\r
19488 \begin_layout Standard
\r
19492 \begin_layout Plain Layout
\r
19502 \begin_inset Formula
\r
19504 A=\frac{B}{c}\cdot\maltese
\r
19510 \begin_inset Formula
\r
19512 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
\r
19521 \begin_layout Plain Layout
\r
19533 \begin_layout Standard
\r
19534 \begin_inset VSpace medskip
\r
19537 Before both formulas the command
\r
19544 The command for the second formula is:
\r
19545 \begin_inset Newline newline
\r
19556 \begin_layout Plain Layout
\r
19571 \begin_layout Plain Layout
\r
19586 \begin_layout Plain Layout
\r
19601 \begin_layout Plain Layout
\r
19611 \begin_inset Formula $\to$
\r
19615 \begin_inset Formula $\to$
\r
19619 \begin_inset Newline newline
\r
19623 \begin_inset space \hspace*{}
\r
19637 \begin_layout Plain Layout
\r
19652 \begin_layout Plain Layout
\r
19667 \begin_layout Plain Layout
\r
19679 \begin_layout Standard
\r
19680 If a symbol cannot be displayed in different sizes, it will always be displayed
\r
19681 in the default size.
\r
19684 \begin_layout Section
\r
19686 \begin_inset Index idx
\r
19689 \begin_layout Plain Layout
\r
19698 \begin_layout Standard
\r
19699 Greek letters can also be inserted via the toolbar button
\r
19700 \begin_inset Graphics
\r
19701 filename ../images/math/alpha.png
\r
19707 All international typesetting norms purport that Greek letters in math
\r
19708 have to be typeset italic/slanted.
\r
19709 In some languages, like French or Russian, they are nevertheless sometimes
\r
19713 \begin_layout Subsection
\r
19715 \begin_inset Index idx
\r
19718 \begin_layout Plain Layout
\r
19719 Greek letters ! small
\r
19727 \begin_layout Standard
\r
19728 \begin_inset space \hfill{}
\r
19732 \begin_inset Tabular
\r
19733 <lyxtabular version="3" rows="11" columns="2">
\r
19734 <features rotate="0" tabularvalignment="middle">
\r
19735 <column alignment="center" valignment="top" width="0pt">
\r
19736 <column alignment="center" valignment="top" width="0pt">
\r
19738 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
19739 \begin_inset Text
\r
19741 \begin_layout Plain Layout
\r
19747 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
19748 \begin_inset Text
\r
19750 \begin_layout Plain Layout
\r
19758 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
19759 \begin_inset Text
\r
19761 \begin_layout Plain Layout
\r
19769 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
19770 \begin_inset Text
\r
19772 \begin_layout Plain Layout
\r
19773 \begin_inset Formula $\alpha$
\r
19783 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
19784 \begin_inset Text
\r
19786 \begin_layout Plain Layout
\r
19794 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
19795 \begin_inset Text
\r
19797 \begin_layout Plain Layout
\r
19798 \begin_inset Formula $\beta$
\r
19808 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
19809 \begin_inset Text
\r
19811 \begin_layout Plain Layout
\r
19819 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
19820 \begin_inset Text
\r
19822 \begin_layout Plain Layout
\r
19823 \begin_inset Formula $\gamma$
\r
19833 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
19834 \begin_inset Text
\r
19836 \begin_layout Plain Layout
\r
19844 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
19845 \begin_inset Text
\r
19847 \begin_layout Plain Layout
\r
19848 \begin_inset Formula $\delta$
\r
19858 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
19859 \begin_inset Text
\r
19861 \begin_layout Plain Layout
\r
19869 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
19870 \begin_inset Text
\r
19872 \begin_layout Plain Layout
\r
19873 \begin_inset Formula $\epsilon$
\r
19883 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
19884 \begin_inset Text
\r
19886 \begin_layout Plain Layout
\r
19894 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
19895 \begin_inset Text
\r
19897 \begin_layout Plain Layout
\r
19898 \begin_inset Formula $\varepsilon$
\r
19908 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
19909 \begin_inset Text
\r
19911 \begin_layout Plain Layout
\r
19919 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
19920 \begin_inset Text
\r
19922 \begin_layout Plain Layout
\r
19923 \begin_inset Formula $\zeta$
\r
19933 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
19934 \begin_inset Text
\r
19936 \begin_layout Plain Layout
\r
19944 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
19945 \begin_inset Text
\r
19947 \begin_layout Plain Layout
\r
19948 \begin_inset Formula $\eta$
\r
19958 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
19959 \begin_inset Text
\r
19961 \begin_layout Plain Layout
\r
19969 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
19970 \begin_inset Text
\r
19972 \begin_layout Plain Layout
\r
19973 \begin_inset Formula $\theta$
\r
19983 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
19984 \begin_inset Text
\r
19986 \begin_layout Plain Layout
\r
19994 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
19995 \begin_inset Text
\r
19997 \begin_layout Plain Layout
\r
19998 \begin_inset Formula $\vartheta$
\r
20012 \begin_inset space \hfill{}
\r
20016 \begin_inset Tabular
\r
20017 <lyxtabular version="3" rows="12" columns="2">
\r
20018 <features rotate="0" tabularvalignment="middle">
\r
20019 <column alignment="center" valignment="top" width="0pt">
\r
20020 <column alignment="center" valignment="top" width="0pt">
\r
20022 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
20023 \begin_inset Text
\r
20025 \begin_layout Plain Layout
\r
20031 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
20032 \begin_inset Text
\r
20034 \begin_layout Plain Layout
\r
20042 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
20043 \begin_inset Text
\r
20045 \begin_layout Plain Layout
\r
20053 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
20054 \begin_inset Text
\r
20056 \begin_layout Plain Layout
\r
20057 \begin_inset Formula $\iota$
\r
20067 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
20068 \begin_inset Text
\r
20070 \begin_layout Plain Layout
\r
20078 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
20079 \begin_inset Text
\r
20081 \begin_layout Plain Layout
\r
20082 \begin_inset Formula $\kappa$
\r
20092 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
20093 \begin_inset Text
\r
20095 \begin_layout Plain Layout
\r
20103 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
20104 \begin_inset Text
\r
20106 \begin_layout Plain Layout
\r
20107 \begin_inset Formula $\varkappa$
\r
20117 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
20118 \begin_inset Text
\r
20120 \begin_layout Plain Layout
\r
20128 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
20129 \begin_inset Text
\r
20131 \begin_layout Plain Layout
\r
20132 \begin_inset Formula $\lambda$
\r
20142 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
20143 \begin_inset Text
\r
20145 \begin_layout Plain Layout
\r
20153 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
20154 \begin_inset Text
\r
20156 \begin_layout Plain Layout
\r
20157 \begin_inset Formula $\mu$
\r
20167 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
20168 \begin_inset Text
\r
20170 \begin_layout Plain Layout
\r
20178 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
20179 \begin_inset Text
\r
20181 \begin_layout Plain Layout
\r
20182 \begin_inset Formula $\nu$
\r
20192 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
20193 \begin_inset Text
\r
20195 \begin_layout Plain Layout
\r
20203 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
20204 \begin_inset Text
\r
20206 \begin_layout Plain Layout
\r
20207 \begin_inset Formula $\xi$
\r
20217 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
20218 \begin_inset Text
\r
20220 \begin_layout Plain Layout
\r
20226 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
20227 \begin_inset Text
\r
20229 \begin_layout Plain Layout
\r
20230 \begin_inset Formula $o$
\r
20240 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
20241 \begin_inset Text
\r
20243 \begin_layout Plain Layout
\r
20251 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
20252 \begin_inset Text
\r
20254 \begin_layout Plain Layout
\r
20255 \begin_inset Formula $\pi$
\r
20265 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
20266 \begin_inset Text
\r
20268 \begin_layout Plain Layout
\r
20276 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
20277 \begin_inset Text
\r
20279 \begin_layout Plain Layout
\r
20280 \begin_inset Formula $\varpi$
\r
20290 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
20291 \begin_inset Text
\r
20293 \begin_layout Plain Layout
\r
20301 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
20302 \begin_inset Text
\r
20304 \begin_layout Plain Layout
\r
20305 \begin_inset Formula $\rho$
\r
20319 \begin_inset space \hfill{}
\r
20323 \begin_inset Tabular
\r
20324 <lyxtabular version="3" rows="11" columns="2">
\r
20325 <features rotate="0" tabularvalignment="middle">
\r
20326 <column alignment="center" valignment="top" width="0pt">
\r
20327 <column alignment="center" valignment="top" width="0pt">
\r
20329 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
20330 \begin_inset Text
\r
20332 \begin_layout Plain Layout
\r
20338 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
20339 \begin_inset Text
\r
20341 \begin_layout Plain Layout
\r
20349 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
20350 \begin_inset Text
\r
20352 \begin_layout Plain Layout
\r
20360 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
20361 \begin_inset Text
\r
20363 \begin_layout Plain Layout
\r
20364 \begin_inset Formula $\varrho$
\r
20374 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
20375 \begin_inset Text
\r
20377 \begin_layout Plain Layout
\r
20385 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
20386 \begin_inset Text
\r
20388 \begin_layout Plain Layout
\r
20389 \begin_inset Formula $\sigma$
\r
20399 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
20400 \begin_inset Text
\r
20402 \begin_layout Plain Layout
\r
20410 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
20411 \begin_inset Text
\r
20413 \begin_layout Plain Layout
\r
20414 \begin_inset Formula $\varsigma$
\r
20424 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
20425 \begin_inset Text
\r
20427 \begin_layout Plain Layout
\r
20435 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
20436 \begin_inset Text
\r
20438 \begin_layout Plain Layout
\r
20439 \begin_inset Formula $\tau$
\r
20449 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
20450 \begin_inset Text
\r
20452 \begin_layout Plain Layout
\r
20460 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
20461 \begin_inset Text
\r
20463 \begin_layout Plain Layout
\r
20464 \begin_inset Formula $\upsilon$
\r
20474 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
20475 \begin_inset Text
\r
20477 \begin_layout Plain Layout
\r
20485 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
20486 \begin_inset Text
\r
20488 \begin_layout Plain Layout
\r
20489 \begin_inset Formula $\phi$
\r
20499 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
20500 \begin_inset Text
\r
20502 \begin_layout Plain Layout
\r
20510 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
20511 \begin_inset Text
\r
20513 \begin_layout Plain Layout
\r
20514 \begin_inset Formula $\varphi$
\r
20524 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
20525 \begin_inset Text
\r
20527 \begin_layout Plain Layout
\r
20535 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
20536 \begin_inset Text
\r
20538 \begin_layout Plain Layout
\r
20539 \begin_inset Formula $\chi$
\r
20549 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
20550 \begin_inset Text
\r
20552 \begin_layout Plain Layout
\r
20560 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
20561 \begin_inset Text
\r
20563 \begin_layout Plain Layout
\r
20564 \begin_inset Formula $\psi$
\r
20574 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
20575 \begin_inset Text
\r
20577 \begin_layout Plain Layout
\r
20585 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
20586 \begin_inset Text
\r
20588 \begin_layout Plain Layout
\r
20589 \begin_inset Formula $\omega$
\r
20603 \begin_inset space \hfill{}
\r
20609 \begin_layout Standard
\r
20610 \begin_inset VSpace medskip
\r
20616 \begin_layout Standard
\r
20617 How to create special upright Greek letters is explained in
\r
20618 \begin_inset CommandInset ref
\r
20620 reference "sub:Upright-small-Greek"
\r
20627 \begin_layout Subsection
\r
20629 \begin_inset Index idx
\r
20632 \begin_layout Plain Layout
\r
20633 Greek letters ! big
\r
20641 \begin_layout Standard
\r
20642 \begin_inset space \hfill{}
\r
20646 \begin_inset Tabular
\r
20647 <lyxtabular version="3" rows="7" columns="2">
\r
20648 <features rotate="0" tabularvalignment="middle">
\r
20649 <column alignment="center" valignment="top" width="0pt">
\r
20650 <column alignment="center" valignment="top" width="0pt">
\r
20652 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
20653 \begin_inset Text
\r
20655 \begin_layout Plain Layout
\r
20661 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
20662 \begin_inset Text
\r
20664 \begin_layout Plain Layout
\r
20672 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
20673 \begin_inset Text
\r
20675 \begin_layout Plain Layout
\r
20683 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
20684 \begin_inset Text
\r
20686 \begin_layout Plain Layout
\r
20687 \begin_inset Formula $\Gamma$
\r
20697 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
20698 \begin_inset Text
\r
20700 \begin_layout Plain Layout
\r
20708 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
20709 \begin_inset Text
\r
20711 \begin_layout Plain Layout
\r
20712 \begin_inset Formula $\Delta$
\r
20722 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
20723 \begin_inset Text
\r
20725 \begin_layout Plain Layout
\r
20733 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
20734 \begin_inset Text
\r
20736 \begin_layout Plain Layout
\r
20737 \begin_inset Formula $\Theta$
\r
20747 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
20748 \begin_inset Text
\r
20750 \begin_layout Plain Layout
\r
20758 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
20759 \begin_inset Text
\r
20761 \begin_layout Plain Layout
\r
20762 \begin_inset Formula $\Lambda$
\r
20772 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
20773 \begin_inset Text
\r
20775 \begin_layout Plain Layout
\r
20783 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
20784 \begin_inset Text
\r
20786 \begin_layout Plain Layout
\r
20787 \begin_inset Formula $\Xi$
\r
20797 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
20798 \begin_inset Text
\r
20800 \begin_layout Plain Layout
\r
20808 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
20809 \begin_inset Text
\r
20811 \begin_layout Plain Layout
\r
20812 \begin_inset Formula $\Pi$
\r
20826 \begin_inset space \hfill{}
\r
20830 \begin_inset Tabular
\r
20831 <lyxtabular version="3" rows="6" columns="2">
\r
20832 <features rotate="0" tabularvalignment="middle">
\r
20833 <column alignment="center" valignment="top" width="0pt">
\r
20834 <column alignment="center" valignment="top" width="0pt">
\r
20836 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
20837 \begin_inset Text
\r
20839 \begin_layout Plain Layout
\r
20845 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
20846 \begin_inset Text
\r
20848 \begin_layout Plain Layout
\r
20856 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
20857 \begin_inset Text
\r
20859 \begin_layout Plain Layout
\r
20867 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
20868 \begin_inset Text
\r
20870 \begin_layout Plain Layout
\r
20871 \begin_inset Formula $\Sigma$
\r
20881 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
20882 \begin_inset Text
\r
20884 \begin_layout Plain Layout
\r
20892 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
20893 \begin_inset Text
\r
20895 \begin_layout Plain Layout
\r
20896 \begin_inset Formula $\Upsilon$
\r
20906 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
20907 \begin_inset Text
\r
20909 \begin_layout Plain Layout
\r
20917 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
20918 \begin_inset Text
\r
20920 \begin_layout Plain Layout
\r
20921 \begin_inset Formula $\Phi$
\r
20931 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
20932 \begin_inset Text
\r
20934 \begin_layout Plain Layout
\r
20942 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
20943 \begin_inset Text
\r
20945 \begin_layout Plain Layout
\r
20946 \begin_inset Formula $\Psi$
\r
20956 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
20957 \begin_inset Text
\r
20959 \begin_layout Plain Layout
\r
20967 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
20968 \begin_inset Text
\r
20970 \begin_layout Plain Layout
\r
20971 \begin_inset Formula $\Omega$
\r
20985 \begin_inset space \hfill{}
\r
20991 \begin_layout Standard
\r
20992 \begin_inset VSpace medskip
\r
20995 That the big Greek letters appear upright is caused by a design bug when
\r
20996 TeX was developed.
\r
20997 To get correct italic big letters, begin every command with
\r
21002 For example the command
\r
21009 \begin_inset Formula $\varGamma$
\r
21013 Another way is to load the package
\r
21018 \begin_inset Foot
\r
21021 \begin_layout Plain Layout
\r
21026 is part of the LaTeX-package
\r
21031 \begin_inset Index idx
\r
21034 \begin_layout Plain Layout
\r
21039 \begin_layout Plain Layout
\r
21059 \begin_inset Index idx
\r
21062 \begin_layout Plain Layout
\r
21063 Packages ! fixmath
\r
21068 with the LaTeX-preamble line
\r
21071 \begin_layout Standard
\r
21076 usepackage{fixmath}
\r
21079 \begin_layout Standard
\r
21080 Then all big Greek letters in a document will automatically be typeset italic.
\r
21083 \begin_layout Subsection
\r
21085 \begin_inset Index idx
\r
21088 \begin_layout Plain Layout
\r
21089 Greek letters ! bold
\r
21097 \begin_layout Standard
\r
21098 Greek letters cannot be set with different font styles like Latin letters.
\r
21099 They can only be made bold with the command
\r
21106 \begin_inset Index idx
\r
21109 \begin_layout Plain Layout
\r
21120 \begin_layout Standard
\r
21122 \begin_inset Tabular
\r
21123 <lyxtabular version="3" rows="3" columns="2">
\r
21124 <features rotate="0" tabularvalignment="middle">
\r
21125 <column alignment="center" valignment="top">
\r
21126 <column alignment="center" valignment="top">
\r
21128 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
21129 \begin_inset Text
\r
21131 \begin_layout Plain Layout
\r
21137 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
21138 \begin_inset Text
\r
21140 \begin_layout Plain Layout
\r
21148 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
21149 \begin_inset Text
\r
21151 \begin_layout Plain Layout
\r
21163 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
21164 \begin_inset Text
\r
21166 \begin_layout Plain Layout
\r
21167 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
\r
21177 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
21178 \begin_inset Text
\r
21180 \begin_layout Plain Layout
\r
21192 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
21193 \begin_inset Text
\r
21195 \begin_layout Plain Layout
\r
21196 \begin_inset Formula $\theta\boldsymbol{\theta}$
\r
21212 \begin_layout Section
\r
21217 \begin_layout Plain Layout
\r
21227 \begin_inset Foot
\r
21230 \begin_layout Plain Layout
\r
21231 A list with all symbols of most of the LaTeX-packages can be found in
\r
21232 \begin_inset CommandInset citation
\r
21233 LatexCommand cite
\r
21247 \begin_layout Plain Layout
\r
21255 \begin_inset Note Note
\r
21258 \begin_layout Plain Layout
\r
21261 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
\r
21264 \begin_layout Plain Layout
\r
21267 texorpdfstring is in section
\r
21268 \begin_inset CommandInset ref
\r
21270 reference "sub:Formulas-in-Section"
\r
21280 \begin_inset Index idx
\r
21283 \begin_layout Plain Layout
\r
21292 \begin_layout Standard
\r
21293 Many of the symbols listed in this section can also be inserted via the
\r
21295 \begin_inset Graphics
\r
21296 filename ../images/math/nabla.png
\r
21302 \begin_inset Graphics
\r
21303 filename ../images/math/digamma.png
\r
21311 \begin_layout Subsection
\r
21312 Mathematical Symbols
\r
21313 \begin_inset CommandInset label
\r
21314 LatexCommand label
\r
21315 name "sub:Mathematical-Symbols"
\r
21320 \begin_inset Index idx
\r
21323 \begin_layout Plain Layout
\r
21324 Symbols ! mathematical
\r
21332 \begin_layout Standard
\r
21333 \begin_inset space \hfill{}
\r
21337 \begin_inset Tabular
\r
21338 <lyxtabular version="3" rows="10" columns="2">
\r
21339 <features rotate="0" tabularvalignment="middle">
\r
21340 <column alignment="center" valignment="top" width="0pt">
\r
21341 <column alignment="center" valignment="top" width="0pt">
\r
21343 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
21344 \begin_inset Text
\r
21346 \begin_layout Plain Layout
\r
21352 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
21353 \begin_inset Text
\r
21355 \begin_layout Plain Layout
\r
21363 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
21364 \begin_inset Text
\r
21366 \begin_layout Plain Layout
\r
21374 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
21375 \begin_inset Text
\r
21377 \begin_layout Plain Layout
\r
21378 \begin_inset Formula $\neg$
\r
21388 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
21389 \begin_inset Text
\r
21391 \begin_layout Plain Layout
\r
21399 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
21400 \begin_inset Text
\r
21402 \begin_layout Plain Layout
\r
21403 \begin_inset Formula $\Im$
\r
21413 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
21414 \begin_inset Text
\r
21416 \begin_layout Plain Layout
\r
21424 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
21425 \begin_inset Text
\r
21427 \begin_layout Plain Layout
\r
21428 \begin_inset Formula $\Re$
\r
21438 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
21439 \begin_inset Text
\r
21441 \begin_layout Plain Layout
\r
21449 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
21450 \begin_inset Text
\r
21452 \begin_layout Plain Layout
\r
21453 \begin_inset Formula $\aleph$
\r
21463 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
21464 \begin_inset Text
\r
21466 \begin_layout Plain Layout
\r
21474 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
21475 \begin_inset Text
\r
21477 \begin_layout Plain Layout
\r
21478 \begin_inset Formula $\partial$
\r
21488 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
21489 \begin_inset Text
\r
21491 \begin_layout Plain Layout
\r
21499 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
21500 \begin_inset Text
\r
21502 \begin_layout Plain Layout
\r
21503 \begin_inset Formula $\infty$
\r
21513 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
21514 \begin_inset Text
\r
21516 \begin_layout Plain Layout
\r
21524 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
21525 \begin_inset Text
\r
21527 \begin_layout Plain Layout
\r
21528 \begin_inset Formula $\wp$
\r
21538 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
21539 \begin_inset Text
\r
21541 \begin_layout Plain Layout
\r
21549 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
21550 \begin_inset Text
\r
21552 \begin_layout Plain Layout
\r
21553 \begin_inset Formula $\imath$
\r
21563 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
21564 \begin_inset Text
\r
21566 \begin_layout Plain Layout
\r
21574 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
21575 \begin_inset Text
\r
21577 \begin_layout Plain Layout
\r
21578 \begin_inset Formula $\jmath$
\r
21592 \begin_inset space \hfill{}
\r
21596 \begin_inset Tabular
\r
21597 <lyxtabular version="3" rows="10" columns="2">
\r
21598 <features rotate="0" tabularvalignment="middle">
\r
21599 <column alignment="center" valignment="top" width="0pt">
\r
21600 <column alignment="center" valignment="top" width="0pt">
\r
21602 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
21603 \begin_inset Text
\r
21605 \begin_layout Plain Layout
\r
21611 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
21612 \begin_inset Text
\r
21614 \begin_layout Plain Layout
\r
21616 \begin_inset Note Note
\r
21619 \begin_layout Plain Layout
\r
21626 is only used as spacer.
\r
21638 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
21639 \begin_inset Text
\r
21641 \begin_layout Plain Layout
\r
21649 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
21650 \begin_inset Text
\r
21652 \begin_layout Plain Layout
\r
21653 \begin_inset Formula $\forall$
\r
21663 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
21664 \begin_inset Text
\r
21666 \begin_layout Plain Layout
\r
21674 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
21675 \begin_inset Text
\r
21677 \begin_layout Plain Layout
\r
21678 \begin_inset Formula $\exists$
\r
21688 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
21689 \begin_inset Text
\r
21691 \begin_layout Plain Layout
\r
21699 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
21700 \begin_inset Text
\r
21702 \begin_layout Plain Layout
\r
21703 \begin_inset Formula $\nexists$
\r
21713 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
21714 \begin_inset Text
\r
21716 \begin_layout Plain Layout
\r
21724 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
21725 \begin_inset Text
\r
21727 \begin_layout Plain Layout
\r
21728 \begin_inset Formula $\emptyset$
\r
21738 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
21739 \begin_inset Text
\r
21741 \begin_layout Plain Layout
\r
21749 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
21750 \begin_inset Text
\r
21752 \begin_layout Plain Layout
\r
21753 \begin_inset Formula $\varnothing$
\r
21763 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
21764 \begin_inset Text
\r
21766 \begin_layout Plain Layout
\r
21774 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
21775 \begin_inset Text
\r
21777 \begin_layout Plain Layout
\r
21778 \begin_inset Formula $\dag$
\r
21788 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
21789 \begin_inset Text
\r
21791 \begin_layout Plain Layout
\r
21799 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
21800 \begin_inset Text
\r
21802 \begin_layout Plain Layout
\r
21803 \begin_inset Formula $\ddag$
\r
21813 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
21814 \begin_inset Text
\r
21816 \begin_layout Plain Layout
\r
21824 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
21825 \begin_inset Text
\r
21827 \begin_layout Plain Layout
\r
21831 \begin_layout Plain Layout
\r
21835 raisebox{-0.8mm}{
\r
21841 \begin_inset Formula $\complement$
\r
21848 \begin_layout Plain Layout
\r
21862 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
21863 \begin_inset Text
\r
21865 \begin_layout Plain Layout
\r
21873 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
21874 \begin_inset Text
\r
21876 \begin_layout Plain Layout
\r
21877 \begin_inset Formula $\Bbbk$
\r
21891 \begin_inset space \hfill{}
\r
21895 \begin_inset Tabular
\r
21896 <lyxtabular version="3" rows="10" columns="2">
\r
21897 <features rotate="0" tabularvalignment="middle">
\r
21898 <column alignment="center" valignment="top" width="0pt">
\r
21899 <column alignment="center" valignment="top" width="0pt">
\r
21901 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
21902 \begin_inset Text
\r
21904 \begin_layout Plain Layout
\r
21910 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
21911 \begin_inset Text
\r
21913 \begin_layout Plain Layout
\r
21921 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
21922 \begin_inset Text
\r
21924 \begin_layout Plain Layout
\r
21932 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
21933 \begin_inset Text
\r
21935 \begin_layout Plain Layout
\r
21936 \begin_inset Formula $\prime$
\r
21946 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
21947 \begin_inset Text
\r
21949 \begin_layout Plain Layout
\r
21957 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
21958 \begin_inset Text
\r
21960 \begin_layout Plain Layout
\r
21961 \begin_inset Formula $\backprime$
\r
21971 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
21972 \begin_inset Text
\r
21974 \begin_layout Plain Layout
\r
21982 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
21983 \begin_inset Text
\r
21985 \begin_layout Plain Layout
\r
21986 \begin_inset Formula $\mho$
\r
21996 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
21997 \begin_inset Text
\r
21999 \begin_layout Plain Layout
\r
22007 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
22008 \begin_inset Text
\r
22010 \begin_layout Plain Layout
\r
22011 \begin_inset Formula $\triangle$
\r
22021 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
22022 \begin_inset Text
\r
22024 \begin_layout Plain Layout
\r
22032 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
22033 \begin_inset Text
\r
22035 \begin_layout Plain Layout
\r
22036 \begin_inset Formula $\angle$
\r
22046 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
22047 \begin_inset Text
\r
22049 \begin_layout Plain Layout
\r
22057 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
22058 \begin_inset Text
\r
22060 \begin_layout Plain Layout
\r
22061 \begin_inset Formula $\measuredangle$
\r
22071 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
22072 \begin_inset Text
\r
22074 \begin_layout Plain Layout
\r
22082 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
22083 \begin_inset Text
\r
22085 \begin_layout Plain Layout
\r
22086 \begin_inset Formula $\sphericalangle$
\r
22096 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
22097 \begin_inset Text
\r
22099 \begin_layout Plain Layout
\r
22107 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
22108 \begin_inset Text
\r
22110 \begin_layout Plain Layout
\r
22111 \begin_inset Formula $\top$
\r
22121 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
22122 \begin_inset Text
\r
22124 \begin_layout Plain Layout
\r
22132 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
22133 \begin_inset Text
\r
22135 \begin_layout Plain Layout
\r
22136 \begin_inset Formula $\bot$
\r
22150 \begin_inset space \hfill{}
\r
22156 \begin_layout Subsection
\r
22157 Miscellaneous Symbols
\r
22158 \begin_inset CommandInset label
\r
22159 LatexCommand label
\r
22160 name "sub:Miscellaneous-Symbols"
\r
22165 \begin_inset Index idx
\r
22168 \begin_layout Plain Layout
\r
22169 Symbols ! miscellaneous
\r
22177 \begin_layout Standard
\r
22180 \begin_inset Tabular
\r
22181 <lyxtabular version="3" rows="10" columns="2">
\r
22182 <features rotate="0" tabularvalignment="middle">
\r
22183 <column alignment="center" valignment="top" width="0pt">
\r
22184 <column alignment="center" valignment="top" width="0pt">
\r
22186 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
22187 \begin_inset Text
\r
22189 \begin_layout Plain Layout
\r
22195 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
22196 \begin_inset Text
\r
22198 \begin_layout Plain Layout
\r
22206 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
22207 \begin_inset Text
\r
22209 \begin_layout Plain Layout
\r
22217 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
22218 \begin_inset Text
\r
22220 \begin_layout Plain Layout
\r
22221 \begin_inset Formula $\flat$
\r
22231 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
22232 \begin_inset Text
\r
22234 \begin_layout Plain Layout
\r
22242 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
22243 \begin_inset Text
\r
22245 \begin_layout Plain Layout
\r
22246 \begin_inset Formula $\natural$
\r
22256 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
22257 \begin_inset Text
\r
22259 \begin_layout Plain Layout
\r
22267 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
22268 \begin_inset Text
\r
22270 \begin_layout Plain Layout
\r
22271 \begin_inset Formula $\sharp$
\r
22281 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
22282 \begin_inset Text
\r
22284 \begin_layout Plain Layout
\r
22292 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
22293 \begin_inset Text
\r
22295 \begin_layout Plain Layout
\r
22296 \begin_inset Formula $\surd$
\r
22306 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
22307 \begin_inset Text
\r
22309 \begin_layout Plain Layout
\r
22317 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
22318 \begin_inset Text
\r
22320 \begin_layout Plain Layout
\r
22321 \begin_inset Formula $\checkmark$
\r
22331 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
22332 \begin_inset Text
\r
22334 \begin_layout Plain Layout
\r
22342 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
22343 \begin_inset Text
\r
22345 \begin_layout Plain Layout
\r
22346 \begin_inset Formula $\yen$
\r
22356 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
22357 \begin_inset Text
\r
22359 \begin_layout Plain Layout
\r
22367 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
22368 \begin_inset Text
\r
22370 \begin_layout Plain Layout
\r
22371 \begin_inset Formula $\pounds$
\r
22381 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
22382 \begin_inset Text
\r
22384 \begin_layout Plain Layout
\r
22390 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
22391 \begin_inset Text
\r
22393 \begin_layout Plain Layout
\r
22394 \begin_inset Formula $\$$
\r
22404 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
22405 \begin_inset Text
\r
22407 \begin_layout Plain Layout
\r
22413 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
22414 \begin_inset Text
\r
22416 \begin_layout Plain Layout
\r
22417 \begin_inset Formula $§$
\r
22431 \begin_inset Tabular
\r
22432 <lyxtabular version="3" rows="10" columns="2">
\r
22433 <features rotate="0" tabularvalignment="middle">
\r
22434 <column alignment="center" valignment="top">
\r
22435 <column alignment="center" valignment="top">
\r
22437 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
22438 \begin_inset Text
\r
22440 \begin_layout Plain Layout
\r
22446 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
22447 \begin_inset Text
\r
22449 \begin_layout Plain Layout
\r
22457 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
22458 \begin_inset Text
\r
22460 \begin_layout Plain Layout
\r
22468 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
22469 \begin_inset Text
\r
22471 \begin_layout Plain Layout
\r
22472 \begin_inset Formula $\hbar$
\r
22482 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
22483 \begin_inset Text
\r
22485 \begin_layout Plain Layout
\r
22493 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
22494 \begin_inset Text
\r
22496 \begin_layout Plain Layout
\r
22497 \begin_inset Formula $\hslash$
\r
22507 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
22508 \begin_inset Text
\r
22510 \begin_layout Plain Layout
\r
22518 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
22519 \begin_inset Text
\r
22521 \begin_layout Plain Layout
\r
22522 \begin_inset Formula $\clubsuit$
\r
22532 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
22533 \begin_inset Text
\r
22535 \begin_layout Plain Layout
\r
22543 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
22544 \begin_inset Text
\r
22546 \begin_layout Plain Layout
\r
22547 \begin_inset Formula $\spadesuit$
\r
22557 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
22558 \begin_inset Text
\r
22560 \begin_layout Plain Layout
\r
22568 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
22569 \begin_inset Text
\r
22571 \begin_layout Plain Layout
\r
22572 \begin_inset Formula $\bigstar$
\r
22582 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
22583 \begin_inset Text
\r
22585 \begin_layout Plain Layout
\r
22593 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
22594 \begin_inset Text
\r
22596 \begin_layout Plain Layout
\r
22597 \begin_inset Formula $\blacklozenge$
\r
22607 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
22608 \begin_inset Text
\r
22610 \begin_layout Plain Layout
\r
22618 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
22619 \begin_inset Text
\r
22621 \begin_layout Plain Layout
\r
22622 \begin_inset Formula $\blacktriangle$
\r
22632 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
22633 \begin_inset Text
\r
22635 \begin_layout Plain Layout
\r
22643 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
22644 \begin_inset Text
\r
22646 \begin_layout Plain Layout
\r
22647 \begin_inset Formula $\blacktriangledown$
\r
22657 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
22658 \begin_inset Text
\r
22660 \begin_layout Plain Layout
\r
22668 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
22669 \begin_inset Text
\r
22671 \begin_layout Plain Layout
\r
22672 \begin_inset Formula $\bullet$
\r
22686 \begin_inset Tabular
\r
22687 <lyxtabular version="3" rows="10" columns="2">
\r
22688 <features rotate="0" tabularvalignment="middle">
\r
22689 <column alignment="center" valignment="top" width="0pt">
\r
22690 <column alignment="center" valignment="top" width="0pt">
\r
22692 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
22693 \begin_inset Text
\r
22695 \begin_layout Plain Layout
\r
22701 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
22702 \begin_inset Text
\r
22704 \begin_layout Plain Layout
\r
22712 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
22713 \begin_inset Text
\r
22715 \begin_layout Plain Layout
\r
22723 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
22724 \begin_inset Text
\r
22726 \begin_layout Plain Layout
\r
22727 \begin_inset Formula $\diamondsuit$
\r
22737 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
22738 \begin_inset Text
\r
22740 \begin_layout Plain Layout
\r
22748 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
22749 \begin_inset Text
\r
22751 \begin_layout Plain Layout
\r
22752 \begin_inset Formula $\Diamond$
\r
22762 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
22763 \begin_inset Text
\r
22765 \begin_layout Plain Layout
\r
22773 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
22774 \begin_inset Text
\r
22776 \begin_layout Plain Layout
\r
22777 \begin_inset Formula $\heartsuit$
\r
22787 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
22788 \begin_inset Text
\r
22790 \begin_layout Plain Layout
\r
22798 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
22799 \begin_inset Text
\r
22801 \begin_layout Plain Layout
\r
22802 \begin_inset Formula $\P$
\r
22812 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
22813 \begin_inset Text
\r
22815 \begin_layout Plain Layout
\r
22823 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
22824 \begin_inset Text
\r
22826 \begin_layout Plain Layout
\r
22827 \begin_inset Formula $\copyright$
\r
22837 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
22838 \begin_inset Text
\r
22840 \begin_layout Plain Layout
\r
22848 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
22849 \begin_inset Text
\r
22851 \begin_layout Plain Layout
\r
22852 \begin_inset Formula $\circledR$
\r
22862 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
22863 \begin_inset Text
\r
22865 \begin_layout Plain Layout
\r
22873 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
22874 \begin_inset Text
\r
22876 \begin_layout Plain Layout
\r
22877 \begin_inset Formula $\maltese$
\r
22887 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
22888 \begin_inset Text
\r
22890 \begin_layout Plain Layout
\r
22898 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
22899 \begin_inset Text
\r
22901 \begin_layout Plain Layout
\r
22902 \begin_inset Formula $\diagup$
\r
22912 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
22913 \begin_inset Text
\r
22915 \begin_layout Plain Layout
\r
22923 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
22924 \begin_inset Text
\r
22926 \begin_layout Plain Layout
\r
22927 \begin_inset Formula $\diagdown$
\r
22943 \begin_layout Standard
\r
22944 \begin_inset VSpace medskip
\r
22947 More symbols are listed in
\r
22948 \begin_inset CommandInset ref
\r
22950 reference "sub:Miscellaneous-special-Characters"
\r
22957 \begin_layout Standard
\r
22958 Some symbols can be displayed in different sizes, see
\r
22959 \begin_inset CommandInset ref
\r
22961 reference "sub:Font-Sizes"
\r
22968 \begin_layout Subsection
\r
22969 The Euro-Symbol €
\r
22970 \begin_inset Index idx
\r
22973 \begin_layout Plain Layout
\r
22974 Symbols ! Euro-symbol
\r
22980 \begin_inset Index idx
\r
22983 \begin_layout Plain Layout
\r
22990 \begin_layout Plain Layout
\r
23007 \begin_layout Standard
\r
23008 To use the Euro symbol in formulas, the LaTeX-package
\r
23013 \begin_inset Index idx
\r
23016 \begin_layout Plain Layout
\r
23017 Packages ! eurosym
\r
23022 must be installed and loaded with the LaTeX-preamble line
\r
23025 \begin_layout Standard
\r
23030 usepackage[gennarrow]{eurosym}
\r
23033 \begin_layout Standard
\r
23034 The Euro symbol can now be inserted with the command
\r
23041 \begin_inset Index idx
\r
23044 \begin_layout Plain Layout
\r
23055 \begin_layout Standard
\r
23056 The Euro symbol can directly be inserted with the € key in mathematical
\r
23057 text, without having
\r
23072 can also be inserted in TeX-mode.
\r
23073 The official currency symbol can then be inserted with the command
\r
23080 \begin_inset Index idx
\r
23083 \begin_layout Plain Layout
\r
23091 , that is only available in TeX-mode.
\r
23094 \begin_layout Standard
\r
23098 \begin_layout Plain Layout
\r
23108 \begin_inset Note Note
\r
23111 \begin_layout Plain Layout
\r
23112 The following table will only be displayed when the LaTeX-package
\r
23124 \begin_layout Standard
\r
23125 An overview about the different Euro symbols:
\r
23128 \begin_layout Standard
\r
23130 \begin_inset Tabular
\r
23131 <lyxtabular version="3" rows="4" columns="3">
\r
23132 <features rotate="0" tabularvalignment="middle">
\r
23133 <column alignment="center" valignment="top" width="0pt">
\r
23134 <column alignment="center" valignment="top" width="0pt">
\r
23135 <column alignment="center" valignment="top" width="0pt">
\r
23137 <cell multicolumn="1" alignment="center" valignment="top" bottomline="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" usebox="none">
\r
23147 \begin_inset Text
\r
23149 \begin_layout Plain Layout
\r
23155 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
23156 \begin_inset Text
\r
23158 \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
23175 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
23176 \begin_inset Text
\r
23178 \begin_layout Plain Layout
\r
23186 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
23187 \begin_inset Text
\r
23189 \begin_layout Plain Layout
\r
23190 \begin_inset Formula $\euro$
\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
23204 mathematical text
\r
23209 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
23210 \begin_inset Text
\r
23212 \begin_layout Plain Layout
\r
23218 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
23219 \begin_inset Text
\r
23221 \begin_layout Plain Layout
\r
23222 \begin_inset Formula $\mbox{€}$
\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
23241 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
23242 \begin_inset Text
\r
23244 \begin_layout Plain Layout
\r
23252 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
23253 \begin_inset Text
\r
23255 \begin_layout Plain Layout
\r
23259 \begin_layout Plain Layout
\r
23281 \begin_layout Standard
\r
23285 \begin_layout Plain Layout
\r
23295 \begin_inset Note Note
\r
23298 \begin_layout Plain Layout
\r
23299 The following will be displayed when the LaTeX-package
\r
23303 is not installed:
\r
23311 \begin_layout Standard
\r
23312 You need to install the LaTeX-package
\r
23316 to see the rest of this subsection in the output.
\r
23319 \begin_layout Standard
\r
23323 \begin_layout Plain Layout
\r
23335 \begin_layout Section
\r
23337 \begin_inset CommandInset label
\r
23338 LatexCommand label
\r
23339 name "sec:Relations"
\r
23344 \begin_inset Index idx
\r
23347 \begin_layout Plain Layout
\r
23354 \begin_inset Index idx
\r
23357 \begin_layout Plain Layout
\r
23362 \begin_layout Plain Layout
\r
23373 \begin_layout Plain Layout
\r
23388 \begin_layout Standard
\r
23389 All relations can also be inserted via the toolbar button
\r
23390 \begin_inset Graphics
\r
23391 filename ../images/math/leq.png
\r
23399 \begin_layout Standard
\r
23400 \begin_inset space \hfill{}
\r
23404 \begin_inset Tabular
\r
23405 <lyxtabular version="3" rows="17" columns="2">
\r
23406 <features rotate="0" tabularvalignment="middle">
\r
23407 <column alignment="center" valignment="top" width="0pt">
\r
23408 <column alignment="center" valignment="top" width="0pt">
\r
23410 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
23411 \begin_inset Text
\r
23413 \begin_layout Plain Layout
\r
23419 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
23420 \begin_inset Text
\r
23422 \begin_layout Plain Layout
\r
23430 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
23431 \begin_inset Text
\r
23433 \begin_layout Plain Layout
\r
23439 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
23440 \begin_inset Text
\r
23442 \begin_layout Plain Layout
\r
23443 \begin_inset Formula $<$
\r
23453 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
23454 \begin_inset Text
\r
23456 \begin_layout Plain Layout
\r
23464 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
23465 \begin_inset Text
\r
23467 \begin_layout Plain Layout
\r
23468 \begin_inset Formula $\le$
\r
23478 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
23479 \begin_inset Text
\r
23481 \begin_layout Plain Layout
\r
23489 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
23490 \begin_inset Text
\r
23492 \begin_layout Plain Layout
\r
23493 \begin_inset Formula $\ll$
\r
23503 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
23504 \begin_inset Text
\r
23506 \begin_layout Plain Layout
\r
23514 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
23515 \begin_inset Text
\r
23517 \begin_layout Plain Layout
\r
23518 \begin_inset Formula $\prec$
\r
23528 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
23529 \begin_inset Text
\r
23531 \begin_layout Plain Layout
\r
23539 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
23540 \begin_inset Text
\r
23542 \begin_layout Plain Layout
\r
23543 \begin_inset Formula $\preceq$
\r
23553 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
23554 \begin_inset Text
\r
23556 \begin_layout Plain Layout
\r
23564 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
23565 \begin_inset Text
\r
23567 \begin_layout Plain Layout
\r
23568 \begin_inset Formula $\subset$
\r
23578 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
23579 \begin_inset Text
\r
23581 \begin_layout Plain Layout
\r
23589 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
23590 \begin_inset Text
\r
23592 \begin_layout Plain Layout
\r
23593 \begin_inset Formula $\subseteq$
\r
23603 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
23604 \begin_inset Text
\r
23606 \begin_layout Plain Layout
\r
23614 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
23615 \begin_inset Text
\r
23617 \begin_layout Plain Layout
\r
23618 \begin_inset Formula $\sqsubseteq$
\r
23628 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
23629 \begin_inset Text
\r
23631 \begin_layout Plain Layout
\r
23639 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
23640 \begin_inset Text
\r
23642 \begin_layout Plain Layout
\r
23643 \begin_inset Formula $\in$
\r
23653 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
23654 \begin_inset Text
\r
23656 \begin_layout Plain Layout
\r
23664 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
23665 \begin_inset Text
\r
23667 \begin_layout Plain Layout
\r
23668 \begin_inset Formula $\vdash$
\r
23678 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
23679 \begin_inset Text
\r
23681 \begin_layout Plain Layout
\r
23689 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
23690 \begin_inset Text
\r
23692 \begin_layout Plain Layout
\r
23693 \begin_inset Formula $\smile$
\r
23703 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
23704 \begin_inset Text
\r
23706 \begin_layout Plain Layout
\r
23714 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
23715 \begin_inset Text
\r
23717 \begin_layout Plain Layout
\r
23718 \begin_inset Formula $\lhd$
\r
23728 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
23729 \begin_inset Text
\r
23731 \begin_layout Plain Layout
\r
23739 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
23740 \begin_inset Text
\r
23742 \begin_layout Plain Layout
\r
23743 \begin_inset Formula $\unlhd$
\r
23753 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
23754 \begin_inset Text
\r
23756 \begin_layout Plain Layout
\r
23764 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
23765 \begin_inset Text
\r
23767 \begin_layout Plain Layout
\r
23768 \begin_inset Formula $\gtrless$
\r
23778 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
23779 \begin_inset Text
\r
23781 \begin_layout Plain Layout
\r
23789 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
23790 \begin_inset Text
\r
23792 \begin_layout Plain Layout
\r
23793 \begin_inset Formula $\mid$
\r
23803 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
23804 \begin_inset Text
\r
23806 \begin_layout Plain Layout
\r
23814 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
23815 \begin_inset Text
\r
23817 \begin_layout Plain Layout
\r
23818 \begin_inset Formula $\nmid$
\r
23832 \begin_inset space \hfill{}
\r
23836 \begin_inset Tabular
\r
23837 <lyxtabular version="3" rows="17" columns="2">
\r
23838 <features rotate="0" tabularvalignment="middle">
\r
23839 <column alignment="center" valignment="top" width="0pt">
\r
23840 <column alignment="center" valignment="top" width="0pt">
\r
23842 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
23843 \begin_inset Text
\r
23845 \begin_layout Plain Layout
\r
23851 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
23852 \begin_inset Text
\r
23854 \begin_layout Plain Layout
\r
23862 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
23863 \begin_inset Text
\r
23865 \begin_layout Plain Layout
\r
23871 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
23872 \begin_inset Text
\r
23874 \begin_layout Plain Layout
\r
23875 \begin_inset Formula $=$
\r
23885 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
23886 \begin_inset Text
\r
23888 \begin_layout Plain Layout
\r
23896 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
23897 \begin_inset Text
\r
23899 \begin_layout Plain Layout
\r
23900 \begin_inset Formula $\not=$
\r
23910 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
23911 \begin_inset Text
\r
23913 \begin_layout Plain Layout
\r
23921 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
23922 \begin_inset Text
\r
23924 \begin_layout Plain Layout
\r
23925 \begin_inset Formula $\equiv$
\r
23935 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
23936 \begin_inset Text
\r
23938 \begin_layout Plain Layout
\r
23946 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
23947 \begin_inset Text
\r
23949 \begin_layout Plain Layout
\r
23950 \begin_inset Formula $\sim$
\r
23960 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
23961 \begin_inset Text
\r
23963 \begin_layout Plain Layout
\r
23971 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
23972 \begin_inset Text
\r
23974 \begin_layout Plain Layout
\r
23975 \begin_inset Formula $\simeq$
\r
23985 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
23986 \begin_inset Text
\r
23988 \begin_layout Plain Layout
\r
23996 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
23997 \begin_inset Text
\r
23999 \begin_layout Plain Layout
\r
24000 \begin_inset Formula $\approx$
\r
24010 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
24011 \begin_inset Text
\r
24013 \begin_layout Plain Layout
\r
24021 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
24022 \begin_inset Text
\r
24024 \begin_layout Plain Layout
\r
24025 \begin_inset Formula $\cong$
\r
24035 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
24036 \begin_inset Text
\r
24038 \begin_layout Plain Layout
\r
24046 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
24047 \begin_inset Text
\r
24049 \begin_layout Plain Layout
\r
24050 \begin_inset Formula $\bowtie$
\r
24060 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
24061 \begin_inset Text
\r
24063 \begin_layout Plain Layout
\r
24071 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
24072 \begin_inset Text
\r
24074 \begin_layout Plain Layout
\r
24075 \begin_inset Formula $\notin$
\r
24085 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
24086 \begin_inset Text
\r
24088 \begin_layout Plain Layout
\r
24096 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
24097 \begin_inset Text
\r
24099 \begin_layout Plain Layout
\r
24100 \begin_inset Formula $\perp$
\r
24110 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
24111 \begin_inset Text
\r
24113 \begin_layout Plain Layout
\r
24121 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
24122 \begin_inset Text
\r
24124 \begin_layout Plain Layout
\r
24125 \begin_inset Formula $\propto$
\r
24135 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
24136 \begin_inset Text
\r
24138 \begin_layout Plain Layout
\r
24146 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
24147 \begin_inset Text
\r
24149 \begin_layout Plain Layout
\r
24150 \begin_inset Formula $\asymp$
\r
24160 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
24161 \begin_inset Text
\r
24163 \begin_layout Plain Layout
\r
24171 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
24172 \begin_inset Text
\r
24174 \begin_layout Plain Layout
\r
24175 \begin_inset Formula $\doteq$
\r
24185 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
24186 \begin_inset Text
\r
24188 \begin_layout Plain Layout
\r
24196 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
24197 \begin_inset Text
\r
24199 \begin_layout Plain Layout
\r
24200 \begin_inset Formula $\circeq$
\r
24210 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
24211 \begin_inset Text
\r
24213 \begin_layout Plain Layout
\r
24221 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
24222 \begin_inset Text
\r
24224 \begin_layout Plain Layout
\r
24225 \begin_inset Formula $\models$
\r
24235 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
24236 \begin_inset Text
\r
24238 \begin_layout Plain Layout
\r
24246 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
24247 \begin_inset Text
\r
24249 \begin_layout Plain Layout
\r
24250 \begin_inset Formula $\widehat{=}$
\r
24264 \begin_inset space \hfill{}
\r
24268 \begin_inset Tabular
\r
24269 <lyxtabular version="3" rows="17" columns="2">
\r
24270 <features rotate="0" tabularvalignment="middle">
\r
24271 <column alignment="center" valignment="top" width="0pt">
\r
24272 <column alignment="center" valignment="top" width="0pt">
\r
24274 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
24275 \begin_inset Text
\r
24277 \begin_layout Plain Layout
\r
24283 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
24284 \begin_inset Text
\r
24286 \begin_layout Plain Layout
\r
24294 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
24295 \begin_inset Text
\r
24297 \begin_layout Plain Layout
\r
24303 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
24304 \begin_inset Text
\r
24306 \begin_layout Plain Layout
\r
24307 \begin_inset Formula $>$
\r
24317 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
24318 \begin_inset Text
\r
24320 \begin_layout Plain Layout
\r
24328 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
24329 \begin_inset Text
\r
24331 \begin_layout Plain Layout
\r
24332 \begin_inset Formula $\ge$
\r
24342 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
24343 \begin_inset Text
\r
24345 \begin_layout Plain Layout
\r
24353 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
24354 \begin_inset Text
\r
24356 \begin_layout Plain Layout
\r
24357 \begin_inset Formula $\gg$
\r
24367 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
24368 \begin_inset Text
\r
24370 \begin_layout Plain Layout
\r
24378 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
24379 \begin_inset Text
\r
24381 \begin_layout Plain Layout
\r
24382 \begin_inset Formula $\succ$
\r
24392 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
24393 \begin_inset Text
\r
24395 \begin_layout Plain Layout
\r
24403 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
24404 \begin_inset Text
\r
24406 \begin_layout Plain Layout
\r
24407 \begin_inset Formula $\succeq$
\r
24417 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
24418 \begin_inset Text
\r
24420 \begin_layout Plain Layout
\r
24428 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
24429 \begin_inset Text
\r
24431 \begin_layout Plain Layout
\r
24432 \begin_inset Formula $\supset$
\r
24442 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
24443 \begin_inset Text
\r
24445 \begin_layout Plain Layout
\r
24453 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
24454 \begin_inset Text
\r
24456 \begin_layout Plain Layout
\r
24457 \begin_inset Formula $\supseteq$
\r
24467 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
24468 \begin_inset Text
\r
24470 \begin_layout Plain Layout
\r
24478 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
24479 \begin_inset Text
\r
24481 \begin_layout Plain Layout
\r
24482 \begin_inset Formula $\sqsupseteq$
\r
24492 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
24493 \begin_inset Text
\r
24495 \begin_layout Plain Layout
\r
24503 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
24504 \begin_inset Text
\r
24506 \begin_layout Plain Layout
\r
24507 \begin_inset Formula $\ni$
\r
24517 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
24518 \begin_inset Text
\r
24520 \begin_layout Plain Layout
\r
24528 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
24529 \begin_inset Text
\r
24531 \begin_layout Plain Layout
\r
24532 \begin_inset Formula $\dashv$
\r
24542 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
24543 \begin_inset Text
\r
24545 \begin_layout Plain Layout
\r
24553 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
24554 \begin_inset Text
\r
24556 \begin_layout Plain Layout
\r
24557 \begin_inset Formula $\frown$
\r
24567 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
24568 \begin_inset Text
\r
24570 \begin_layout Plain Layout
\r
24578 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
24579 \begin_inset Text
\r
24581 \begin_layout Plain Layout
\r
24582 \begin_inset Formula $\rhd$
\r
24592 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
24593 \begin_inset Text
\r
24595 \begin_layout Plain Layout
\r
24603 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
24604 \begin_inset Text
\r
24606 \begin_layout Plain Layout
\r
24607 \begin_inset Formula $\unrhd$
\r
24617 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
24618 \begin_inset Text
\r
24620 \begin_layout Plain Layout
\r
24628 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
24629 \begin_inset Text
\r
24631 \begin_layout Plain Layout
\r
24632 \begin_inset Formula $\lessgtr$
\r
24642 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
24643 \begin_inset Text
\r
24645 \begin_layout Plain Layout
\r
24653 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
24654 \begin_inset Text
\r
24656 \begin_layout Plain Layout
\r
24657 \begin_inset Formula $\parallel$
\r
24667 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
24668 \begin_inset Text
\r
24670 \begin_layout Plain Layout
\r
24678 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
24679 \begin_inset Text
\r
24681 \begin_layout Plain Layout
\r
24682 \begin_inset Formula $\nparallel$
\r
24696 \begin_inset space \hfill{}
\r
24702 \begin_layout Standard
\r
24703 \begin_inset VSpace medskip
\r
24718 are bigger than the equal looking operators
\r
24733 \begin_layout Standard
\r
24734 Relations are, in contrary to symbols, always surrounded by space.
\r
24737 \begin_layout Standard
\r
24738 Relations with labels can be created with the command
\r
24745 \begin_inset Index idx
\r
24748 \begin_layout Plain Layout
\r
24759 \begin_layout Standard
\r
24761 \begin_inset Tabular
\r
24762 <lyxtabular version="3" rows="2" columns="2">
\r
24763 <features rotate="0" tabularvalignment="middle">
\r
24764 <column alignment="center" valignment="top">
\r
24765 <column alignment="center" valignment="top">
\r
24767 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
24768 \begin_inset Text
\r
24770 \begin_layout Plain Layout
\r
24776 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
24777 \begin_inset Text
\r
24779 \begin_layout Plain Layout
\r
24781 \begin_inset Note Note
\r
24784 \begin_layout Plain Layout
\r
24791 is only used as spacer.
\r
24803 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
24804 \begin_inset Text
\r
24806 \begin_layout Plain Layout
\r
24813 \begin_layout Plain Layout
\r
24830 \begin_layout Plain Layout
\r
24840 \begin_inset Formula $\downarrow$
\r
24849 \begin_layout Plain Layout
\r
24862 \begin_layout Plain Layout
\r
24876 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
24877 \begin_inset Text
\r
24879 \begin_layout Plain Layout
\r
24880 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
\r
24896 \begin_layout Section
\r
24900 \begin_layout Subsection
\r
24901 Predefined Functions
\r
24902 \begin_inset CommandInset label
\r
24903 LatexCommand label
\r
24904 name "sub:Predefined-Functions"
\r
24909 \begin_inset Index idx
\r
24912 \begin_layout Plain Layout
\r
24913 Functions ! predefined
\r
24921 \begin_layout Standard
\r
24922 In general, variables are set
\r
24926 in mathematical expressions, but not function names, because
\r
24927 \begin_inset Formula $sin$
\r
24930 could be misunderstood as
\r
24931 \begin_inset Formula $s\cdot i\cdot n$
\r
24935 Therefore there are predefined functionswhich are additionally a bit separated
\r
24937 They are inserted as commands starting with a backslash before their name.
\r
24940 \begin_layout Standard
\r
24942 \begin_inset Tabular
\r
24943 <lyxtabular version="3" rows="2" columns="4">
\r
24944 <features rotate="0" tabularvalignment="middle">
\r
24945 <column alignment="center" valignment="top" width="0pt">
\r
24946 <column alignment="center" valignment="top" width="0pt">
\r
24947 <column alignment="center" valignment="top" width="0pt">
\r
24948 <column alignment="center" valignment="top" width="0pt">
\r
24950 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="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" rightline="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" usebox="none">
\r
24969 \begin_inset Text
\r
24971 \begin_layout Plain Layout
\r
24977 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
24978 \begin_inset Text
\r
24980 \begin_layout Plain Layout
\r
24988 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
24989 \begin_inset Text
\r
24991 \begin_layout Plain Layout
\r
24997 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
24998 \begin_inset Text
\r
25000 \begin_layout Plain Layout
\r
25001 \begin_inset Formula $Asin(x)+B$
\r
25009 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
25010 \begin_inset Text
\r
25012 \begin_layout Plain Layout
\r
25020 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
25021 \begin_inset Text
\r
25023 \begin_layout Plain Layout
\r
25024 \begin_inset Formula $A\sin(x)+B$
\r
25040 \begin_layout Standard
\r
25041 The following functions are predefined:
\r
25044 \begin_layout Standard
\r
25045 \begin_inset VSpace -2mm
\r
25051 \begin_layout Standard
\r
25053 \begin_inset Tabular
\r
25054 <lyxtabular version="3" rows="9" columns="4">
\r
25055 <features rotate="0" tabularvalignment="middle">
\r
25056 <column alignment="center" valignment="top" width="0pt">
\r
25057 <column alignment="center" valignment="top" width="0pt">
\r
25058 <column alignment="center" valignment="top" width="0pt">
\r
25059 <column alignment="center" valignment="top" width="0pt">
\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" usebox="none">
\r
25080 \begin_inset Text
\r
25082 \begin_layout Plain Layout
\r
25088 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
25089 \begin_inset Text
\r
25091 \begin_layout Plain Layout
\r
25099 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
25100 \begin_inset Text
\r
25102 \begin_layout Plain Layout
\r
25110 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
25111 \begin_inset Text
\r
25113 \begin_layout Plain Layout
\r
25121 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
25122 \begin_inset Text
\r
25124 \begin_layout Plain Layout
\r
25132 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
25133 \begin_inset Text
\r
25135 \begin_layout Plain Layout
\r
25145 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
25146 \begin_inset Text
\r
25148 \begin_layout Plain Layout
\r
25156 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
25157 \begin_inset Text
\r
25159 \begin_layout Plain Layout
\r
25167 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
25168 \begin_inset Text
\r
25170 \begin_layout Plain Layout
\r
25178 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
25179 \begin_inset Text
\r
25181 \begin_layout Plain Layout
\r
25191 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
25192 \begin_inset Text
\r
25194 \begin_layout Plain Layout
\r
25202 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
25203 \begin_inset Text
\r
25205 \begin_layout Plain Layout
\r
25213 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
25214 \begin_inset Text
\r
25216 \begin_layout Plain Layout
\r
25224 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
25225 \begin_inset Text
\r
25227 \begin_layout Plain Layout
\r
25237 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
25238 \begin_inset Text
\r
25240 \begin_layout Plain Layout
\r
25248 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
25249 \begin_inset Text
\r
25251 \begin_layout Plain Layout
\r
25259 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
25260 \begin_inset Text
\r
25262 \begin_layout Plain Layout
\r
25270 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
25271 \begin_inset Text
\r
25273 \begin_layout Plain Layout
\r
25283 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
25284 \begin_inset Text
\r
25286 \begin_layout Plain Layout
\r
25294 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
25295 \begin_inset Text
\r
25297 \begin_layout Plain Layout
\r
25305 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
25306 \begin_inset Text
\r
25308 \begin_layout Plain Layout
\r
25316 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
25317 \begin_inset Text
\r
25319 \begin_layout Plain Layout
\r
25329 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
25330 \begin_inset Text
\r
25332 \begin_layout Plain Layout
\r
25340 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
25341 \begin_inset Text
\r
25343 \begin_layout Plain Layout
\r
25351 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
25352 \begin_inset Text
\r
25354 \begin_layout Plain Layout
\r
25362 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
25363 \begin_inset Text
\r
25365 \begin_layout Plain Layout
\r
25375 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
25376 \begin_inset Text
\r
25378 \begin_layout Plain Layout
\r
25386 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
25387 \begin_inset Text
\r
25389 \begin_layout Plain Layout
\r
25397 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
25398 \begin_inset Text
\r
25400 \begin_layout Plain Layout
\r
25408 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
25409 \begin_inset Text
\r
25411 \begin_layout Plain Layout
\r
25421 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
25422 \begin_inset Text
\r
25424 \begin_layout Plain Layout
\r
25432 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
25433 \begin_inset Text
\r
25435 \begin_layout Plain Layout
\r
25443 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
25444 \begin_inset Text
\r
25446 \begin_layout Plain Layout
\r
25454 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
25455 \begin_inset Text
\r
25457 \begin_layout Plain Layout
\r
25473 \begin_layout Standard
\r
25474 They can also be inserted with the math toolbar button
\r
25475 \begin_inset Graphics
\r
25476 filename ../images/math/functions.png
\r
25484 \begin_layout Subsection
\r
25485 Self-defined Functions
\r
25486 \begin_inset Index idx
\r
25489 \begin_layout Plain Layout
\r
25490 Functions ! self-defined
\r
25498 \begin_layout Standard
\r
25499 To use a function that is not predefined, like for example the sign function
\r
25500 sgn(x), there are two possibilities:
\r
25503 \begin_layout Itemize
\r
25504 Define the function by inserting the following line to the LaTeX-preamble
\r
25505 \begin_inset Foot
\r
25508 \begin_layout Plain Layout
\r
25513 DeclareMathOperator
\r
25516 \begin_inset CommandInset ref
\r
25518 reference "sub:Self-defined-Operators"
\r
25528 \begin_inset Newline newline
\r
25532 \begin_inset VSpace -3mm
\r
25536 \begin_inset Newline newline
\r
25543 DeclareMathOperator{
\r
25548 \begin_inset Index idx
\r
25551 \begin_layout Plain Layout
\r
25556 DeclareMathOperator
\r
25562 \begin_inset Newline newline
\r
25566 \begin_inset VSpace -2mm
\r
25570 \begin_inset Newline newline
\r
25573 Now the new defined function can be called with the command
\r
25582 \begin_layout Itemize
\r
25583 Write the formula as usual, mark the formula name, in our example the letters
\r
25588 , and change it to mathematical text.
\r
25589 Finally, a space is inserted between prefactor and function.
\r
25592 \begin_layout Standard
\r
25593 The result is the same with both methods as with a predefined function
\r
25594 \begin_inset Foot
\r
25597 \begin_layout Plain Layout
\r
25598 In LyX self-defined functions are displayed red, predefined ones black.
\r
25606 \begin_layout Standard
\r
25608 \begin_inset Tabular
\r
25609 <lyxtabular version="3" rows="3" columns="2">
\r
25610 <features rotate="0" tabularvalignment="middle">
\r
25611 <column alignment="center" valignment="top" width="0pt">
\r
25612 <column alignment="center" valignment="top" width="0pt">
\r
25614 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
25615 \begin_inset Text
\r
25617 \begin_layout Plain Layout
\r
25623 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
25624 \begin_inset Text
\r
25626 \begin_layout Plain Layout
\r
25634 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
25635 \begin_inset Text
\r
25637 \begin_layout Plain Layout
\r
25645 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
25646 \begin_inset Text
\r
25648 \begin_layout Plain Layout
\r
25649 \begin_inset Formula $A\sgn(x)+B$
\r
25659 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
25660 \begin_inset Text
\r
25662 \begin_layout Plain Layout
\r
25666 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
\r
25674 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
25675 \begin_inset Text
\r
25677 \begin_layout Plain Layout
\r
25678 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
\r
25694 \begin_layout Standard
\r
25695 The first method is more suitable when the self-defined function should
\r
25696 be used several times.
\r
25699 \begin_layout Subsection
\r
25701 \begin_inset Index idx
\r
25704 \begin_layout Plain Layout
\r
25713 \begin_layout Standard
\r
25714 For limits, in addition to the commands
\r
25721 \begin_inset Index idx
\r
25724 \begin_layout Plain Layout
\r
25744 the following functions are defined:
\r
25747 \begin_layout Standard
\r
25749 \begin_inset Tabular
\r
25750 <lyxtabular version="3" rows="5" columns="2">
\r
25751 <features rotate="0" tabularvalignment="middle">
\r
25752 <column alignment="center" valignment="top">
\r
25753 <column alignment="center" valignment="top">
\r
25755 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
25756 \begin_inset Text
\r
25758 \begin_layout Plain Layout
\r
25764 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
25765 \begin_inset Text
\r
25767 \begin_layout Plain Layout
\r
25769 \begin_inset Note Note
\r
25772 \begin_layout Plain Layout
\r
25779 is only used as spacer.
\r
25791 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
25792 \begin_inset Text
\r
25794 \begin_layout Plain Layout
\r
25802 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
25803 \begin_inset Text
\r
25805 \begin_layout Plain Layout
\r
25806 \begin_inset Formula $\varliminf$
\r
25816 <cell alignment="center" valignment="top" leftline="true" usebox="none">
\r
25817 \begin_inset Text
\r
25819 \begin_layout Plain Layout
\r
25827 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
\r
25828 \begin_inset Text
\r
25830 \begin_layout Plain Layout
\r
25831 \begin_inset Formula $\varlimsup$
\r
25841 <cell alignment="center" valignment="top" leftline="true" usebox="none">
\r
25842 \begin_inset Text
\r
25844 \begin_layout Plain Layout
\r
25852 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
\r
25853 \begin_inset Text
\r
25855 \begin_layout Plain Layout
\r
25856 \begin_inset Formula $\varprojlim$
\r
25866 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
25867 \begin_inset Text
\r
25869 \begin_layout Plain Layout
\r
25877 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
25878 \begin_inset Text
\r
25880 \begin_layout Plain Layout
\r
25881 \begin_inset Formula $\varinjlim$
\r
25885 \begin_inset Formula $\raisebox{-2.5mm}{}$
\r
25901 \begin_layout Standard
\r
25902 \begin_inset VSpace medskip
\r
25905 The limit is created by inserting a subscript.
\r
25906 It is set right beside the function in an inline formula:
\r
25909 \begin_layout Standard
\r
25911 \begin_inset Tabular
\r
25912 <lyxtabular version="3" rows="2" columns="2">
\r
25913 <features rotate="0" tabularvalignment="middle">
\r
25914 <column alignment="center" valignment="top" width="0pt">
\r
25915 <column alignment="center" valignment="top" width="0pt">
\r
25917 <cell alignment="center" valignment="top" usebox="none">
\r
25918 \begin_inset Text
\r
25920 \begin_layout Plain Layout
\r
25926 <cell alignment="center" valignment="top" usebox="none">
\r
25927 \begin_inset Text
\r
25929 \begin_layout Plain Layout
\r
25930 \begin_inset space \hspace{}
\r
25935 \begin_inset Note Note
\r
25938 \begin_layout Plain Layout
\r
25945 are used here as spacer.
\r
25957 <cell alignment="center" valignment="top" usebox="none">
\r
25958 \begin_inset Text
\r
25960 \begin_layout Plain Layout
\r
25969 \begin_layout Plain Layout
\r
25982 \begin_layout Plain Layout
\r
25996 <cell alignment="center" valignment="top" usebox="none">
\r
25997 \begin_inset Text
\r
25999 \begin_layout Plain Layout
\r
26000 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
\r
26016 \begin_layout Standard
\r
26017 In a displayed formula the limit is set below the formula, as usual:
\r
26018 \begin_inset Formula
\r
26028 \begin_layout Subsection
\r
26030 \begin_inset Index idx
\r
26033 \begin_layout Plain Layout
\r
26034 Functions ! modulo-
\r
26042 \begin_layout Standard
\r
26043 The modulo-function is special, because it exists in four variants.
\r
26044 The variants in a displayed formula are:
\r
26045 \begin_inset Formula
\r
26047 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
\r
26048 \mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
\r
26049 \mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
\r
26050 \mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
\r
26051 \mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b
\r
26059 \begin_layout Standard
\r
26060 In an inline formula less space is set before the function names for all
\r
26062 By default the modulo-functions take only the first following character
\r
26064 To use more than one character, one has to put them into TeX-braces:
\r
26065 \begin_inset Formula
\r
26067 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
\r
26068 \mathrm{a\backslash pod\textrm{\spce}bcd} & & a\pod bcd\\
\r
26069 \mathrm{a\backslash pod\backslash\{bc\to d} & & a\pod{bc}d
\r
26077 \begin_layout Section
\r
26078 Special Characters
\r
26079 \begin_inset Index idx
\r
26082 \begin_layout Plain Layout
\r
26083 Special characters
\r
26091 \begin_layout Subsection
\r
26092 Special Characters in Mathematical Text
\r
26095 \begin_layout Standard
\r
26096 The following commands can only be used in mathematical text or in TeX-mode:
\r
26099 \begin_layout Standard
\r
26100 \begin_inset space \hfill{}
\r
26104 \begin_inset Tabular
\r
26105 <lyxtabular version="3" rows="8" columns="2">
\r
26106 <features rotate="0" tabularvalignment="middle">
\r
26107 <column alignment="block" valignment="top">
\r
26108 <column alignment="block" valignment="top">
\r
26110 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
26111 \begin_inset Text
\r
26113 \begin_layout Plain Layout
\r
26119 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
26120 \begin_inset Text
\r
26122 \begin_layout Plain Layout
\r
26130 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
26131 \begin_inset Text
\r
26133 \begin_layout Plain Layout
\r
26141 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
26142 \begin_inset Text
\r
26144 \begin_layout Plain Layout
\r
26145 \begin_inset Formula $\textrm{œ}$
\r
26155 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
26156 \begin_inset Text
\r
26158 \begin_layout Plain Layout
\r
26166 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
26167 \begin_inset Text
\r
26169 \begin_layout Plain Layout
\r
26170 \begin_inset Formula $\textrm{Œ}$
\r
26180 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
26181 \begin_inset Text
\r
26183 \begin_layout Plain Layout
\r
26191 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
26192 \begin_inset Text
\r
26194 \begin_layout Plain Layout
\r
26195 \begin_inset Formula $\textrm{æ}$
\r
26205 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
26206 \begin_inset Text
\r
26208 \begin_layout Plain Layout
\r
26216 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
26217 \begin_inset Text
\r
26219 \begin_layout Plain Layout
\r
26220 \begin_inset Formula $\textrm{Æ}$
\r
26230 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
26231 \begin_inset Text
\r
26233 \begin_layout Plain Layout
\r
26241 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
26242 \begin_inset Text
\r
26244 \begin_layout Plain Layout
\r
26245 \begin_inset Formula $\textrm{\aa}$
\r
26255 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
26256 \begin_inset Text
\r
26258 \begin_layout Plain Layout
\r
26262 \begin_inset Index idx
\r
26265 \begin_layout Plain Layout
\r
26272 \begin_layout Plain Layout
\r
26293 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
26294 \begin_inset Text
\r
26296 \begin_layout Plain Layout
\r
26297 \begin_inset Formula $\textrm{Å}$
\r
26307 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
26308 \begin_inset Text
\r
26310 \begin_layout Plain Layout
\r
26318 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
26319 \begin_inset Text
\r
26321 \begin_layout Plain Layout
\r
26322 \begin_inset Formula $\textrm{ı}$
\r
26336 \begin_inset space \hfill{}
\r
26340 \begin_inset Tabular
\r
26341 <lyxtabular version="3" rows="8" columns="2">
\r
26342 <features rotate="0" tabularvalignment="middle">
\r
26343 <column alignment="block" valignment="top">
\r
26344 <column alignment="center" valignment="top">
\r
26346 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
26347 \begin_inset Text
\r
26349 \begin_layout Plain Layout
\r
26351 \begin_inset Note Note
\r
26354 \begin_layout Plain Layout
\r
26356 \begin_inset space \thinspace{}
\r
26359 mm is used for separation, because otherwise the output will be ¡ and ¿
\r
26370 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
26371 \begin_inset Text
\r
26373 \begin_layout Plain Layout
\r
26381 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
26382 \begin_inset Text
\r
26384 \begin_layout Plain Layout
\r
26392 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
26393 \begin_inset Text
\r
26395 \begin_layout Plain Layout
\r
26396 \begin_inset Formula $\textrm{ø}$
\r
26406 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
26407 \begin_inset Text
\r
26409 \begin_layout Plain Layout
\r
26417 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
26418 \begin_inset Text
\r
26420 \begin_layout Plain Layout
\r
26421 \begin_inset Formula $\textrm{Ø}$
\r
26431 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
26432 \begin_inset Text
\r
26434 \begin_layout Plain Layout
\r
26442 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
26443 \begin_inset Text
\r
26445 \begin_layout Plain Layout
\r
26446 \begin_inset Formula $\textrm{ł}$
\r
26456 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
26457 \begin_inset Text
\r
26459 \begin_layout Plain Layout
\r
26467 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
26468 \begin_inset Text
\r
26470 \begin_layout Plain Layout
\r
26471 \begin_inset Formula $\textrm{Ł}$
\r
26481 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
26482 \begin_inset Text
\r
26484 \begin_layout Plain Layout
\r
26486 \begin_inset space \hspace{}
\r
26494 \begin_layout Plain Layout
\r
26508 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
26509 \begin_inset Text
\r
26511 \begin_layout Plain Layout
\r
26512 \begin_inset Formula $\textrm{!`}$
\r
26522 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
26523 \begin_inset Text
\r
26525 \begin_layout Plain Layout
\r
26527 \begin_inset space \hspace{}
\r
26535 \begin_layout Plain Layout
\r
26549 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
26550 \begin_inset Text
\r
26552 \begin_layout Plain Layout
\r
26553 \begin_inset Formula $\textrm{?`}$
\r
26563 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
26564 \begin_inset Text
\r
26566 \begin_layout Plain Layout
\r
26574 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
26575 \begin_inset Text
\r
26577 \begin_layout Plain Layout
\r
26578 \begin_inset Formula $\textrm{ȷ}$
\r
26592 \begin_inset space \hfill{}
\r
26598 \begin_layout Standard
\r
26600 \begin_inset Formula $\textrm{\textrm{Å}}$
\r
26604 \begin_inset Formula $\textrm{\textrm{Ø}}$
\r
26607 can also be inserted via the math toolbar button
\r
26608 \begin_inset Graphics
\r
26609 filename ../images/math/digamma.png
\r
26617 \begin_layout Standard
\r
26618 An exception are the commands
\r
26621 \begin_inset space \hspace{}
\r
26630 \begin_inset space \hspace{}
\r
26636 , because they can be inserted in LyX directly to text.
\r
26639 \begin_layout Subsection
\r
26641 \begin_inset CommandInset label
\r
26642 LatexCommand label
\r
26643 name "sub:Accents-in-Text"
\r
26648 \begin_inset Index idx
\r
26651 \begin_layout Plain Layout
\r
26652 Accents ! in text
\r
26660 \begin_layout Standard
\r
26661 With the following commands all letters can be accented.
\r
26662 The commands must be inserted in TeX-mode.
\r
26665 \begin_layout Standard
\r
26666 \begin_inset space \hfill{}
\r
26670 \begin_inset Tabular
\r
26671 <lyxtabular version="3" rows="8" columns="2">
\r
26672 <features rotate="0" tabularvalignment="middle">
\r
26673 <column alignment="block" valignment="top">
\r
26674 <column alignment="block" valignment="top">
\r
26676 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
26677 \begin_inset Text
\r
26679 \begin_layout Plain Layout
\r
26685 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
26686 \begin_inset Text
\r
26688 \begin_layout Plain Layout
\r
26696 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
26697 \begin_inset Text
\r
26699 \begin_layout Plain Layout
\r
26703 \begin_inset Quotes grd
\r
26711 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
26712 \begin_inset Text
\r
26714 \begin_layout Plain Layout
\r
26718 \begin_layout Plain Layout
\r
26734 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
26735 \begin_inset Text
\r
26737 \begin_layout Plain Layout
\r
26745 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
26746 \begin_inset Text
\r
26748 \begin_layout Plain Layout
\r
26752 \begin_layout Plain Layout
\r
26768 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
26769 \begin_inset Text
\r
26771 \begin_layout Plain Layout
\r
26778 \begin_layout Plain Layout
\r
26792 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
26793 \begin_inset Text
\r
26795 \begin_layout Plain Layout
\r
26799 \begin_layout Plain Layout
\r
26815 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
26816 \begin_inset Text
\r
26818 \begin_layout Plain Layout
\r
26826 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
26827 \begin_inset Text
\r
26829 \begin_layout Plain Layout
\r
26833 \begin_layout Plain Layout
\r
26849 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
26850 \begin_inset Text
\r
26852 \begin_layout Plain Layout
\r
26859 \begin_layout Plain Layout
\r
26873 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
26874 \begin_inset Text
\r
26876 \begin_layout Plain Layout
\r
26880 \begin_layout Plain Layout
\r
26896 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
26897 \begin_inset Text
\r
26899 \begin_layout Plain Layout
\r
26906 \begin_layout Plain Layout
\r
26920 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
26921 \begin_inset Text
\r
26923 \begin_layout Plain Layout
\r
26927 \begin_layout Plain Layout
\r
26943 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
26944 \begin_inset Text
\r
26946 \begin_layout Plain Layout
\r
26953 \begin_layout Plain Layout
\r
26967 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
26968 \begin_inset Text
\r
26970 \begin_layout Plain Layout
\r
26974 \begin_layout Plain Layout
\r
26994 \begin_inset space \hfill{}
\r
26998 \begin_inset Tabular
\r
26999 <lyxtabular version="3" rows="8" columns="2">
\r
27000 <features rotate="0" tabularvalignment="middle">
\r
27001 <column alignment="block" valignment="top">
\r
27002 <column alignment="center" valignment="top">
\r
27004 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
27005 \begin_inset Text
\r
27007 \begin_layout Plain Layout
\r
27013 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
27014 \begin_inset Text
\r
27016 \begin_layout Plain Layout
\r
27024 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
27025 \begin_inset Text
\r
27027 \begin_layout Plain Layout
\r
27034 \begin_layout Plain Layout
\r
27048 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
27049 \begin_inset Text
\r
27051 \begin_layout Plain Layout
\r
27055 \begin_layout Plain Layout
\r
27071 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
27072 \begin_inset Text
\r
27074 \begin_layout Plain Layout
\r
27082 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
27083 \begin_inset Text
\r
27085 \begin_layout Plain Layout
\r
27089 \begin_layout Plain Layout
\r
27105 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
27106 \begin_inset Text
\r
27108 \begin_layout Plain Layout
\r
27112 \begin_inset Index idx
\r
27115 \begin_layout Plain Layout
\r
27126 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
27127 \begin_inset Text
\r
27129 \begin_layout Plain Layout
\r
27133 \begin_layout Plain Layout
\r
27149 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
27150 \begin_inset Text
\r
27152 \begin_layout Plain Layout
\r
27160 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
27161 \begin_inset Text
\r
27163 \begin_layout Plain Layout
\r
27167 \begin_layout Plain Layout
\r
27183 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
27184 \begin_inset Text
\r
27186 \begin_layout Plain Layout
\r
27193 \begin_layout Plain Layout
\r
27207 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
27208 \begin_inset Text
\r
27210 \begin_layout Plain Layout
\r
27214 \begin_layout Plain Layout
\r
27230 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
27231 \begin_inset Text
\r
27233 \begin_layout Plain Layout
\r
27240 \begin_layout Plain Layout
\r
27254 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
27255 \begin_inset Text
\r
27257 \begin_layout Plain Layout
\r
27261 \begin_layout Plain Layout
\r
27277 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\r
27278 \begin_inset Text
\r
27280 \begin_layout Plain Layout
\r
27287 \begin_layout Plain Layout
\r
27301 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
27302 \begin_inset Text
\r
27304 \begin_layout Plain Layout
\r
27308 \begin_layout Plain Layout
\r
27328 \begin_inset space \hfill{}
\r
27334 \begin_layout Standard
\r
27335 \begin_inset VSpace medskip
\r
27338 With the command
\r
27344 also two different characters can be accented.
\r
27353 \begin_layout Plain Layout
\r
27368 \begin_layout Plain Layout
\r
27380 \begin_layout Standard
\r
27393 can in combination with vowels directly be inserted with the keyboard without
\r
27395 The same applies for the tilde
\r
27396 \begin_inset Foot
\r
27399 \begin_layout Plain Layout
\r
27400 This only applies for keyboards where the tilde is defined as accent.
\r
27409 in combination with
\r
27424 \begin_layout Standard
\r
27467 and accents that are inserted directly with the keyboard are also available
\r
27468 in mathematical text.
\r
27469 For the other accents there are special math commands to be used in formulas,
\r
27471 \begin_inset CommandInset ref
\r
27473 reference "sub:Accents-for-one"
\r
27480 \begin_layout Standard
\r
27481 \begin_inset VSpace bigskip
\r
27484 Furthermore, with the command
\r
27491 \begin_inset Index idx
\r
27494 \begin_layout Plain Layout
\r
27502 all numbers and letters can be set into a circle, quasi accented with a
\r
27503 circle, similar to the copyright symbol.
\r
27506 \begin_layout Standard
\r
27508 \begin_inset Tabular
\r
27509 <lyxtabular version="3" rows="3" columns="2">
\r
27510 <features rotate="0" tabularvalignment="middle">
\r
27511 <column alignment="center" valignment="top">
\r
27512 <column alignment="center" valignment="top">
\r
27514 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
27515 \begin_inset Text
\r
27517 \begin_layout Plain Layout
\r
27523 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
27524 \begin_inset Text
\r
27526 \begin_layout Plain Layout
\r
27528 \begin_inset Note Note
\r
27531 \begin_layout Plain Layout
\r
27538 is only used as spacer.
\r
27550 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
27551 \begin_inset Text
\r
27553 \begin_layout Plain Layout
\r
27561 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
27562 \begin_inset Text
\r
27564 \begin_layout Plain Layout
\r
27568 \begin_layout Plain Layout
\r
27584 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
27585 \begin_inset Text
\r
27587 \begin_layout Plain Layout
\r
27598 raisebox{-1.5pt}{W}}
\r
27603 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
27604 \begin_inset Text
\r
27606 \begin_layout Plain Layout
\r
27607 \begin_inset Formula $\raisebox{4.5mm}{}$
\r
27614 \begin_layout Plain Layout
\r
27626 raisebox{-1.5pt}W}
\r
27632 \begin_inset Formula $\raisebox{-2mm}{}$
\r
27648 \begin_layout Standard
\r
27649 One has to take care that the character fits in the circle.
\r
27657 \begin_inset Foot
\r
27660 \begin_layout Plain Layout
\r
27662 \begin_inset CommandInset ref
\r
27664 reference "sub:Font-Sizes"
\r
27673 specifies thereby the size of the circle.
\r
27674 With the help of
\r
27681 \begin_inset Foot
\r
27684 \begin_layout Plain Layout
\r
27686 \begin_inset CommandInset ref
\r
27688 reference "sub:Boxes-without-Frame"
\r
27697 the character can be centered.
\r
27700 \begin_layout Subsection
\r
27701 Old-style Figures
\r
27702 \begin_inset Index idx
\r
27705 \begin_layout Plain Layout
\r
27706 Old-style Figures
\r
27714 \begin_layout Standard
\r
27715 Old-style figures (also known as old-style numerals) are created with the
\r
27723 \begin_inset Index idx
\r
27726 \begin_layout Plain Layout
\r
27735 The command can be used in formulas and in TeX-mode.
\r
27736 The command scheme is:
\r
27739 \begin_layout Standard
\r
27744 oldstylenums{number}
\r
27747 \begin_layout Standard
\r
27752 oldstylenums{0123456789
\r
27755 \begin_inset Formula $\oldstylenums{0123456789}$
\r
27761 \begin_layout Subsection
\r
27762 Miscellaneous special Characters
\r
27763 \begin_inset CommandInset label
\r
27764 LatexCommand label
\r
27765 name "sub:Miscellaneous-special-Characters"
\r
27770 \begin_inset Index idx
\r
27773 \begin_layout Plain Layout
\r
27774 Special characters ! miscellaneous
\r
27782 \begin_layout Standard
\r
27783 The following characters can only be inserted to formulas by using commands:
\r
27786 \begin_layout Standard
\r
27788 \begin_inset Tabular
\r
27789 <lyxtabular version="3" rows="4" columns="2">
\r
27790 <features rotate="0" tabularvalignment="middle">
\r
27791 <column alignment="center" valignment="top">
\r
27792 <column alignment="center" valignment="top">
\r
27794 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
27795 \begin_inset Text
\r
27797 \begin_layout Plain Layout
\r
27803 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
27804 \begin_inset Text
\r
27806 \begin_layout Plain Layout
\r
27814 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
27815 \begin_inset Text
\r
27817 \begin_layout Plain Layout
\r
27824 \begin_layout Plain Layout
\r
27838 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
27839 \begin_inset Text
\r
27841 \begin_layout Plain Layout
\r
27842 \begin_inset Formula $\mathcircumflex$
\r
27852 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
27853 \begin_inset Text
\r
27855 \begin_layout Plain Layout
\r
27863 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
27864 \begin_inset Text
\r
27866 \begin_layout Plain Layout
\r
27867 \begin_inset Formula $\_$
\r
27877 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
27878 \begin_inset Text
\r
27880 \begin_layout Plain Layout
\r
27885 \begin_layout Plain Layout
\r
27897 \begin_inset Index idx
\r
27900 \begin_layout Plain Layout
\r
27913 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
27914 \begin_inset Text
\r
27916 \begin_layout Plain Layout
\r
27917 \begin_inset Formula $^{\circ}$
\r
27933 \begin_layout Standard
\r
27934 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
\r
27935 contains the following line
\r
27936 \begin_inset Foot
\r
27939 \begin_layout Plain Layout
\r
27940 More about this is described in
\r
27941 \begin_inset CommandInset ref
\r
27943 reference "sub:Text-Characters-in"
\r
27955 \begin_layout Standard
\r
27960 DeclareInputtext{176}{
\r
27973 \begin_layout Section
\r
27975 \begin_inset CommandInset label
\r
27976 LatexCommand label
\r
27977 name "sec:Formula-Styles"
\r
27982 \begin_inset Index idx
\r
27985 \begin_layout Plain Layout
\r
27994 \begin_layout Itemize
\r
27995 There are two different alignment styles:
\r
27999 \begin_layout Description
\r
28000 Centered is the predefined standard
\r
28003 \begin_layout Description
\r
28004 Indented for this the option
\r
28008 must be inserted in the menu
\r
28010 Document\SpecialChar \menuseparator
\r
28016 \begin_inset space ~
\r
28022 \begin_layout Standard
\r
28027 is used, the indentation can be adjusted with the length
\r
28034 \begin_inset Index idx
\r
28037 \begin_layout Plain Layout
\r
28046 Should the distance be 15
\r
28047 \begin_inset space \thinspace{}
\r
28050 mm, the following command line is inserted in the LaTeX-preamble
\r
28053 \begin_layout Standard
\r
28060 mathindent}{15mm}
\r
28063 \begin_layout Standard
\r
28064 When no length is specified, the predefined value of 30
\r
28065 \begin_inset space \thinspace{}
\r
28072 \begin_layout Itemize
\r
28073 And two different numbering styles:
\r
28077 \begin_layout Description
\r
28078 Right is the predefined standard
\r
28081 \begin_layout Description
\r
28082 Left for this the option
\r
28086 must be inserted in the menu
\r
28088 Document\SpecialChar \menuseparator
\r
28094 \begin_inset space ~
\r
28101 \begin_layout Standard
\r
28110 can also be used together.
\r
28111 In this case both options are inserted, separated by a comma.
\r
28114 \begin_layout Standard
\r
28115 The chosen styles are used for all displayed formulas of the document.
\r
28116 When both, centered and indented formulas should be created in a document,
\r
28122 The indented formulas are then set in a flalign environment, see
\r
28123 \begin_inset CommandInset ref
\r
28125 reference "sub:Flalign-Environment"
\r
28132 \begin_layout Section
\r
28133 Multiline Formulas
\r
28134 \begin_inset CommandInset label
\r
28135 LatexCommand label
\r
28136 name "sec:Multiline-Formulas"
\r
28141 \begin_inset Index idx
\r
28144 \begin_layout Plain Layout
\r
28145 Formula ! multiline
\r
28153 \begin_layout Subsection
\r
28157 \begin_layout Standard
\r
28158 In LyX multiline formulas are created by pressing
\r
28161 \begin_inset Info
\r
28163 arg "newline-insert newline"
\r
28168 inside a formula.
\r
28169 This creates either an
\r
28171 eqnarray environment
\r
28173 that is described in
\r
28174 \begin_inset CommandInset ref
\r
28176 reference "sub:Eqnarray-Environment"
\r
28180 or, when the option
\r
28182 Use AMS math package
\r
28184 in the document settings is selected, an
\r
28186 align environment
\r
28188 that is described in
\r
28189 \begin_inset CommandInset ref
\r
28191 reference "sub:Standard-align-Environment"
\r
28196 The align environment is recommended because it provides in any case a
\r
28197 typographically correct output.
\r
28200 \begin_layout Standard
\r
28201 There are other multiline formula environments that can be created via the
\r
28204 Insert\SpecialChar \menuseparator
\r
28208 These environments are described in the following sections.
\r
28211 \begin_layout Standard
\r
28212 In all multiline formula environments a new line is created by pressing
\r
28214 \begin_inset Info
\r
28216 arg "newline-insert newline"
\r
28220 To add or delete lines, the math toolbar buttons
\r
28221 \begin_inset Graphics
\r
28222 filename ../images/tabular-feature_append-row.png
\r
28228 \begin_inset Graphics
\r
28229 filename ../images/tabular-feature_delete-row.png
\r
28234 , respectively, or the menu
\r
28236 Edit\SpecialChar \menuseparator
\r
28242 \begin_layout Subsubsection
\r
28244 \begin_inset CommandInset label
\r
28245 LatexCommand label
\r
28246 name "sub:Line-Separation"
\r
28251 \begin_inset Index idx
\r
28254 \begin_layout Plain Layout
\r
28255 Formula ! multiline ! Line separation
\r
28263 \begin_layout Standard
\r
28264 There is sometimes not enough space in multiline formulas between the lines:
\r
28265 \begin_inset Formula
\r
28266 \begin{eqnarray*}
\r
28267 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
28268 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
28276 \begin_layout Standard
\r
28277 In LaTeX additional line space is specified as optional argument of the
\r
28278 new line command.
\r
28279 This is not yet possible in LyX
\r
28280 \begin_inset Foot
\r
28283 \begin_layout Plain Layout
\r
28285 \begin_inset CommandInset href
\r
28286 LatexCommand href
\r
28287 name "LyX-bug #1505"
\r
28288 target "http://www.lyx.org/trac/ticket/1505"
\r
28297 , therefore the whole formula must be inserted in TeX-mode.
\r
28298 To add in our example space, the command
\r
28306 is inserted at the end of the first line.
\r
28311 \begin_layout Plain Layout
\r
28318 \begin_layout Plain Layout
\r
28320 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
\r
28323 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
\r
28330 \begin_layout Plain Layout
\r
28334 left(B^{2}+x_{0}^{2}
\r
28342 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
\r
28347 \begin_layout Plain Layout
\r
28359 \begin_layout Standard
\r
28360 \begin_inset VSpace bigskip
\r
28363 To set the line separation for all lines in a formula, the length
\r
28370 \begin_inset Index idx
\r
28373 \begin_layout Plain Layout
\r
28382 The definition is:
\r
28383 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
\r
28394 \begin_inset space \thinspace{}
\r
28399 \begin_inset space \thinspace{}
\r
28402 mm additional line separation as in the previous example, the command
\r
28405 \begin_layout Standard
\r
28415 \begin_layout Standard
\r
28416 is inserted in TeX-mode before the formula.
\r
28417 This requires that the LaTeX-package
\r
28422 \begin_inset Foot
\r
28425 \begin_layout Plain Layout
\r
28430 is part of every LaTeX standard installation.
\r
28436 \begin_inset Index idx
\r
28439 \begin_layout Plain Layout
\r
28445 was loaded in LaTeX-preamble with the line
\r
28448 \begin_layout Standard
\r
28456 \begin_layout Standard
\r
28461 \begin_layout Plain Layout
\r
28473 \begin_inset Formula
\r
28474 \begin{eqnarray*}
\r
28475 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
28476 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
28484 \begin_layout Standard
\r
28488 \begin_layout Plain Layout
\r
28499 To get back to the predefined distance,
\r
28505 is set to the value 3
\r
28506 \begin_inset space \thinspace{}
\r
28512 \begin_layout Subsubsection
\r
28513 Column Separation
\r
28514 \begin_inset CommandInset label
\r
28515 LatexCommand label
\r
28516 name "sub:Column-Separation"
\r
28521 \begin_inset Index idx
\r
28524 \begin_layout Plain Layout
\r
28525 Formula ! multiline ! Column separation
\r
28533 \begin_layout Standard
\r
28534 Multiline formulas form a matrix.
\r
28535 A formula in the eqnarray environment is for example a matrix with three
\r
28537 By changing the column separation in this environment, the space beside
\r
28538 the relation sign can be changed.
\r
28541 \begin_layout Standard
\r
28542 The column separation is specified with the length
\r
28549 \begin_inset Index idx
\r
28552 \begin_layout Plain Layout
\r
28561 \begin_inset Newline newline
\r
28564 column separation = 2
\r
28565 \begin_inset space \thinspace{}
\r
28575 \begin_inset Newline newline
\r
28578 Thus, the command
\r
28581 \begin_layout Standard
\r
28588 arraycolsep}{1cm}
\r
28591 \begin_layout Standard
\r
28592 inserted in TeX-mode, sets for all following formulas a column separation
\r
28594 \begin_inset space \thinspace{}
\r
28598 To get back to the predefined distance,
\r
28605 \begin_inset space \thinspace{}
\r
28611 \begin_layout Standard
\r
28613 \begin_inset space \thinspace{}
\r
28616 cm column separation:
\r
28620 \begin_layout Plain Layout
\r
28626 arraycolsep}{1cm}
\r
28632 \begin_inset Formula
\r
28633 \begin{eqnarray*}
\r
28640 A formula with the predefined column separation for matrices of 10
\r
28641 \begin_inset space \thinspace{}
\r
28648 \begin_layout Plain Layout
\r
28654 arraycolsep}{5pt}
\r
28660 \begin_inset Formula
\r
28661 \begin{eqnarray*}
\r
28671 \begin_layout Subsubsection
\r
28673 \begin_inset Index idx
\r
28676 \begin_layout Plain Layout
\r
28685 \begin_layout Standard
\r
28686 Long formulas can be typeset using these methods:
\r
28689 \begin_layout Itemize
\r
28690 When one side of the equation is much shorter than the line width, this
\r
28691 one is chosen for the left side and the right side is typeset over two
\r
28693 \begin_inset Formula
\r
28695 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
28696 & & -\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
28701 The minus sign at the beginning of the second line does normally not appear
\r
28702 as an operator because it is the first character of the line.
\r
28703 Thus it would not be surrounded by space and could not be distinguished
\r
28704 from the fraction bar.
\r
28706 \begin_inset space \thinspace{}
\r
28709 pt space was inserted behind the minus sign with the command
\r
28716 \begin_inset Foot
\r
28719 \begin_layout Plain Layout
\r
28727 \begin_inset CommandInset ref
\r
28729 reference "sub:Variable-Space"
\r
28739 \begin_inset Index idx
\r
28742 \begin_layout Plain Layout
\r
28753 \begin_layout Itemize
\r
28754 When both sides of the equation are too long, the command
\r
28761 \begin_inset Index idx
\r
28764 \begin_layout Plain Layout
\r
28773 It is inserted in the first column of the first line and causes all further
\r
28774 insertions to overwrite the following columns:
\r
28775 \begin_inset Formula
\r
28777 \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
28778 & & -\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
28779 & & =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
28784 After the insertion of
\r
28790 , the cursor is in a purple box that is a bit shifted to the left from the
\r
28792 In this the formula is inserted.
\r
28793 \begin_inset Newline newline
\r
28796 The content of the further lines is inserted to the second or another formula
\r
28798 The greater the column number where it was inserted, the larger the indentation.
\r
28799 \begin_inset VSpace medskip
\r
28803 \begin_inset Newline newline
\r
28807 \begin_inset Note Greyedout
\r
28810 \begin_layout Plain Layout
\r
28811 Note the following when using
\r
28820 \begin_layout Itemize
\r
28821 The formula doesn't use the full page width.
\r
28823 \begin_inset space \thinspace{}
\r
28827 \begin_inset space \space{}
\r
28831 \begin_inset Formula $-B^{2}$
\r
28834 is added to the first line in the above example, it would have been outside
\r
28836 To better use the width, negative space can be inserted at the beginning
\r
28837 of the first line.
\r
28840 \begin_layout Itemize
\r
28841 Due to a bug in LyX the cursor cannot be set with the mouse into the first
\r
28843 \begin_inset Foot
\r
28846 \begin_layout Plain Layout
\r
28847 \begin_inset CommandInset href
\r
28848 LatexCommand href
\r
28849 name "LyX-bug #1429"
\r
28850 target "http://www.lyx.org/trac/ticket/1429"
\r
28859 One can only set the cursor at the beginning of the line and move it with
\r
28868 \begin_layout Itemize
\r
28869 Other methods to set long formulas are offered by the environments described
\r
28871 \begin_inset CommandInset ref
\r
28873 reference "sub:Multline-Environment"
\r
28878 \begin_inset CommandInset ref
\r
28880 reference "sub:Multiline-Formula-Parts"
\r
28887 \begin_layout Subsubsection
\r
28888 Multiline Brackets
\r
28889 \begin_inset CommandInset label
\r
28890 LatexCommand label
\r
28891 name "sub:Multiline-Brackets"
\r
28896 \begin_inset Index idx
\r
28899 \begin_layout Plain Layout
\r
28900 Brackets ! for multiline expressions
\r
28908 \begin_layout Standard
\r
28909 For brackets spanning multiple lines the following problem occurs:
\r
28910 \begin_inset Formula
\r
28911 \begin{eqnarray*}
\r
28912 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
\r
28913 & & \left.\cdots+B-D\right]
\r
28921 \begin_layout Standard
\r
28922 The closing bracket is smaller than the opening bracket because brackets
\r
28923 with variable size may not span multiple lines.
\r
28926 \begin_layout Standard
\r
28927 To set the bracket size for the second line correctly, the first line is
\r
28935 \begin_inset Index idx
\r
28938 \begin_layout Plain Layout
\r
28946 and the second line with
\r
28951 \begin_inset Foot
\r
28954 \begin_layout Plain Layout
\r
28968 \begin_inset CommandInset ref
\r
28970 reference "sub:Automatic-Bracket-Size"
\r
28982 \begin_inset Index idx
\r
28985 \begin_layout Plain Layout
\r
29011 \begin_layout Plain Layout
\r
29030 \begin_layout Plain Layout
\r
29049 \begin_layout Plain Layout
\r
29061 \begin_inset Formula $\downarrow$
\r
29067 \begin_inset Index idx
\r
29070 \begin_layout Plain Layout
\r
29078 is inserted, because the multiplication operator with its limits is the
\r
29079 largest symbol in the first line and this should be the size for the bracket
\r
29080 in the second line.
\r
29083 \begin_layout Standard
\r
29084 The result is this:
\r
29085 \begin_inset Formula
\r
29086 \begin{eqnarray*}
\r
29087 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
\r
29088 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
\r
29096 \begin_layout Subsection
\r
29097 Align Environments
\r
29100 \begin_layout Standard
\r
29101 Align environments can be used for every kind of multiline formulas.
\r
29102 They are especially useful to set several formulas side by side.
\r
29105 \begin_layout Standard
\r
29106 Align environments consist of columns.
\r
29107 The odd columns are right aligned, the even ones left aligned.
\r
29108 Every line in an Align environment can be numbered.
\r
29111 \begin_layout Standard
\r
29112 Align environments are created via the menu
\r
29114 Insert\SpecialChar \menuseparator
\r
29120 Edit\SpecialChar \menuseparator
\r
29121 Math\SpecialChar \menuseparator
\r
29122 Change Formula Type
\r
29124 already existing formulas can be converted to Align environments.
\r
29127 \begin_layout Standard
\r
29128 To add or delete columns, the math toolbar buttons
\r
29129 \begin_inset Graphics
\r
29130 filename ../images/tabular-feature_append-column.png
\r
29136 \begin_inset Graphics
\r
29137 filename ../images/tabular-feature_delete-column.png
\r
29142 , respectively, or the menu
\r
29144 Edit\SpecialChar \menuseparator
\r
29150 \begin_layout Subsubsection
\r
29151 Standard align Environment
\r
29152 \begin_inset CommandInset label
\r
29153 LatexCommand label
\r
29154 name "sub:Standard-align-Environment"
\r
29159 \begin_inset Index idx
\r
29162 \begin_layout Plain Layout
\r
29163 Formula ! multiline ! align environment
\r
29171 \begin_layout Standard
\r
29172 This Align environment is created by pressing
\r
29173 \begin_inset Info
\r
29175 arg "newline-insert newline"
\r
29178 in a formula or by the menu
\r
29180 Insert\SpecialChar \menuseparator
\r
29181 Math\SpecialChar \menuseparator
\r
29182 AMS align Environment
\r
29187 \begin_layout Standard
\r
29188 An example for two formulas set side by side, that are created with a four
\r
29189 column align environment:
\r
29190 \begin_inset Formula
\r
29192 A & =\sin(B) & C & =D\\
\r
29193 C & \ne A & B & \ne D
\r
29198 As it can be seen, the formulas in this environment are placed so as if
\r
29199 there would be a
\r
29204 \begin_inset Foot
\r
29207 \begin_layout Plain Layout
\r
29215 \begin_inset CommandInset ref
\r
29217 reference "sub:Variable-Space"
\r
29228 before the first and after every even column.
\r
29229 When the formula style
\r
29232 \begin_inset Foot
\r
29235 \begin_layout Plain Layout
\r
29236 formula styles see
\r
29237 \begin_inset CommandInset ref
\r
29239 reference "sec:Formula-Styles"
\r
29250 is used, the formula is set without the
\r
29256 before the first column.
\r
29259 \begin_layout Subsubsection
\r
29260 Alignat Environment
\r
29261 \begin_inset Index idx
\r
29264 \begin_layout Plain Layout
\r
29265 Formula ! multiline ! alignat environment
\r
29273 \begin_layout Standard
\r
29274 The alignat environment has no predefined column separation.
\r
29275 It can be inserted manually with the spaces that are described
\r
29276 \begin_inset CommandInset ref
\r
29278 reference "sub:Space"
\r
29285 \begin_layout Standard
\r
29286 The above example in the alignat environment where 1
\r
29287 \begin_inset space \thinspace{}
\r
29290 cm space was inserted at the beginning of the second formula:
\r
29291 \begin_inset Formula
\r
29292 \begin{alignat*}{2}
\r
29293 A & =\sin(B) & \hspace{1cm}C & =D\\
\r
29294 C & \ne A & B & \ne D
\r
29299 Because the column separation can be set separately for every column, this
\r
29300 environment is especially suitable to set three and more formulas side
\r
29304 \begin_layout Subsubsection
\r
29305 Flalign Environment
\r
29306 \begin_inset CommandInset label
\r
29307 LatexCommand label
\r
29308 name "sub:Flalign-Environment"
\r
29313 \begin_inset Index idx
\r
29316 \begin_layout Plain Layout
\r
29317 Formula ! multiline ! flalign environment
\r
29325 \begin_layout Standard
\r
29326 In this environment the first two columns are always set as much as possible
\r
29327 to the left and the last two ones to the right.
\r
29329 \begin_inset Formula
\r
29331 A & =1 & B & =2 & C & =3\\
\r
29332 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
\r
29340 \begin_layout Standard
\r
29341 By creating a flalign environment with an odd number of columns where an
\r
29342 empty TeX-brace is inserted to the last column, several formulas in a document
\r
29343 can be set to the left, although the formula style
\r
29348 As example the indented formula
\r
29349 \begin_inset CommandInset ref
\r
29350 LatexCommand eqref
\r
29351 reference "eq:VolInt"
\r
29356 \begin_inset Formula
\r
29358 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}
\r
29363 The first two columns contain the formula.
\r
29364 To indent it as with the formula style
\r
29369 \begin_inset space \thinspace{}
\r
29372 pt space was inserted at the beginning of the first column.
\r
29375 \begin_layout Subsection
\r
29376 Eqnarray Environment
\r
29377 \begin_inset CommandInset label
\r
29378 LatexCommand label
\r
29379 name "sub:Eqnarray-Environment"
\r
29384 \begin_inset Index idx
\r
29387 \begin_layout Plain Layout
\r
29388 Formula ! multiline ! eqnarray environment
\r
29396 \begin_layout Standard
\r
29397 When this environment has been created, three blue boxes appear.
\r
29398 The content of the first box is right aligned, the content of the last
\r
29399 one left aligned.
\r
29400 The content of the middle box appears centered and a bit smaller, because
\r
29401 it is designed to insert there only relation characters.
\r
29402 \begin_inset Formula
\r
29403 \begin{eqnarray*}
\r
29404 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
\r
29414 \begin_layout Subsection
\r
29415 Gather Environment
\r
29416 \begin_inset Index idx
\r
29419 \begin_layout Plain Layout
\r
29420 Formula ! multiline ! gather environment
\r
29428 \begin_layout Standard
\r
29429 This environment consists of only one centered column.
\r
29430 Every line can be numbered.
\r
29431 \begin_inset Formula
\r
29442 \begin_layout Subsection
\r
29443 Multline Environment
\r
29444 \begin_inset CommandInset label
\r
29445 LatexCommand label
\r
29446 name "sub:Multline-Environment"
\r
29451 \begin_inset Index idx
\r
29454 \begin_layout Plain Layout
\r
29455 Formula ! multiline ! multline environment
\r
29463 \begin_layout Standard
\r
29464 The multline environment consists, like the gather environment, of only
\r
29466 But the first line is left aligned, the last one right aligned.
\r
29467 All other lines are centered.
\r
29468 Therefore this environment is suitable for long formulas.
\r
29469 As example formula
\r
29470 \begin_inset CommandInset ref
\r
29471 LatexCommand eqref
\r
29472 reference "eq:lefteqn"
\r
29476 in the multline environment:
\r
29477 \begin_inset Formula
\r
29479 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
29480 -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
29481 =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
29489 \begin_layout Standard
\r
29490 In the output only the last (first) line of a multline environment appears
\r
29491 numbered when the document numbering is right (left).
\r
29492 \begin_inset Foot
\r
29495 \begin_layout Plain Layout
\r
29496 numbering styles see
\r
29497 \begin_inset CommandInset ref
\r
29499 reference "sec:Formula-Styles"
\r
29511 \begin_layout Standard
\r
29512 With the commands
\r
29519 \begin_inset Index idx
\r
29522 \begin_layout Plain Layout
\r
29537 \begin_inset Index idx
\r
29540 \begin_layout Plain Layout
\r
29548 a centered line can be right or left aligned, respectively.
\r
29549 The commands are used as follows:
\r
29552 \begin_layout Standard
\r
29557 shoveright{line content}
\r
29563 shoveleft{line content}
\r
29566 \begin_layout Standard
\r
29567 \begin_inset VSpace medskip
\r
29577 \begin_inset Index idx
\r
29580 \begin_layout Plain Layout
\r
29588 specifies the distance of the first line from the left page margin.
\r
29589 Predefined is the length 0
\r
29590 \begin_inset space \thinspace{}
\r
29596 \begin_layout Standard
\r
29597 As example the above formula where the command
\r
29600 \begin_layout Standard
\r
29607 multlinegap}{2cm}
\r
29610 \begin_layout Standard
\r
29611 was inserted in TeX-mode before:
\r
29615 \begin_layout Plain Layout
\r
29621 multlinegap}{2cm}
\r
29627 \begin_inset Formula
\r
29629 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
29630 \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
29631 =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
29640 \begin_layout Plain Layout
\r
29646 multlinegap}{0pt}
\r
29651 The second line was left aligned using
\r
29660 \begin_layout Subsection
\r
29661 Multiline Formula Parts
\r
29662 \begin_inset CommandInset label
\r
29663 LatexCommand label
\r
29664 name "sub:Multiline-Formula-Parts"
\r
29669 \begin_inset Index idx
\r
29672 \begin_layout Plain Layout
\r
29673 Formula ! multiline ! formula parts
\r
29681 \begin_layout Standard
\r
29682 To display only parts of a formula with multiple lines, one of the following
\r
29683 environments is used:
\r
29700 They can be inserted via the menu
\r
29702 Insert\SpecialChar \menuseparator
\r
29705 or by using the commands described in this section.
\r
29708 \begin_layout Standard
\r
29709 The first three have the same properties as the corresponding multiline
\r
29710 formula environments, but it is possible to set further formula parts beside
\r
29713 \begin_inset Formula
\r
29715 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
\r
29716 \Delta E\Delta t & \ge\frac{\hbar}{2}
\r
29718 \right\} \textrm{Uncertainty relations}
\r
29726 \begin_layout Standard
\r
29727 To get this formula, a displayed formula is created where the command
\r
29734 \begin_inset Index idx
\r
29737 \begin_layout Plain Layout
\r
29746 A purple box appears around the blue formula box where now columns and
\r
29747 lines can be added.
\r
29748 Outside the multiline environment other formula parts can be set, like
\r
29752 \begin_layout Standard
\r
29753 The aligned environment is also suitable for long formulas whose lines are
\r
29754 horizontally aligned.
\r
29755 Using aligned in a displayed formula has the advantage that the formula
\r
29756 number is vertically centered behind the lines.
\r
29757 As example formula
\r
29758 \begin_inset CommandInset ref
\r
29759 LatexCommand eqref
\r
29760 reference "eq:shortlong"
\r
29764 in the aligned environment:
\r
29765 \begin_inset Formula
\r
29767 \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
29768 & -\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
29777 \begin_layout Standard
\r
29778 To use the environments
\r
29797 \begin_inset Index idx
\r
29800 \begin_layout Plain Layout
\r
29815 \begin_inset Index idx
\r
29818 \begin_layout Plain Layout
\r
29833 \begin_inset Index idx
\r
29836 \begin_layout Plain Layout
\r
29844 are inserted, respectively.
\r
29845 The split environment has the same properties as the aligned environment
\r
29846 but it can only have two columns.
\r
29849 \begin_layout Subsection
\r
29850 Text in multiline Formulas
\r
29851 \begin_inset CommandInset label
\r
29852 LatexCommand label
\r
29853 name "sub:Text-in-multiline"
\r
29858 \begin_inset Index idx
\r
29861 \begin_layout Plain Layout
\r
29862 Text ! in formulas
\r
29868 \begin_inset Index idx
\r
29871 \begin_layout Plain Layout
\r
29872 Formula ! multiline ! text
\r
29880 \begin_layout Standard
\r
29881 In the Align environments, and the multline and gather environment, text
\r
29882 can be inserted that will appear in a separate line and doesn't affect
\r
29883 the column alignment.
\r
29884 To do this, the command
\r
29891 \begin_inset Index idx
\r
29894 \begin_layout Plain Layout
\r
29902 is used in the following scheme:
\r
29905 \begin_layout Standard
\r
29913 \begin_layout Standard
\r
29914 The text should not be longer than a line because it cannot be hyphenated.
\r
29915 As LyX doesn't yet support
\r
29921 directly, the text is written as mathematical text.
\r
29928 must hereby be at the beginning of a line and appears in the output above
\r
29930 An example where the text was inserted at the beginning of the second line:
\r
29931 \begin_inset Formula
\r
29933 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
\r
29934 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
\r
29942 \begin_layout Section
\r
29943 Formula Numbering
\r
29944 \begin_inset Index idx
\r
29947 \begin_layout Plain Layout
\r
29948 Formula numbering
\r
29954 \begin_inset Index idx
\r
29957 \begin_layout Plain Layout
\r
29958 Formula ! numbering|see
\r
29962 \begin_layout Plain Layout
\r
29969 Formula numbering
\r
29973 \begin_layout Plain Layout
\r
29988 \begin_layout Subsection
\r
29992 \begin_layout Standard
\r
29993 Numbered formulas can be created with the menu
\r
29995 Insert\SpecialChar \menuseparator
\r
29996 Math\SpecialChar \menuseparator
\r
29998 \begin_inset space ~
\r
30006 \begin_inset space ~
\r
30012 Existing formulas can be numbered with the menu
\r
30014 Edit\SpecialChar \menuseparator
\r
30015 Math\SpecialChar \menuseparator
\r
30017 \begin_inset space ~
\r
30023 \begin_inset Info
\r
30025 arg "math-number-toggle"
\r
30029 The formula number is displayed in LyX behind the formula as a number sign
\r
30031 The number sign is replaced in the output by the formula number.
\r
30034 \begin_layout Standard
\r
30035 When numbering is turned on in multiline formulas, all lines will be numbered.
\r
30036 But the numbering can be controlled with the menu
\r
30038 Edit\SpecialChar \menuseparator
\r
30039 Math\SpecialChar \menuseparator
\r
30041 \begin_inset space ~
\r
30045 \begin_inset space ~
\r
30049 \begin_inset space ~
\r
30055 \begin_inset Info
\r
30057 arg "math-number-line-toggle"
\r
30060 ) for every line.
\r
30063 \begin_layout Standard
\r
30064 Except for inline formulas, all formulas can be numbered with two different
\r
30066 \begin_inset CommandInset ref
\r
30068 reference "sec:Formula-Styles"
\r
30075 \begin_layout Subsection
\r
30077 \begin_inset Index idx
\r
30080 \begin_layout Plain Layout
\r
30081 Cross-references ! to formulas
\r
30089 \begin_layout Standard
\r
30090 All labeled formulas can be cross-referenced.
\r
30091 A label is added by the menu
\r
30093 Insert\SpecialChar \menuseparator
\r
30096 or the toolbar button
\r
30097 \begin_inset Graphics
\r
30098 filename ../images/label-insert.png
\r
30104 The cursor must hereby be inside a displayed formula.
\r
30105 Alternatively you can right-click on the formula and choose
\r
30110 A dialog pops up displaying the prefix
\r
30115 The label is inserted there behind the prefix.
\r
30116 The predefined prefix means
\r
30117 \begin_inset Quotes eld
\r
30121 \begin_inset Quotes erd
\r
30124 and makes it easier to find labels in large documents because it marks
\r
30125 it as formula label to divide it from e.
\r
30126 \begin_inset space \thinspace{}
\r
30130 \begin_inset space \space{}
\r
30134 To change a label, the menu
\r
30136 Insert\SpecialChar \menuseparator
\r
30139 is used again or you right-click on a formula and then on
\r
30146 \begin_layout Standard
\r
30147 The name of the label is displayed in LyX within two parentheses behind
\r
30149 A formula with a label is always numbered.
\r
30152 \begin_layout Standard
\r
30153 Cross-references are inserted via the menu
\r
30155 Insert\SpecialChar \menuseparator
\r
30158 or with the toolbar button
\r
30159 \begin_inset Graphics
\r
30160 filename ../images/dialog-show-new-inset_ref.png
\r
30166 A formula cross-reference appears in the output as formula number.
\r
30167 When in the cross-reference dialog window the format
\r
30171 is chosen, the cross-reference appears in the output as formula number
\r
30173 \begin_inset Newline newline
\r
30176 By right-clicking on a cross-reference in LyX, one jumps to the formula
\r
30177 that is referenced.
\r
30180 \begin_layout Standard
\r
30181 Here are as examples cross-references to formulas of the following subsections:
\r
30182 \begin_inset Note Note
\r
30185 \begin_layout Plain Layout
\r
30186 Note the different cross-reference types.
\r
30194 \begin_layout Standard
\r
30196 \begin_inset CommandInset ref
\r
30197 LatexCommand eqref
\r
30198 reference "eq:tag"
\r
30203 \begin_inset CommandInset ref
\r
30204 LatexCommand eqref
\r
30211 \begin_inset CommandInset ref
\r
30213 reference "eq:Lat"
\r
30217 ) big Latin letters are used for the numbering in contrary to (
\r
30218 \begin_inset CommandInset ref
\r
30220 reference "eq:Rom"
\r
30227 \begin_layout Standard
\r
30228 \begin_inset VSpace medskip
\r
30231 When the argument of
\r
30236 \begin_inset Foot
\r
30239 \begin_layout Plain Layout
\r
30247 \begin_inset CommandInset ref
\r
30249 reference "sub:User-defined-Numbering"
\r
30260 contains a box like in
\r
30261 \begin_inset CommandInset ref
\r
30263 reference "sub:Paragraph-Boxes"
\r
30267 , the formula cannot be referenced.
\r
30270 \begin_layout Subsection
\r
30272 \begin_inset Index idx
\r
30275 \begin_layout Plain Layout
\r
30276 Formula numbering ! subnumbering
\r
30284 \begin_layout Standard
\r
30285 With the help of the commands
\r
30289 begin{subequations}
\r
30295 end{subequations}
\r
30297 formulas can be subnumbered.
\r
30298 Both commands are inserted in TeX-mode.
\r
30301 \begin_layout Standard
\r
30303 \begin_inset Formula
\r
30305 A=C-B\label{eq:a}
\r
30314 \begin_layout Plain Layout
\r
30318 addtocounter{equation}{-1}
\r
30327 \begin_layout Plain Layout
\r
30331 begin{subequations}
\r
30337 \begin_inset VSpace -5mm
\r
30341 \begin_inset Formula
\r
30343 B=C-A\label{eq:b}
\r
30349 \begin_inset Formula
\r
30351 C=A+B\label{eq:c}
\r
30359 \begin_layout Standard
\r
30363 \begin_layout Plain Layout
\r
30367 end{subequations}
\r
30375 \begin_layout Standard
\r
30376 To create the example, the following is done:
\r
30379 \begin_layout Enumerate
\r
30380 first formula is inserted
\r
30383 \begin_layout Enumerate
\r
30388 addtocounter{equation}{-1}
\r
30390 begin{subequations}
\r
30391 \begin_inset Index idx
\r
30394 \begin_layout Plain Layout
\r
30403 \begin_inset Newline newline
\r
30408 is inserted after the first formula
\r
30411 \begin_layout Enumerate
\r
30412 second formula is inserted
\r
30415 \begin_layout Enumerate
\r
30416 third formula is inserted
\r
30419 \begin_layout Enumerate
\r
30424 end{subequations}
\r
30426 is inserted after the third formula
\r
30429 \begin_layout Standard
\r
30430 Every formula between the commands
\r
30442 is subnumbered as a, b,
\r
30443 \begin_inset Newline linebreak
\r
30446 c, \SpecialChar \ldots{}
\r
30447 For multiline formulas every line will be subnumbered.
\r
30448 All subnumbered formulas are treated as
\r
30452 numbered formula.
\r
30453 But as every numbered formula increases the counter
\r
30457 by one, the command
\r
30463 is needed to decrease it.
\r
30464 Otherwise the formulas
\r
30465 \begin_inset CommandInset ref
\r
30466 LatexCommand eqref
\r
30472 \begin_inset CommandInset ref
\r
30473 LatexCommand eqref
\r
30479 \begin_inset CommandInset ref
\r
30480 LatexCommand eqref
\r
30485 would be numbered as
\r
30486 \begin_inset CommandInset ref
\r
30487 LatexCommand eqref
\r
30493 \begin_inset CommandInset ref
\r
30494 LatexCommand eqref
\r
30500 \begin_inset CommandInset ref
\r
30501 LatexCommand eqref
\r
30509 \begin_layout Standard
\r
30510 By inserting the commands in TeX-mode, a space is created between the first
\r
30512 To revert this -5
\r
30513 \begin_inset space \thinspace{}
\r
30516 mm vertical space is inserted after the command
\r
30520 begin{subequations}
\r
30523 When the formula style
\r
30526 \begin_inset Foot
\r
30529 \begin_layout Plain Layout
\r
30530 formula styles see
\r
30531 \begin_inset CommandInset ref
\r
30533 reference "sec:Formula-Styles"
\r
30545 \begin_inset space \thinspace{}
\r
30548 mm space is inserted instead.
\r
30551 \begin_layout Standard
\r
30552 Here is an example for a multiline formula where the numbering was turned
\r
30553 off for the second line:
\r
30557 \begin_layout Plain Layout
\r
30561 begin{subequations}
\r
30567 \begin_inset Formula
\r
30569 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
\r
30570 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
\r
30571 & = & B^{2}-2BZ+Z^{2}\label{eq:f}
\r
30580 \begin_layout Plain Layout
\r
30584 end{subequations}
\r
30592 \begin_layout Subsection
\r
30593 User-defined Numbering
\r
30594 \begin_inset CommandInset label
\r
30595 LatexCommand label
\r
30596 name "sub:User-defined-Numbering"
\r
30601 \begin_inset Index idx
\r
30604 \begin_layout Plain Layout
\r
30605 Formula numbering ! user-defined
\r
30613 \begin_layout Standard
\r
30614 \begin_inset Index idx
\r
30617 \begin_layout Plain Layout
\r
30618 Formula numbering ! self-defined delimiters
\r
30623 With the standard numbering parentheses are set around the formula number.
\r
30624 To replace the parentheses for example by vertical bars, the following
\r
30625 line is added to the LaTeX-preamble:
\r
30628 \begin_layout Standard
\r
30637 maketag@@@{|#1|}}
\r
30640 \begin_inset Note Note
\r
30643 \begin_layout Plain Layout
\r
30644 This macro is already declared in the LaTeX-preamble for testing.
\r
30645 To activate it, remove the percent sign at the beginning.
\r
30653 \begin_layout Standard
\r
30654 To use other characters, the vertical bars besides the
\r
30658 are replaced by one ore more characters.
\r
30659 To get only the formula number the vertical bars are omitted.
\r
30662 \begin_layout Standard
\r
30663 \begin_inset VSpace bigskip
\r
30666 When there should be an expression of your choice instead of the consecutive
\r
30667 formula number in parentheses behind the formula, the command
\r
30674 \begin_inset Index idx
\r
30677 \begin_layout Plain Layout
\r
30686 \begin_inset Formula
\r
30688 A+B=C\tag{something}\label{eq:tag}
\r
30693 In this example the command
\r
30701 \begin_layout Plain Layout
\r
30712 was inserted in the formula.
\r
30715 \begin_layout Standard
\r
30716 When the command
\r
30724 \begin_layout Plain Layout
\r
30735 is inserted instead, the star prevents the parentheses around the expression:
\r
30736 \begin_inset Formula
\r
30738 A+B=C\tag*{something}
\r
30746 \begin_layout Standard
\r
30747 \begin_inset VSpace bigskip
\r
30750 To restart the formula numbering with new document parts or sections, the
\r
30751 following command is used:
\r
30754 \begin_layout Standard
\r
30759 @addtoreset{equation}{part}
\r
30762 \begin_inset Index idx
\r
30765 \begin_layout Plain Layout
\r
30770 \begin_layout Plain Layout
\r
30781 \begin_layout Plain Layout
\r
30794 \begin_layout Plain Layout
\r
30805 \begin_layout Plain Layout
\r
30818 \begin_inset Newline newline
\r
30822 \begin_inset Newline newline
\r
30829 @addtoreset{equation}{section}
\r
30832 \begin_layout Standard
\r
30833 To be able to use these commands in TeX-mode, the
\r
30834 \begin_inset Quotes eld
\r
30838 \begin_inset Quotes erd
\r
30841 character has to be made
\r
30842 \begin_inset Quotes eld
\r
30846 \begin_inset Quotes erd
\r
30849 for LaTeX using the command
\r
30863 So the command sequence in TeX-mode is:
\r
30866 \begin_layout Standard
\r
30872 \begin_inset Newline newline
\r
30877 @addtoreset{equation}{section}
\r
30878 \begin_inset Newline newline
\r
30886 \begin_layout Standard
\r
30887 In the LaTeX-preamble
\r
30899 can be omitted as they are automatically internally inserted by LyX.
\r
30902 \begin_layout Standard
\r
30914 \begin_inset Foot
\r
30917 \begin_layout Plain Layout
\r
30922 is part of the LaTeX-package
\r
30927 \begin_inset Index idx
\r
30930 \begin_layout Plain Layout
\r
30931 Packages ! carlisle
\r
30936 that is part of every LaTeX standard installation.
\r
30942 \begin_inset Index idx
\r
30945 \begin_layout Plain Layout
\r
30946 Packages ! remreset
\r
30951 has to be loaded in the LaTeX-preamble with the line
\r
30954 \begin_layout Standard
\r
30959 usepackage{remreset}
\r
30962 \begin_layout Standard
\r
30963 Then the command
\r
30970 \begin_inset Index idx
\r
30973 \begin_layout Plain Layout
\r
30978 \begin_layout Plain Layout
\r
30989 \begin_layout Plain Layout
\r
31002 \begin_layout Plain Layout
\r
31013 \begin_layout Plain Layout
\r
31025 can be used with the same scheme as
\r
31034 \begin_layout Standard
\r
31035 \begin_inset VSpace bigskip
\r
31038 Sometimes formulas should be numbered in the following form:
\r
31041 \begin_layout Standard
\r
31043 \family typewriter
\r
31044 (section number.formula number)
\r
31047 \begin_layout Standard
\r
31048 The formula number should start with every section with
\r
31049 \begin_inset Quotes eld
\r
31053 \begin_inset Quotes erd
\r
31059 \begin_layout Standard
\r
31060 For this case there is the command
\r
31067 \begin_inset Index idx
\r
31070 \begin_layout Plain Layout
\r
31078 , which is used with the following scheme:
\r
31081 \begin_layout Standard
\r
31086 numberwithin{counter}{sectioning}
\r
31089 \begin_layout Standard
\r
31090 Counter denotes what kind of numbering is affected, sectioning denotes what
\r
31091 number is before the dot.
\r
31094 \begin_layout Standard
\r
31095 Thus in our case the following LaTeX-preamble or TeX code line is used:
\r
31098 \begin_layout Standard
\r
31103 numberwithin{equation}{section}
\r
31106 \begin_layout Standard
\r
31107 This is the result:
\r
31111 \begin_layout Plain Layout
\r
31115 numberwithin{equation}{section}
\r
31121 \begin_inset Formula
\r
31131 \begin_layout Standard
\r
31133 \begin_inset space \thinspace{}
\r
31137 \begin_inset space \space{}
\r
31140 tables so that the number of the part is the sectioning,
\r
31141 \begin_inset Newline newline
\r
31148 numberwithin{table}{part}
\r
31153 \begin_layout Standard
\r
31154 To go back to the standard numbering or to prevent this kind of numbering
\r
31155 when it is defined by the document class, the following command is inserted
\r
31156 as TeX code or to the LaTeX-preamble:
\r
31159 \begin_layout Standard
\r
31168 arabic{equation}}
\r
31169 \begin_inset Index idx
\r
31172 \begin_layout Plain Layout
\r
31186 \begin_layout Plain Layout
\r
31194 arabic{equation}}
\r
31202 \begin_inset Newline newline
\r
31210 \begin_inset Newline newline
\r
31222 \begin_layout Standard
\r
31229 uses internally the command
\r
31235 , described above, that also needs to be reverted.
\r
31239 \begin_layout Plain Layout
\r
31246 \begin_layout Plain Layout
\r
31250 @removefromreset{equation}{section}
\r
31253 \begin_layout Plain Layout
\r
31265 \begin_layout Subsection
\r
31266 Numbering with Roman Numbers and Letters
\r
31267 \begin_inset Index idx
\r
31270 \begin_layout Plain Layout
\r
31271 Formula numbering ! with letters
\r
31277 \begin_inset Index idx
\r
31280 \begin_layout Plain Layout
\r
31281 Formula numbering ! with Roman numbers
\r
31289 \begin_layout Standard
\r
31290 Formulas can also be numbered with Roman numbers and Latin letters.
\r
31291 To number for example with small Roman numbers, the command
\r
31294 \begin_layout Standard
\r
31306 \begin_layout Standard
\r
31307 is inserted before the formula in TeX-mode.
\r
31315 \begin_inset Index idx
\r
31318 \begin_layout Plain Layout
\r
31326 redefines the predefined command
\r
31339 \begin_inset Foot
\r
31342 \begin_layout Plain Layout
\r
31349 has the same scheme like the command
\r
31355 that is described in
\r
31356 \begin_inset CommandInset ref
\r
31358 reference "sub:The-Command-newcommand"
\r
31371 is the formula counter.
\r
31372 When the command
\r
31378 is used as prefix for a counter, the value of the counter is output as
\r
31380 When a formula is numbered, LaTeX sets internally the command
\r
31386 behind the formula.
\r
31392 \begin_inset Index idx
\r
31395 \begin_layout Plain Layout
\r
31405 outputs the counter as small Roman number.
\r
31408 \begin_layout Standard
\r
31409 All formulas behind the command
\r
31419 are now numbered Roman.
\r
31420 To switch to numbering with big Roman numbers, the command is inserted
\r
31434 \begin_inset Index idx
\r
31437 \begin_layout Plain Layout
\r
31449 \begin_inset Quotes eld
\r
31453 \begin_inset Quotes erd
\r
31456 with small Latin letters there is the command
\r
31463 \begin_inset Index idx
\r
31466 \begin_layout Plain Layout
\r
31474 , for big ones there is the command
\r
31481 \begin_inset Index idx
\r
31484 \begin_layout Plain Layout
\r
31497 \begin_layout Standard
\r
31498 \begin_inset Note Greyedout
\r
31501 \begin_layout Plain Layout
\r
31508 \begin_inset space ~
\r
31511 formulas can be numbered with Latin letters in one document.
\r
31519 \begin_layout Standard
\r
31523 \begin_layout Plain Layout
\r
31539 \begin_layout Standard
\r
31540 \begin_inset Formula
\r
31542 A=\textrm{small roman}
\r
31551 \begin_layout Plain Layout
\r
31565 \begin_inset Formula
\r
31567 B=\textrm{big Roman}\label{eq:Rom}
\r
31576 \begin_layout Plain Layout
\r
31590 \begin_inset Formula
\r
31592 C=\textrm{small Latin}
\r
31601 \begin_layout Plain Layout
\r
31615 \begin_inset Formula
\r
31617 D=\textrm{big Latin}\label{eq:Lat}
\r
31625 \begin_layout Standard
\r
31626 To switch back to the default numbering, insert the command:
\r
31629 \begin_layout Standard
\r
31638 arabic{equation}}
\r
31639 \begin_inset Index idx
\r
31642 \begin_layout Plain Layout
\r
31653 \begin_layout Standard
\r
31657 \begin_layout Plain Layout
\r
31665 arabic{equation}}
\r
31671 \begin_inset Formula
\r
31673 E=\textrm{Arabic}
\r
31681 \begin_layout Standard
\r
31682 \begin_inset VSpace medskip
\r
31685 As you see, formulas are numbered serially independent from the numbering
\r
31687 When then numbering should start with
\r
31688 \begin_inset Quotes eld
\r
31692 \begin_inset Quotes erd
\r
31695 when the style is changed, new equation counters have to be defined.
\r
31696 A description about this can be found in the file
\r
31697 \begin_inset CommandInset href
\r
31698 LatexCommand href
\r
31699 name "Formula-numbering.lyx"
\r
31700 target "run:Formula-numbering.lyx"
\r
31707 \begin_layout Standard
\r
31708 \begin_inset Newpage newpage
\r
31714 \begin_layout Section
\r
31715 Chemical Symbols and Equations
\r
31716 \begin_inset CommandInset label
\r
31717 LatexCommand label
\r
31718 name "sub:Chemical-Symbols-and"
\r
31723 \begin_inset Index idx
\r
31726 \begin_layout Plain Layout
\r
31727 Chemical characters ! Symbols
\r
31733 \begin_inset Index idx
\r
31736 \begin_layout Plain Layout
\r
31737 Chemical equations
\r
31743 \begin_inset Index idx
\r
31746 \begin_layout Plain Layout
\r
31747 Symbols ! chemical
\r
31755 \begin_layout Standard
\r
31756 An example text from chemistry:
\r
31759 \begin_layout Quote
\r
31761 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
\r
31764 -ion reacts with two
\r
31765 \begin_inset Formula $\mathrm{Na^{+}}$
\r
31768 -ions to sodium sulfate
\r
31769 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
\r
31773 The chemical equation for this is:
\r
31774 \begin_inset Formula
\r
31776 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
\r
31784 \begin_layout Standard
\r
31785 This chemical equation can directly be created as formula.
\r
31786 To avoid that the symbols appear italic, everything is highlighted and
\r
31787 changed by the shortcut
\r
31788 \begin_inset Info
\r
31793 to the upright font style.
\r
31794 \begin_inset Foot
\r
31797 \begin_layout Plain Layout
\r
31803 \begin_inset CommandInset ref
\r
31805 reference "sub:Font-Styles"
\r
31817 \begin_layout Standard
\r
31818 A more convenient way to typeset chemical formulas is to use the command
\r
31826 \begin_inset Index idx
\r
31829 \begin_layout Plain Layout
\r
31837 that is available when the LaTeX-package
\r
31842 \begin_inset Index idx
\r
31845 \begin_layout Plain Layout
\r
31846 Packages ! mhchem
\r
31858 to a formula a new blue box appears where chemical formulas can be inserted
\r
31859 in an intuitive way.
\r
31862 \begin_layout Standard
\r
31864 \begin_inset Tabular
\r
31865 <lyxtabular version="3" rows="9" columns="2">
\r
31866 <features rotate="0" tabularvalignment="middle">
\r
31867 <column alignment="center" valignment="top">
\r
31868 <column alignment="center" valignment="top">
\r
31870 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
31871 \begin_inset Text
\r
31873 \begin_layout Plain Layout
\r
31879 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
31880 \begin_inset Text
\r
31882 \begin_layout Plain Layout
\r
31884 \begin_inset Note Note
\r
31887 \begin_layout Plain Layout
\r
31894 is only used as spacer.
\r
31906 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
31907 \begin_inset Text
\r
31909 \begin_layout Plain Layout
\r
31916 \begin_layout Plain Layout
\r
31930 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
31931 \begin_inset Text
\r
31933 \begin_layout Plain Layout
\r
31934 \begin_inset Formula $\raisebox{4.5mm}{}\ce{H2CO3}\raisebox{-2mm}{}$
\r
31944 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
31945 \begin_inset Text
\r
31947 \begin_layout Plain Layout
\r
31954 \begin_layout Plain Layout
\r
31968 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
31969 \begin_inset Text
\r
31971 \begin_layout Plain Layout
\r
31972 \begin_inset Formula $\raisebox{5mm}{}\ce{SO4^{2-}}\raisebox{-2mm}{}$
\r
31982 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
31983 \begin_inset Text
\r
31985 \begin_layout Plain Layout
\r
31992 \begin_layout Plain Layout
\r
32006 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
32007 \begin_inset Text
\r
32009 \begin_layout Plain Layout
\r
32010 \begin_inset Formula $\raisebox{4.5mm}{}\ce{(NH4)2S}\raisebox{-2mm}{}$
\r
32020 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
32021 \begin_inset Text
\r
32023 \begin_layout Plain Layout
\r
32030 \begin_layout Plain Layout
\r
32044 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
32045 \begin_inset Text
\r
32047 \begin_layout Plain Layout
\r
32048 \begin_inset Formula $\raisebox{4.5mm}{}\ce{KCr(SO4)2.12H2O}\raisebox{-2mm}{}$
\r
32058 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
32059 \begin_inset Text
\r
32061 \begin_layout Plain Layout
\r
32068 \begin_layout Plain Layout
\r
32083 \begin_layout Plain Layout
\r
32098 \begin_layout Plain Layout
\r
32112 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
32113 \begin_inset Text
\r
32115 \begin_layout Plain Layout
\r
32116 \begin_inset Formula $\raisebox{4.5mm}{}\ce{A-B\dbond C\tbond D}\raisebox{-2mm}{}$
\r
32126 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
32127 \begin_inset Text
\r
32129 \begin_layout Plain Layout
\r
32136 \begin_layout Plain Layout
\r
32146 \begin_inset Formula $\downarrow$
\r
32150 \begin_inset Formula $\to$
\r
32158 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
32159 \begin_inset Text
\r
32161 \begin_layout Plain Layout
\r
32162 \begin_inset Formula $\raisebox{5mm}{}\ce{_{90}^{227}Th+}\raisebox{-2mm}{}$
\r
32172 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
32173 \begin_inset Text
\r
32175 \begin_layout Plain Layout
\r
32182 \begin_layout Plain Layout
\r
32195 \begin_layout Plain Layout
\r
32208 \begin_layout Plain Layout
\r
32221 \begin_layout Plain Layout
\r
32234 \begin_layout Plain Layout
\r
32248 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
32249 \begin_inset Text
\r
32251 \begin_layout Plain Layout
\r
32252 \begin_inset Formula $\raisebox{4.5mm}{}\ce{CO2 + C <=> 2CO}\raisebox{-2mm}{}$
\r
32262 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
32263 \begin_inset Text
\r
32265 \begin_layout Plain Layout
\r
32272 \begin_layout Plain Layout
\r
32285 \begin_layout Plain Layout
\r
32298 \begin_layout Plain Layout
\r
32311 \begin_layout Plain Layout
\r
32328 \begin_layout Plain Layout
\r
32342 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
32343 \begin_inset Text
\r
32345 \begin_layout Plain Layout
\r
32346 \begin_inset Formula $\raisebox{5mm}{}\ce{CO2 + C ->[\alpha][\beta] 2CO}\raisebox{-4mm}{}$
\r
32362 \begin_layout Standard
\r
32363 \begin_inset Note Greyedout
\r
32366 \begin_layout Plain Layout
\r
32372 Inserting a formula to a
\r
32378 box will lead to LaTeX errors due to a LyX bug.
\r
32381 \begin_inset Foot
\r
32384 \begin_layout Plain Layout
\r
32385 \begin_inset CommandInset href
\r
32386 LatexCommand href
\r
32387 name "LyX-bug #8566"
\r
32388 target "http://www.lyx.org/trac/ticket/8566"
\r
32399 In this case TeX code has to be used like for
\r
32413 \begin_layout Plain Layout
\r
32434 \begin_layout Standard
\r
32435 \begin_inset Note Greyedout
\r
32438 \begin_layout Plain Layout
\r
32444 It is not possible in LyX to use the character ^ to get an up-arrow as
\r
32445 described in the
\r
32450 One instead uses a negative thin space followed by the command
\r
32457 \begin_inset Formula $\ce{Fe + 2H+ -> Fe^{2+} + H2\negthinspace\uparrow}$
\r
32468 \begin_layout Standard
\r
32475 the command for equation
\r
32476 \begin_inset space ~
\r
32480 \begin_inset CommandInset ref
\r
32481 LatexCommand eqref
\r
32482 reference "eq:chem-reaction"
\r
32487 \begin_inset Newline newline
\r
32498 \begin_layout Plain Layout
\r
32511 \begin_layout Plain Layout
\r
32524 \begin_layout Plain Layout
\r
32537 \begin_layout Plain Layout
\r
32550 \begin_layout Plain Layout
\r
32563 \begin_layout Plain Layout
\r
32575 \begin_layout Standard
\r
32576 To create multiline chemical equations first a multiline formula is created
\r
32578 \begin_inset CommandInset ref
\r
32580 reference "sec:Multiline-Formulas"
\r
32585 Afterwards the command
\r
32591 is used in every small blue box of the formula.
\r
32593 \begin_inset CommandInset ref
\r
32594 LatexCommand eqref
\r
32595 reference "eq:TEOS-reaction-1"
\r
32600 \begin_inset CommandInset ref
\r
32601 LatexCommand eqref
\r
32602 reference "eq:TEOS-reaction-2"
\r
32606 are an example of a multi-stage chemical reaction where every equation
\r
32607 has its own number.
\r
32608 \begin_inset Formula
\r
32610 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
\r
32611 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
\r
32619 \begin_layout Standard
\r
32630 package provides the command
\r
32637 \begin_inset Index idx
\r
32640 \begin_layout Plain Layout
\r
32648 that has to be used for special cases.
\r
32649 For more information about
\r
32655 and more examples have a look at the documentation of
\r
32660 \begin_inset CommandInset citation
\r
32661 LatexCommand cite
\r
32669 \begin_layout Section
\r
32673 \begin_layout Standard
\r
32674 LyX supports two types of commutative diagrams:
\r
32682 that are explained in the following.
\r
32685 \begin_layout Subsection
\r
32687 \begin_inset Index idx
\r
32690 \begin_layout Plain Layout
\r
32699 \begin_layout Standard
\r
32700 Diagrams of this type visualize relations by vertical and horizontal lines
\r
32702 \begin_inset Formula
\r
32704 \begin{CD}A@>>>B@>>>C\\
\r
32715 \begin_layout Standard
\r
32716 To get them, the command
\r
32721 \begin_inset Index idx
\r
32724 \begin_layout Plain Layout
\r
32734 is inserted to a formula.
\r
32735 A blue box appears with two dashed lines where further commands can be
\r
32738 \begin_inset Info
\r
32740 arg "newline-insert newline"
\r
32743 a new line is created.
\r
32744 Horizontal relations are inserted in odd, vertical in even formula lines.
\r
32747 \begin_layout Standard
\r
32748 To create the relations there are the following commands:
\r
32751 \begin_layout Itemize
\r
32756 creates a left arrow,
\r
32760 a right arrow and
\r
32764 a long equal sign
\r
32767 \begin_layout Itemize
\r
32772 creates an up arrow,
\r
32776 a down arrow and
\r
32780 a vertical equal sign
\r
32783 \begin_layout Itemize
\r
32789 is a placeholder for non-existent relations
\r
32792 \begin_layout Standard
\r
32793 All arrows can be labeled as follows:
\r
32796 \begin_layout Itemize
\r
32797 If text inserted between the first and second < or >, resp., it is placed
\r
32799 When it is inserted between the second and third one, it appears under
\r
32803 \begin_layout Itemize
\r
32804 When text for vertical arrows is inserted between the first and second A
\r
32805 or V, resp., it is placed left beside the arrow.
\r
32806 When it is inserted between the second and third one, it appears right
\r
32807 beside the arrow.
\r
32808 If the text contains an A or V, these letters must be set into a TeX-brace.
\r
32811 \begin_layout Standard
\r
32812 As example a diagram with all possible relations:
\r
32815 \begin_layout Standard
\r
32816 \begin_inset Formula
\r
32818 \begin{CD}A@>j>>B@>>k>C@=F\\
\r
32819 @AmAA@.@VV{V}V@|\\
\r
32829 \begin_layout Standard
\r
32830 The command for this is:
\r
32831 \begin_inset Newline newline
\r
32842 \begin_layout Plain Layout
\r
32851 A@>j>>B@>>k>C@=F Ctrl+Return
\r
32852 \begin_inset Newline newline
\r
32856 \begin_inset Phantom HPhantom
\r
32859 \begin_layout Plain Layout
\r
32868 \begin_layout Plain Layout
\r
32887 \begin_inset Formula $\to$
\r
32893 \begin_inset Newline newline
\r
32897 \begin_inset Phantom HPhantom
\r
32900 \begin_layout Plain Layout
\r
32909 \begin_layout Plain Layout
\r
32926 \begin_layout Subsection
\r
32927 Xymatrix Diagrams
\r
32928 \begin_inset Index idx
\r
32931 \begin_layout Plain Layout
\r
32932 Diagrams ! xymatrix
\r
32940 \begin_layout Standard
\r
32941 To be able to use xymatrices, the LaTeX-package
\r
32945 must be installed.
\r
32946 A xymatrix is created by inserting the command
\r
32953 Then you are able to add new matrix columns and rows like for normal matrices,
\r
32955 \begin_inset CommandInset ref
\r
32957 reference "sec:Matrices"
\r
32964 \begin_layout Standard
\r
32965 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
\r
32967 All possibilities to create commutative diagrams and decorations are explained
\r
32968 in detail in the
\r
32972 that you find in the menu
\r
32974 Help\SpecialChar \menuseparator
\r
32976 \begin_inset space ~
\r
32984 \begin_layout Subsection
\r
32990 \begin_inset Index idx
\r
32993 \begin_layout Plain Layout
\r
32994 Diagrams ! Feynman
\r
33002 \begin_layout Standard
\r
33003 To be able to use
\r
33007 -diagrams, the LaTeX-package
\r
33011 must be installed.
\r
33016 -diagram is created by inserting the command
\r
33023 Then you are able to add new matrix columns and rows like for normal matrices,
\r
33025 \begin_inset CommandInset ref
\r
33027 reference "sec:Matrices"
\r
33034 \begin_layout Standard
\r
33035 Examples how to create
\r
33039 diagrams in LyX is given in the
\r
33041 Feynman-diagram manual
\r
33043 that you find in the menu
\r
33045 Help\SpecialChar \menuseparator
\r
33047 \begin_inset space ~
\r
33055 \begin_layout Standard
\r
33056 \begin_inset Newpage newpage
\r
33062 \begin_layout Section
\r
33063 User-defined Commands
\r
33064 \begin_inset Index idx
\r
33067 \begin_layout Plain Layout
\r
33068 User-defined commands
\r
33076 \begin_layout Standard
\r
33077 \begin_inset Note Greyedout
\r
33080 \begin_layout Plain Layout
\r
33085 The names of user-defined commands and macros may only consist of Latin
\r
33094 \begin_layout Subsection
\r
33098 \begin_inset CommandInset label
\r
33099 LatexCommand label
\r
33100 name "sub:The-Command-newcommand"
\r
33105 \begin_inset Index idx
\r
33108 \begin_layout Plain Layout
\r
33109 User-defined commands !
\r
33117 \begin_inset Index idx
\r
33120 \begin_layout Plain Layout
\r
33131 \begin_layout Standard
\r
33132 Many LaTeX-commands are too long to be used frequently.
\r
33133 But it is possible to define with the command
\r
33139 new shorter commands.
\r
33142 \begin_layout Standard
\r
33143 The command scheme of
\r
33152 \begin_layout Standard
\r
33157 newcommand{new command name}[number of arguments][optional
\r
33162 \begin_inset Newline newline
\r
33166 \begin_inset Phantom HPhantom
\r
33169 \begin_layout Plain Layout
\r
33179 {command definition}
\r
33182 \begin_layout Standard
\r
33183 \begin_inset Note Greyedout
\r
33186 \begin_layout Plain Layout
\r
33191 Assure that the name of the new command is not already used in your document
\r
33192 or by LaTeX-packages that you use.
\r
33193 When you for example define the command
\r
33205 , you get an error message because
\r
33211 is already defined as command for
\r
33212 \begin_inset Quotes eld
\r
33216 \begin_inset Formula $\le$
\r
33220 \begin_inset Quotes erd
\r
33231 \begin_layout Standard
\r
33232 The number of arguments is an integer in the range 0
\r
33233 \begin_inset space \thinspace{}
\r
33237 \begin_inset space \thinspace{}
\r
33240 9 and specifies how many arguments the new command should have.
\r
33241 With the optional value a value for an optional argument can be predefined.
\r
33242 When this is done, the
\r
33250 rgument of the new command is automatically an optional one.
\r
33253 \begin_layout Standard
\r
33254 Here are some examples:
\r
33257 \begin_layout Itemize
\r
33258 To define the command
\r
33270 , the LaTeX-preamble line is:
\r
33271 \begin_inset VSpace medskip
\r
33275 \begin_inset Newline newline
\r
33289 \begin_layout Itemize
\r
33290 To define the command
\r
33302 , the argument (that should be underlined) must be taken into account.
\r
33303 For this the preamble line is:
\r
33304 \begin_inset VSpace medskip
\r
33308 \begin_inset Newline newline
\r
33322 \begin_inset VSpace medskip
\r
33326 \begin_inset Newline newline
\r
33333 acts as argument placeholder, the
\r
33337 behind it denotes that it is the placeholder for the first argument.
\r
33340 \begin_layout Itemize
\r
33348 \begin_inset space \thinspace{}
\r
33352 \begin_inset space \space{}
\r
33355 define the command
\r
33362 \begin_inset VSpace medskip
\r
33366 \begin_inset Newline newline
\r
33377 framebox#1#2{$#3$}}
\r
33380 \begin_inset VSpace medskip
\r
33384 \begin_inset Newline newline
\r
33387 The two Dollar signs creates the extra formula needed for
\r
33394 \begin_inset CommandInset ref
\r
33396 reference "sub:Boxes-with-Frame"
\r
33403 \begin_layout Itemize
\r
33404 To create a new command for
\r
33410 where the color for the box need not be specified, the argument for the
\r
33411 color is defined optional:
\r
33412 \begin_inset VSpace medskip
\r
33416 \begin_inset Newline newline
\r
33427 fcolorbox{#2}{#1}{$#3$}}
\r
33430 \begin_inset VSpace medskip
\r
33434 \begin_inset Newline newline
\r
33437 When the color is not specified when using
\r
33443 , the predefined color
\r
33450 \begin_layout Standard
\r
33451 A test of the new defined commands:
\r
33454 \begin_layout Standard
\r
33456 \begin_inset Tabular
\r
33457 <lyxtabular version="3" rows="6" columns="2">
\r
33458 <features rotate="0" tabularvalignment="middle">
\r
33459 <column alignment="center" valignment="top">
\r
33460 <column alignment="center" valignment="top">
\r
33462 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
33463 \begin_inset Text
\r
33465 \begin_layout Plain Layout
\r
33471 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
33472 \begin_inset Text
\r
33474 \begin_layout Plain Layout
\r
33476 \begin_inset Note Note
\r
33479 \begin_layout Plain Layout
\r
33486 is only used as spacer.
\r
33498 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
33499 \begin_inset Text
\r
33501 \begin_layout Plain Layout
\r
33508 \begin_layout Plain Layout
\r
33522 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
33523 \begin_inset Text
\r
33525 \begin_layout Plain Layout
\r
33526 \begin_inset Formula $A\gr B$
\r
33536 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
33537 \begin_inset Text
\r
33539 \begin_layout Plain Layout
\r
33547 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
33548 \begin_inset Text
\r
33550 \begin_layout Plain Layout
\r
33551 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
\r
33561 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
33562 \begin_inset Text
\r
33564 \begin_layout Plain Layout
\r
33568 \begin_inset Formula $\to$
\r
33574 \begin_inset Formula $\to$
\r
33585 \begin_layout Plain Layout
\r
33599 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
33600 \begin_inset Text
\r
33602 \begin_layout Plain Layout
\r
33603 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
\r
33613 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
33614 \begin_inset Text
\r
33616 \begin_layout Plain Layout
\r
33620 \begin_inset Formula $\to$
\r
33631 \begin_layout Plain Layout
\r
33645 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
33646 \begin_inset Text
\r
33648 \begin_layout Plain Layout
\r
33649 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
\r
33659 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
33660 \begin_inset Text
\r
33662 \begin_layout Plain Layout
\r
33668 \begin_inset Formula $\to$
\r
33679 \begin_layout Plain Layout
\r
33693 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
33694 \begin_inset Text
\r
33696 \begin_layout Plain Layout
\r
33697 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
\r
33713 \begin_layout Subsection
\r
33715 \begin_inset Index idx
\r
33718 \begin_layout Plain Layout
\r
33719 User-defined commands! Math macros
\r
33725 \begin_inset Index idx
\r
33728 \begin_layout Plain Layout
\r
33737 \begin_layout Standard
\r
33738 User-defined commands are especially convenient for complex expressions.
\r
33739 When you are for example dealing with a document that has quadratic equations,
\r
33740 the same solution type occurs several times.
\r
33741 The general form of a quadratic equation is
\r
33742 \begin_inset Formula
\r
33744 0=\lambda^{2}+p\lambda+q
\r
33749 The general form of the solution is
\r
33750 \begin_inset Formula
\r
33752 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
\r
33760 \begin_layout Standard
\r
33761 To define a command for the solution formula where only the three parameters
\r
33763 \begin_inset Formula $\lambda$
\r
33767 \begin_inset Formula $p$
\r
33771 \begin_inset Formula $q$
\r
33774 need to be specified and the index of
\r
33775 \begin_inset Formula $\lambda$
\r
33778 can be given optionally, the LaTeX-preamble line is
\r
33779 \begin_inset Newline newline
\r
33795 \begin_inset Newline newline
\r
33799 \begin_inset Phantom HPhantom
\r
33802 \begin_layout Plain Layout
\r
33816 frac{#3^{2}}{4}-#4}}
\r
33819 \begin_layout Standard
\r
33820 To create with this the solution formula, the command
\r
33821 \begin_inset Newline newline
\r
33831 \begin_inset Formula $\to$
\r
33837 \begin_inset Formula $\to$
\r
33844 is inserted to a formula
\r
33849 \begin_layout Standard
\r
33850 The definition of the new command is unintuitive because one has to know
\r
33851 the schemes of all used LaTeX commands, e.
\r
33852 \begin_inset space \thinspace{}
\r
33856 \begin_inset space \space{}
\r
33859 that a fraction is inserted in LaTeX as
\r
33863 frac{numerator}{denominator}
\r
33866 Furthermore one can easily forget a brace in the definition and cannot
\r
33867 see in LyX what the new command is doing.
\r
33868 To avoid these problems LyX offers the possibility to use math macros instead
\r
33878 \begin_layout Standard
\r
33879 A math macro is created by using the menu
\r
33881 Insert\SpecialChar \menuseparator
\r
33882 Math\SpecialChar \menuseparator
\r
33885 or the toolbar button
\r
33886 \begin_inset Graphics
\r
33887 filename ../images/math-macro_newmacroname_newcommand.png
\r
33893 The math macro toolbar appears together with the following box where the
\r
33894 macro is defined:
\r
33895 \begin_inset Newline newline
\r
33899 \begin_inset space \hspace*{\fill}
\r
33903 \begin_inset Graphics
\r
33904 filename clipart/macrobox.png
\r
33909 \begin_inset space \hspace*{\fill}
\r
33913 \begin_inset Newline newline
\r
33917 \begin_inset FormulaMacro
\r
33918 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
\r
33923 newmacroname is the default name of the macro that should be changed to
\r
33924 something sensible.
\r
33925 The wanted formula is inserted in the first blue box.
\r
33926 An argument placeholder is inserted with the command
\r
33933 \begin_inset space \thinspace{}
\r
33937 \begin_inset space \space{}
\r
33946 or by using the macro toolbar button
\r
33947 \begin_inset Graphics
\r
33948 filename ../images/math-macro-add-param.png
\r
33954 Argument placeholders are displayed red.
\r
33956 \begin_inset space ~
\r
33959 arguments are possible.
\r
33960 Optional arguments are created with the toolbar button
\r
33961 \begin_inset Graphics
\r
33962 filename ../images/math-macro-add-optional-param.png
\r
33968 The first non-optional argument can be transformed to an optional one with
\r
33969 the toolbar button
\r
33970 \begin_inset Graphics
\r
33971 filename ../images/math-macro-make-optional.png
\r
33977 In the second blue box the appearance of the macro in LyX can be defined.
\r
33978 Normally you want to see it as it is defined, so the box is kept empty.
\r
33979 But when you have created a macro that needs lot of space on the screen,
\r
33980 you can insert in the box for example
\r
33981 \begin_inset Newline newline
\r
34011 \begin_inset Newline newline
\r
34016 For the macro only the arguments with the macro name in front of them will
\r
34017 then be displayed in LyX, leading to a better overview.
\r
34018 The formula appears in the output as defined in the first box.
\r
34019 \begin_inset Newline newline
\r
34022 The appearance of macros in formulas can furthermore be changed for single
\r
34023 macros by setting the cursor in the macro and using the menu
\r
34025 View\SpecialChar \menuseparator
\r
34027 \begin_inset space ~
\r
34031 \begin_inset space ~
\r
34039 \begin_layout Standard
\r
34040 To use a macro, the macro name is inserted as command to a formula, in our
\r
34048 Our macro looks in LyX like this:
\r
34049 \begin_inset Newline newline
\r
34053 \begin_inset space \hspace*{\fill}
\r
34057 \begin_inset Graphics
\r
34058 filename clipart/macrouse.png
\r
34063 \begin_inset space \hspace*{\fill}
\r
34067 \begin_inset Newline newline
\r
34070 Here is our macro example with the arguments
\r
34071 \begin_inset Formula $x$
\r
34075 \begin_inset Formula $\ln(x)$
\r
34079 \begin_inset Formula $B$
\r
34085 \begin_layout Standard
\r
34086 \begin_inset Formula
\r
34096 \begin_layout Standard
\r
34097 LyX offers in the menu
\r
34099 Tools\SpecialChar \menuseparator
\r
34100 Preferences\SpecialChar \menuseparator
\r
34101 Editing\SpecialChar \menuseparator
\r
34104 different styles to edit macros.
\r
34105 To find the style that suits you the most, choose a style and set the cursor
\r
34106 in a macro formula to see the difference.
\r
34109 \begin_layout Standard
\r
34110 A math macro is transformed internally to a
\r
34116 command when exporting the document.
\r
34123 command is not placed in the LaTeX-preamble, therefore macros can only
\r
34124 be used in formulas that are in the document below the macro definition
\r
34128 \begin_layout Standard
\r
34129 Math macros can also be directly created from a
\r
34136 When writing for example the command
\r
34139 \begin_inset Newline newline
\r
34148 xleftarrow[#2]{#1}}
\r
34149 \begin_inset Newline newline
\r
34154 in LyX as normal text, highlighting it completely and using then the shortcut
\r
34159 , the command will be transformed to a math macro.
\r
34160 Using this method you need to be careful that the
\r
34166 command is typed correctly, otherwise you get a faulty macro leading to
\r
34170 \begin_layout Standard
\r
34171 Math macros currently have the problem that further formulas in macro definition
\r
34172 s are handled wrongly.
\r
34173 Therefore the example
\r
34180 \begin_inset CommandInset ref
\r
34182 reference "sub:The-Command-newcommand"
\r
34186 cannot be created as macro.
\r
34189 \begin_layout Standard
\r
34190 When the cursor is in a macro definition box, you will see the macro toolbar
\r
34194 \begin_layout Standard
\r
34195 \begin_inset VSpace defskip
\r
34201 \begin_layout Standard
\r
34202 \begin_inset Graphics
\r
34203 filename clipart/MacroToolbar.png
\r
34208 \begin_inset Index idx
\r
34211 \begin_layout Plain Layout
\r
34220 \begin_layout Standard
\r
34221 \begin_inset VSpace defskip
\r
34227 \begin_layout Standard
\r
34228 The macro toolbar contains from left to right the following buttons:
\r
34231 \begin_layout Standard
\r
34232 \begin_inset VSpace defskip
\r
34238 \begin_layout Standard
\r
34239 \begin_inset Tabular
\r
34240 <lyxtabular version="3" rows="9" columns="2">
\r
34241 <features rotate="0" islongtable="true" longtabularalignment="center">
\r
34242 <column alignment="left" valignment="top">
\r
34243 <column alignment="left" valignment="top" width="85col%">
\r
34244 <row interlinespace="2.5mm">
\r
34245 <cell alignment="center" valignment="top" usebox="none">
\r
34246 \begin_inset Text
\r
34248 \begin_layout Plain Layout
\r
34249 \begin_inset Graphics
\r
34250 filename ../images/math-macro-remove-param.png
\r
34251 rotateOrigin center
\r
34260 <cell alignment="center" valignment="top" usebox="none">
\r
34261 \begin_inset Text
\r
34263 \begin_layout Plain Layout
\r
34266 Edit\SpecialChar \menuseparator
\r
34267 Math\SpecialChar \menuseparator
\r
34269 \begin_inset space ~
\r
34272 Definition\SpecialChar \menuseparator
\r
34273 Remove Last Argument
\r
34279 <row interlinespace="2.5mm">
\r
34280 <cell alignment="center" valignment="top" usebox="none">
\r
34281 \begin_inset Text
\r
34283 \begin_layout Plain Layout
\r
34284 \begin_inset Graphics
\r
34285 filename ../images/math-macro-add-param.png
\r
34286 rotateOrigin center
\r
34295 <cell alignment="center" valignment="top" usebox="none">
\r
34296 \begin_inset Text
\r
34298 \begin_layout Plain Layout
\r
34301 Edit\SpecialChar \menuseparator
\r
34302 Math\SpecialChar \menuseparator
\r
34304 \begin_inset space ~
\r
34307 Definition\SpecialChar \menuseparator
\r
34314 <row interlinespace="2.5mm">
\r
34315 <cell alignment="center" valignment="top" usebox="none">
\r
34316 \begin_inset Text
\r
34318 \begin_layout Plain Layout
\r
34319 \begin_inset Graphics
\r
34320 filename ../images/math-macro-make-optional.png
\r
34321 rotateOrigin center
\r
34330 <cell alignment="center" valignment="top" usebox="none">
\r
34331 \begin_inset Text
\r
34333 \begin_layout Plain Layout
\r
34336 Edit\SpecialChar \menuseparator
\r
34337 Math\SpecialChar \menuseparator
\r
34339 \begin_inset space ~
\r
34342 Definition\SpecialChar \menuseparator
\r
34343 Make First Non-Optional into
\r
34344 \begin_inset Newline newline
\r
34348 \begin_inset Phantom HPhantom
\r
34351 \begin_layout Plain Layout
\r
34354 Edit\SpecialChar \menuseparator
\r
34355 Math\SpecialChar \menuseparator
\r
34357 \begin_inset space ~
\r
34360 Definition\SpecialChar \menuseparator
\r
34366 Optional Argument
\r
34372 <row interlinespace="2.5mm">
\r
34373 <cell alignment="center" valignment="top" usebox="none">
\r
34374 \begin_inset Text
\r
34376 \begin_layout Plain Layout
\r
34377 \begin_inset Graphics
\r
34378 filename ../images/math-macro-make-nonoptional.png
\r
34379 rotateOrigin center
\r
34388 <cell alignment="center" valignment="top" usebox="none">
\r
34389 \begin_inset Text
\r
34391 \begin_layout Plain Layout
\r
34394 Edit\SpecialChar \menuseparator
\r
34395 Math\SpecialChar \menuseparator
\r
34397 \begin_inset space ~
\r
34400 Definition\SpecialChar \menuseparator
\r
34401 Make Last Optional into
\r
34402 \begin_inset Newline newline
\r
34406 \begin_inset Phantom HPhantom
\r
34409 \begin_layout Plain Layout
\r
34412 Edit\SpecialChar \menuseparator
\r
34413 Math\SpecialChar \menuseparator
\r
34415 \begin_inset space ~
\r
34418 Definition\SpecialChar \menuseparator
\r
34424 Non-Optional Argument
\r
34430 <row interlinespace="2.5mm">
\r
34431 <cell alignment="center" valignment="top" usebox="none">
\r
34432 \begin_inset Text
\r
34434 \begin_layout Plain Layout
\r
34435 \begin_inset Graphics
\r
34436 filename ../images/math-macro-remove-optional-param.png
\r
34437 rotateOrigin center
\r
34446 <cell alignment="center" valignment="top" usebox="none">
\r
34447 \begin_inset Text
\r
34449 \begin_layout Plain Layout
\r
34452 Edit\SpecialChar \menuseparator
\r
34453 Math\SpecialChar \menuseparator
\r
34455 \begin_inset space ~
\r
34458 Definition\SpecialChar \menuseparator
\r
34459 Remove Optional Argument
\r
34465 <row interlinespace="2.5mm">
\r
34466 <cell alignment="center" valignment="top" usebox="none">
\r
34467 \begin_inset Text
\r
34469 \begin_layout Plain Layout
\r
34470 \begin_inset Graphics
\r
34471 filename ../images/math-macro-add-optional-param.png
\r
34472 rotateOrigin center
\r
34481 <cell alignment="center" valignment="top" usebox="none">
\r
34482 \begin_inset Text
\r
34484 \begin_layout Plain Layout
\r
34487 Edit\SpecialChar \menuseparator
\r
34488 Math\SpecialChar \menuseparator
\r
34490 \begin_inset space ~
\r
34493 Definition\SpecialChar \menuseparator
\r
34494 Insert Optional Argument
\r
34500 <row interlinespace="2.5mm">
\r
34501 <cell alignment="center" valignment="top" usebox="none">
\r
34502 \begin_inset Text
\r
34504 \begin_layout Plain Layout
\r
34505 \begin_inset Graphics
\r
34506 filename ../images/math-macro-remove-greedy-param.png
\r
34507 rotateOrigin center
\r
34516 <cell alignment="center" valignment="top" usebox="none">
\r
34517 \begin_inset Text
\r
34519 \begin_layout Plain Layout
\r
34522 Edit\SpecialChar \menuseparator
\r
34523 Math\SpecialChar \menuseparator
\r
34525 \begin_inset space ~
\r
34528 Definition\SpecialChar \menuseparator
\r
34529 Remove Last Argument
\r
34530 \begin_inset Newline newline
\r
34534 \begin_inset Phantom HPhantom
\r
34537 \begin_layout Plain Layout
\r
34540 Edit\SpecialChar \menuseparator
\r
34541 Math\SpecialChar \menuseparator
\r
34543 \begin_inset space ~
\r
34546 Definition\SpecialChar \menuseparator
\r
34552 Spitting Out To The Right
\r
34558 <row interlinespace="2.5mm">
\r
34559 <cell alignment="center" valignment="top" usebox="none">
\r
34560 \begin_inset Text
\r
34562 \begin_layout Plain Layout
\r
34563 \begin_inset Graphics
\r
34564 filename ../images/math-macro-append-greedy-param.png
\r
34565 rotateOrigin center
\r
34574 <cell alignment="center" valignment="top" usebox="none">
\r
34575 \begin_inset Text
\r
34577 \begin_layout Plain Layout
\r
34580 Edit\SpecialChar \menuseparator
\r
34581 Math\SpecialChar \menuseparator
\r
34583 \begin_inset space ~
\r
34586 Definition\SpecialChar \menuseparator
\r
34588 \begin_inset Newline newline
\r
34592 \begin_inset Phantom HPhantom
\r
34595 \begin_layout Plain Layout
\r
34598 Edit\SpecialChar \menuseparator
\r
34599 Math\SpecialChar \menuseparator
\r
34601 \begin_inset space ~
\r
34604 Definition\SpecialChar \menuseparator
\r
34610 Eating From The Right
\r
34616 <row interlinespace="2.5mm">
\r
34617 <cell alignment="center" valignment="top" usebox="none">
\r
34618 \begin_inset Text
\r
34620 \begin_layout Plain Layout
\r
34621 \begin_inset Graphics
\r
34622 filename ../images/math-macro-add-greedy-optional-param.png
\r
34623 rotateOrigin center
\r
34632 <cell alignment="center" valignment="top" usebox="none">
\r
34633 \begin_inset Text
\r
34635 \begin_layout Plain Layout
\r
34638 Edit\SpecialChar \menuseparator
\r
34639 Math\SpecialChar \menuseparator
\r
34641 \begin_inset space ~
\r
34644 Definition\SpecialChar \menuseparator
\r
34645 Append Optional Argument
\r
34646 \begin_inset Newline newline
\r
34650 \begin_inset Phantom HPhantom
\r
34653 \begin_layout Plain Layout
\r
34656 Edit\SpecialChar \menuseparator
\r
34657 Math\SpecialChar \menuseparator
\r
34659 \begin_inset space ~
\r
34662 Definition\SpecialChar \menuseparator
\r
34668 Eating From The Right
\r
34681 \begin_layout Section
\r
34682 Computer Algebra Systems
\r
34685 \begin_layout Standard
\r
34686 LyX offers the exchange between mathematical expressions written in LyX's
\r
34687 math editor and external applications or user defined scripts.
\r
34688 Currently supported applications are
\r
34705 Note that the set of supported mathematical constructs is limited only
\r
34706 to very simple cases.
\r
34709 \begin_layout Subsection
\r
34713 \begin_layout Standard
\r
34714 Write some expression in a formula, go to the
\r
34716 Edit\SpecialChar \menuseparator
\r
34717 Math\SpecialChar \menuseparator
\r
34718 Use Computer Algebra System
\r
34720 menu and choose the application you have installed on the computer.
\r
34721 After that the result of computation should show on the right side of the
\r
34722 expression together with the
\r
34723 \begin_inset Quotes eld
\r
34727 \begin_inset Quotes erd
\r
34733 \begin_layout Standard
\r
34734 Here are few simple examples (with results from
\r
34735 \family typewriter
\r
34738 ) to show what kind of computations can be performed:
\r
34741 \begin_layout Itemize
\r
34742 \begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$
\r
34748 \begin_layout Itemize
\r
34749 \begin_inset Formula $\frac{37.0}{3}=12.33333333333333$
\r
34755 \begin_layout Itemize
\r
34756 \begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$
\r
34762 \begin_layout Itemize
\r
34763 \begin_inset Formula $\det\left[\begin{array}{ccc}
\r
34767 \end{array}\right]=-56$
\r
34773 \begin_layout Itemize
\r
34774 \begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$
\r
34780 \begin_layout Subsection
\r
34781 Keyboard shortcut
\r
34784 \begin_layout Standard
\r
34785 Currently there is no keyboard shortcut for calling the algebra applications.
\r
34786 One can easily bind a shortcut to the
\r
34790 LyX function (see the
\r
34798 \begin_inset space \thinspace{}
\r
34802 \begin_inset space \space{}
\r
34809 key inside the math editor.
\r
34811 \family typewriter
\r
34814 one would use this shortcut definition command:
\r
34817 \begin_layout Standard
\r
34820 command-alternatives break-paragraph;math-extern maxima
\r
34823 \begin_layout Section
\r
34825 \begin_inset Index idx
\r
34828 \begin_layout Plain Layout
\r
34837 \begin_layout Subsection
\r
34839 \begin_inset Index idx
\r
34842 \begin_layout Plain Layout
\r
34843 Numbers ! negative
\r
34851 \begin_layout Standard
\r
34852 Negative numbers often look ugly in formulas because the minus sign before
\r
34853 the number is set with the same length as the minus operator sign.
\r
34854 When writing the negative number in normal text, the minus sign appears
\r
34858 \begin_layout Standard
\r
34859 Thus, the problem disappears when converting the minus sign to mathematical
\r
34863 \begin_layout Standard
\r
34864 An example to visualize the problem:
\r
34867 \begin_layout Standard
\r
34869 \begin_inset Tabular
\r
34870 <lyxtabular version="3" rows="3" columns="2">
\r
34871 <features rotate="0" tabularvalignment="middle">
\r
34872 <column alignment="right" valignment="top">
\r
34873 <column alignment="left" valignment="top">
\r
34875 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
34876 \begin_inset Text
\r
34878 \begin_layout Plain Layout
\r
34884 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
\r
34885 \begin_inset Text
\r
34887 \begin_layout Plain Layout
\r
34895 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
34896 \begin_inset Text
\r
34898 \begin_layout Plain Layout
\r
34904 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
\r
34905 \begin_inset Text
\r
34907 \begin_layout Plain Layout
\r
34908 \begin_inset Formula $x=-2$
\r
34918 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
34919 \begin_inset Text
\r
34921 \begin_layout Plain Layout
\r
34927 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
\r
34928 \begin_inset Text
\r
34930 \begin_layout Plain Layout
\r
34931 \begin_inset Formula $x=\textrm{-}2$
\r
34947 \begin_layout Subsection
\r
34948 Comma as decimal Separator
\r
34949 \begin_inset Index idx
\r
34952 \begin_layout Plain Layout
\r
34961 \begin_layout Standard
\r
34962 In LaTeX a comma inside a formula is used, according to the English convention,
\r
34963 as number group separator.
\r
34964 So there will be space added behind all commas in formulas.
\r
34967 \begin_layout Standard
\r
34968 To avoid this, the comma is highlighted and changed to mathematical text
\r
34970 \begin_inset Info
\r
34978 \begin_layout Standard
\r
34979 To use all formula commas in the document as decimal separator, the file
\r
34985 \begin_inset Foot
\r
34988 \begin_layout Plain Layout
\r
34993 is part of the LaTeX-package
\r
34998 \begin_inset Index idx
\r
35001 \begin_layout Plain Layout
\r
35006 \begin_layout Plain Layout
\r
35026 \begin_inset Index idx
\r
35029 \begin_layout Plain Layout
\r
35030 Packages ! icomma
\r
35035 is loaded with the LaTeX-preamble line
\r
35038 \begin_layout Standard
\r
35043 usepackage{icomma}
\r
35046 \begin_layout Subsection
\r
35048 \begin_inset CommandInset label
\r
35049 LatexCommand label
\r
35050 name "sub:Physical-Vectors"
\r
35055 \begin_inset Index idx
\r
35058 \begin_layout Plain Layout
\r
35059 Vectors ! physical
\r
35067 \begin_layout Standard
\r
35068 Predefined vectors are offered by the LaTeX-package
\r
35073 \begin_inset Index idx
\r
35076 \begin_layout Plain Layout
\r
35077 Packages ! braket
\r
35082 that is loaded with the LaTeX-preamble line
\r
35085 \begin_layout Standard
\r
35090 usepackage{braket}
\r
35093 \begin_layout Standard
\r
35097 \begin_layout Plain Layout
\r
35107 \begin_inset Note Note
\r
35110 \begin_layout Plain Layout
\r
35111 The following table will only be displayed when the LaTeX-package
\r
35123 \begin_layout Standard
\r
35124 The following commands are defined:
\r
35127 \begin_layout Standard
\r
35129 \begin_inset Tabular
\r
35130 <lyxtabular version="3" rows="4" columns="2">
\r
35131 <features rotate="0" tabularvalignment="middle">
\r
35132 <column alignment="center" valignment="top">
\r
35133 <column alignment="center" valignment="top">
\r
35135 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
35136 \begin_inset Text
\r
35138 \begin_layout Plain Layout
\r
35144 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
35145 \begin_inset Text
\r
35147 \begin_layout Plain Layout
\r
35155 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
35156 \begin_inset Text
\r
35158 \begin_layout Plain Layout
\r
35168 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
35169 \begin_inset Text
\r
35171 \begin_layout Plain Layout
\r
35172 \begin_inset Formula $\Bra{\psi}$
\r
35182 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
35183 \begin_inset Text
\r
35185 \begin_layout Plain Layout
\r
35195 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
35196 \begin_inset Text
\r
35198 \begin_layout Plain Layout
\r
35199 \begin_inset Formula $\Ket{\psi}$
\r
35209 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
35210 \begin_inset Text
\r
35212 \begin_layout Plain Layout
\r
35224 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
35225 \begin_inset Text
\r
35227 \begin_layout Plain Layout
\r
35228 \begin_inset Formula $\Braket{\psi|\phi}$
\r
35244 \begin_layout Standard
\r
35251 assures that all vertical bars are set in the size of the surrounding brackets:
\r
35252 \begin_inset Formula
\r
35254 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}
\r
35263 \begin_layout Plain Layout
\r
35273 \begin_inset Note Note
\r
35276 \begin_layout Plain Layout
\r
35277 The following will be displayed when the LaTeX-package
\r
35281 is not installed:
\r
35289 \begin_layout Standard
\r
35290 You need to install the LaTeX-package
\r
35294 to see the rest of this subsection in the output.
\r
35297 \begin_layout Standard
\r
35301 \begin_layout Plain Layout
\r
35313 \begin_layout Standard
\r
35320 can also be achieved using the command
\r
35326 , that is described in
\r
35327 \begin_inset CommandInset ref
\r
35329 reference "sub:Automatic-Bracket-Size"
\r
35336 \begin_layout Subsection
\r
35337 Self-defined Fractions
\r
35338 \begin_inset CommandInset label
\r
35339 LatexCommand label
\r
35340 name "sub:Self-defined-Fractions"
\r
35345 \begin_inset Index idx
\r
35348 \begin_layout Plain Layout
\r
35349 Fractions ! self-defined
\r
35357 \begin_layout Standard
\r
35358 To define custom commands for fractions, the command
\r
35365 \begin_inset Index idx
\r
35368 \begin_layout Plain Layout
\r
35375 \begin_layout Plain Layout
\r
35389 is used in the following scheme:
\r
35392 \begin_layout Standard
\r
35405 bracket}{fraction bar thickness}{style}
\r
35406 \begin_inset Newline newline
\r
35410 \begin_inset Phantom HPhantom
\r
35413 \begin_layout Plain Layout
\r
35423 {numerator}{denominator}
\r
35426 \begin_layout Standard
\r
35427 The style is a number in the range of 0
\r
35428 \begin_inset space \thinspace{}
\r
35432 \begin_inset space \thinspace{}
\r
35438 \begin_layout Standard
\r
35440 \begin_inset Tabular
\r
35441 <lyxtabular version="3" rows="5" columns="2">
\r
35442 <features rotate="0" tabularvalignment="middle">
\r
35443 <column alignment="center" valignment="top">
\r
35444 <column alignment="center" valignment="top">
\r
35446 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
35447 \begin_inset Text
\r
35449 \begin_layout Plain Layout
\r
35455 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
35456 \begin_inset Text
\r
35458 \begin_layout Plain Layout
\r
35466 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
35467 \begin_inset Text
\r
35469 \begin_layout Plain Layout
\r
35475 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
35476 \begin_inset Text
\r
35478 \begin_layout Plain Layout
\r
35479 display style formula
\r
35486 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
35487 \begin_inset Text
\r
35489 \begin_layout Plain Layout
\r
35495 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
35496 \begin_inset Text
\r
35498 \begin_layout Plain Layout
\r
35506 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
35507 \begin_inset Text
\r
35509 \begin_layout Plain Layout
\r
35515 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
35516 \begin_inset Text
\r
35518 \begin_layout Plain Layout
\r
35526 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
35527 \begin_inset Text
\r
35529 \begin_layout Plain Layout
\r
35535 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
35536 \begin_inset Text
\r
35538 \begin_layout Plain Layout
\r
35552 \begin_layout Standard
\r
35553 When no style is given, the size is adjusted to the surrounding environment
\r
35554 like for the command
\r
35563 \begin_layout Standard
\r
35564 When no fraction bar thickness is given, the predefined value of 0.4
\r
35565 \begin_inset space \thinspace{}
\r
35571 \begin_layout Standard
\r
35572 \begin_inset VSpace medskip
\r
35575 For example, the commands
\r
35588 \begin_inset CommandInset ref
\r
35590 reference "sub:Fractions"
\r
35594 are defined with the commands
\r
35597 \begin_layout Standard
\r
35606 genfrac{}{}{}{0}{#1}{#2}}
\r
35609 \begin_layout Standard
\r
35613 \begin_layout Standard
\r
35622 genfrac{(}{)}{0pt}{1}{#1}{#2}}
\r
35625 \begin_layout Standard
\r
35626 \begin_inset VSpace medskip
\r
35629 To define a fraction where the fraction bar thickness can be given as optional
\r
35630 argument, the following line is inserted to the LaTeX-preamble:
\r
35633 \begin_layout Standard
\r
35642 genfrac{}{}{#1}{}{#2}{#3}}
\r
35645 \begin_layout Standard
\r
35647 \begin_inset Formula
\r
35649 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
\r
35650 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
\r
35655 As one can see, the distance of the numerator and the denominator to the
\r
35656 fraction bar is round about three times the bar thickness.
\r
35659 \begin_layout Subsection
\r
35660 Canceled Formulas
\r
35661 \begin_inset Index idx
\r
35664 \begin_layout Plain Layout
\r
35665 Formula ! canceled
\r
35673 \begin_layout Standard
\r
35674 To cancel formulas or formula parts, the LaTeX-package
\r
35679 \begin_inset Index idx
\r
35682 \begin_layout Plain Layout
\r
35683 Packages ! cancel
\r
35688 has to be loaded with the LaTeX-preamble line
\r
35691 \begin_layout Standard
\r
35696 usepackage{cancel}
\r
35699 \begin_layout Standard
\r
35703 \begin_layout Plain Layout
\r
35713 \begin_inset Note Note
\r
35716 \begin_layout Plain Layout
\r
35717 The following table will only be displayed when the LaTeX-package
\r
35729 \begin_layout Standard
\r
35730 There are four ways to cancel formulas:
\r
35733 \begin_layout Standard
\r
35735 \begin_inset Tabular
\r
35736 <lyxtabular version="3" rows="5" columns="2">
\r
35737 <features rotate="0" tabularvalignment="middle">
\r
35738 <column alignment="center" valignment="top">
\r
35739 <column alignment="center" valignment="top">
\r
35741 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
35742 \begin_inset Text
\r
35744 \begin_layout Plain Layout
\r
35750 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
35751 \begin_inset Text
\r
35753 \begin_layout Plain Layout
\r
35755 \begin_inset Note Note
\r
35758 \begin_layout Plain Layout
\r
35765 are used here as spacer.
\r
35777 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
35778 \begin_inset Text
\r
35780 \begin_layout Plain Layout
\r
35789 \begin_layout Plain Layout
\r
35803 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
35804 \begin_inset Text
\r
35806 \begin_layout Plain Layout
\r
35807 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
\r
35817 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
35818 \begin_inset Text
\r
35820 \begin_layout Plain Layout
\r
35829 \begin_layout Plain Layout
\r
35843 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
35844 \begin_inset Text
\r
35846 \begin_layout Plain Layout
\r
35847 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
\r
35857 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
35858 \begin_inset Text
\r
35860 \begin_layout Plain Layout
\r
35869 \begin_layout Plain Layout
\r
35883 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
35884 \begin_inset Text
\r
35886 \begin_layout Plain Layout
\r
35887 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
\r
35897 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
35898 \begin_inset Text
\r
35900 \begin_layout Plain Layout
\r
35904 \begin_inset Formula $\to$
\r
35915 \begin_layout Plain Layout
\r
35929 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
35930 \begin_inset Text
\r
35932 \begin_layout Plain Layout
\r
35933 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
\r
35949 \begin_layout Standard
\r
35956 is especially suitable to visualize the reduction of fractions within formulas:
\r
35957 \begin_inset Formula
\r
35959 \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
35967 \begin_layout Standard
\r
35968 To change the size of
\r
35975 \begin_inset Quotes eld
\r
35979 \begin_inset Quotes erd
\r
35982 value one can load the package
\r
35986 with either the option
\r
35990 which leads to the same size as for the canceled value or with the option
\r
35995 which makes is it a bit smaller than the size one gets without using a
\r
35997 In this document
\r
36001 was loaded with this line:
\r
36004 \begin_layout Standard
\r
36009 usepackage[samesize]{cancel}
\r
36012 \begin_layout Standard
\r
36013 To color the cancellation bar one adds this command as TeX code:
\r
36016 \begin_layout Standard
\r
36028 \begin_layout Standard
\r
36033 can be replaced by a color of your choice.
\r
36036 \begin_layout Standard
\r
36040 \begin_layout Plain Layout
\r
36056 \begin_layout Standard
\r
36057 \begin_inset Formula
\r
36059 \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
36067 \begin_layout Standard
\r
36071 \begin_layout Plain Layout
\r
36085 \begin_inset Note Note
\r
36088 \begin_layout Plain Layout
\r
36097 \begin_layout Standard
\r
36098 For further customizations, see the documentation of the package
\r
36103 \begin_inset CommandInset citation
\r
36104 LatexCommand cite
\r
36112 \begin_layout Standard
\r
36116 \begin_layout Plain Layout
\r
36126 \begin_inset Note Note
\r
36129 \begin_layout Plain Layout
\r
36130 The following will be displayed when the LaTeX-package
\r
36134 is not installed:
\r
36142 \begin_layout Standard
\r
36143 You need to install the LaTeX-package
\r
36147 to see the rest of this subsection in the output.
\r
36150 \begin_layout Standard
\r
36154 \begin_layout Plain Layout
\r
36166 \begin_layout Standard
\r
36167 \begin_inset Newpage newpage
\r
36173 \begin_layout Subsection
\r
36174 Formulas in Section Headings
\r
36175 \begin_inset CommandInset label
\r
36176 LatexCommand label
\r
36177 name "sub:Formulas-in-Section"
\r
36182 \begin_inset Index idx
\r
36185 \begin_layout Plain Layout
\r
36186 Formula ! in section headings
\r
36194 \begin_layout Standard
\r
36195 When formulas are used in section headings, the following has to be taken
\r
36199 \begin_layout Standard
\r
36200 \begin_inset Note Greyedout
\r
36203 \begin_layout Plain Layout
\r
36209 \begin_inset Index idx
\r
36212 \begin_layout Plain Layout
\r
36213 Packages ! hyperref
\r
36218 support is enabled in the document settings dialog under
\r
36221 \begin_inset space ~
\r
36226 , PDF-bookmarks are created for every section heading in the table of contents.
\r
36227 If a section heading contains formulas, they are incorrectly displayed
\r
36228 in the bookmark text, because formulas in bookmarks infringe the PDF convention
\r
36237 \begin_layout Standard
\r
36238 Both problems can be solved by inserting at the end of the section heading
\r
36239 a short title with the menu
\r
36241 Insert\SpecialChar \menuseparator
\r
36243 \begin_inset space ~
\r
36249 Short titles are used as alternative for multiline section headings to
\r
36250 keep the table of contents clearly arranged.
\r
36251 Only the short title appears in the table of contents and therefore also
\r
36252 in the PDF-bookmark.
\r
36255 \begin_layout Standard
\r
36256 When formulas should be used in the table of contents but
\r
36260 is used, one can use the following command in TeX-mode:
\r
36263 \begin_layout Standard
\r
36268 texorpdfstring{part}{alternative}
\r
36269 \begin_inset Index idx
\r
36272 \begin_layout Plain Layout
\r
36283 \begin_layout Standard
\r
36284 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
\r
36285 This can be characters, formulas, footnotes, but also cross-references.
\r
36286 The alternative is used instead of the part for the bookmark.
\r
36289 \begin_layout Standard
\r
36290 Here are two example headings:
\r
36291 \begin_inset VSpace -3mm
\r
36298 \begin_layout Plain Layout
\r
36310 \begin_layout Subsubsection
\r
36311 Heading without formula in table of contents
\r
36312 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
\r
36316 \begin_inset Argument 1
\r
36319 \begin_layout Plain Layout
\r
36320 Heading without formula in table of contents
\r
36328 \begin_layout Subsubsection
\r
36329 Heading with formula in table of contents
\r
36333 \begin_layout Plain Layout
\r
36343 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
\r
36350 \begin_layout Plain Layout
\r
36360 \begin_layout Standard
\r
36364 \begin_layout Plain Layout
\r
36373 In the first heading a short title was used, in the second one
\r
36382 \begin_layout Standard
\r
36383 To get the same formatting as for the other headings, the complete heading
\r
36389 \begin_inset Foot
\r
36392 \begin_layout Plain Layout
\r
36394 \begin_inset CommandInset ref
\r
36396 reference "sub:Bold-Formulas"
\r
36408 \begin_layout Subsection
\r
36409 Formulas in multi-column Text
\r
36410 \begin_inset Index idx
\r
36413 \begin_layout Plain Layout
\r
36414 Formula ! in multi-column text
\r
36422 \begin_layout Standard
\r
36423 Formulas in multi-column text are often too wide to fit into a column and
\r
36424 thus need to be set over the whole page width.
\r
36425 This is done by using the LaTeX-package
\r
36430 \begin_inset Foot
\r
36433 \begin_layout Plain Layout
\r
36438 is part of every LaTeX standard installation.
\r
36444 \begin_inset Index idx
\r
36447 \begin_layout Plain Layout
\r
36448 Packages ! multicol
\r
36453 , that is loaded with the LaTeX-preamble line
\r
36456 \begin_layout Standard
\r
36461 usepackage{multicol}
\r
36464 \begin_layout Standard
\r
36465 \begin_inset Note Greyedout
\r
36468 \begin_layout Plain Layout
\r
36469 Note that in this case the setting
\r
36472 \begin_inset space ~
\r
36479 Document\SpecialChar \menuseparator
\r
36485 \begin_inset space ~
\r
36505 \begin_layout Standard
\r
36506 Before the multi-column text the command
\r
36509 \begin_layout Standard
\r
36514 begin{multicols}{column number}
\r
36517 \begin_layout Standard
\r
36518 is written in TeX-mode.
\r
36519 The column number is a number in the range of 2
\r
36520 \begin_inset space \thinspace{}
\r
36524 \begin_inset space \thinspace{}
\r
36528 Before the formula the multi-column text is ended by inserting the command
\r
36531 \begin_layout Standard
\r
36539 \begin_layout Standard
\r
36543 \begin_layout Standard
\r
36544 Due to the command some space is automatically added before the formula.
\r
36545 To revert this, -6
\r
36546 \begin_inset space \thinspace{}
\r
36549 mm vertical space is inserted before the formula.
\r
36550 When the formula style
\r
36553 \begin_inset Foot
\r
36556 \begin_layout Plain Layout
\r
36557 formula styles see
\r
36558 \begin_inset CommandInset ref
\r
36560 reference "sec:Formula-Styles"
\r
36572 \begin_inset space \thinspace{}
\r
36575 mm space is inserted instead.
\r
36578 \begin_layout Standard
\r
36579 As example a multi-column text with a displayed formula:
\r
36582 \begin_layout Standard
\r
36588 \begin_layout Plain Layout
\r
36592 begin{multicols}{2}
\r
36597 Das Spektrum wird fouriertransformiert.
\r
36598 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
\r
36599 , Lösungsmittel) zu trennen.
\r
36600 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
\r
36601 nun das Aussehen des Ausgangssignals.
\r
36602 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
\r
36603 über alle Phasen integrieren muss.
\r
36605 \begin_inset Formula $S$
\r
36608 unser normiertes Ausgangssignal und
\r
36609 \begin_inset Formula $P$
\r
36612 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
\r
36616 \begin_layout Plain Layout
\r
36626 \begin_inset VSpace -6mm
\r
36630 \begin_inset Formula
\r
36632 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
\r
36641 \begin_layout Plain Layout
\r
36645 begin{multicols}{2}
\r
36651 \begin_inset Formula $S_{0}$
\r
36654 das Signal ohne Gradient ist und die Normierungsbedingung
\r
36655 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
\r
36659 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
\r
36661 \begin_inset Formula $\nicefrac{\pi}{2}$
\r
36665 \begin_inset space \thinspace{}
\r
36668 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
\r
36669 das Signal zusätzlich abschwächt.
\r
36670 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
\r
36672 \begin_inset Formula $T_{2}$
\r
36678 \begin_layout Standard
\r
36684 \begin_layout Plain Layout
\r
36696 \begin_layout Subsection
\r
36697 Formulas with Description of Variables
\r
36698 \begin_inset Index idx
\r
36701 \begin_layout Plain Layout
\r
36702 Formula ! with description of variables
\r
36710 \begin_layout Standard
\r
36711 To describe variables within a formula, like in formula
\r
36712 \begin_inset CommandInset ref
\r
36713 LatexCommand eqref
\r
36714 reference "eq:within"
\r
36723 \begin_inset Formula $n$
\r
36727 \begin_inset space ~
\r
36730 matrix is used with left aligned columns for the
\r
36731 \begin_inset Formula $n$
\r
36735 \begin_inset Foot
\r
36738 \begin_layout Plain Layout
\r
36740 \begin_inset CommandInset ref
\r
36742 reference "sec:Matrices"
\r
36751 To set the description in a smaller size, before the matrix e.
\r
36752 \begin_inset space \thinspace{}
\r
36756 \begin_inset space \space{}
\r
36766 \begin_inset Foot
\r
36769 \begin_layout Plain Layout
\r
36771 \begin_inset CommandInset ref
\r
36773 reference "sub:Font-Sizes"
\r
36785 \begin_layout Standard
\r
36786 When the formula style
\r
36789 \begin_inset Foot
\r
36792 \begin_layout Plain Layout
\r
36793 formula styles see
\r
36794 \begin_inset CommandInset ref
\r
36796 reference "sec:Formula-Styles"
\r
36814 \begin_inset Foot
\r
36817 \begin_layout Plain Layout
\r
36824 only works in formulas with the style
\r
36829 \begin_inset CommandInset ref
\r
36831 reference "sub:Variable-Space"
\r
36840 is inserted before and after the matrix to have the same separation of
\r
36841 the matrix from the equation and the side margin.
\r
36844 \begin_layout Standard
\r
36845 When the formula style
\r
36849 is used, the method described in
\r
36850 \begin_inset CommandInset ref
\r
36852 reference "sub:Flalign-Environment"
\r
36856 is used to indent formulas.
\r
36858 \begin_inset CommandInset ref
\r
36859 LatexCommand eqref
\r
36860 reference "eq:within"
\r
36864 consists of five columns where in the first two columns contain the equation,
\r
36865 the third the matrix and the last one an empty TeX-brace.
\r
36866 \begin_inset Formula
\r
36868 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
\r
36869 \rho & \textrm{density}\\
\r
36870 V & \textrm{volume}\\
\r
36871 g & \textrm{gravitational acceleration}
\r
36872 \end{array} & & {}\label{eq:within}
\r
36880 \begin_layout Subsection
\r
36881 Upright small Greek Letters
\r
36882 \begin_inset CommandInset label
\r
36883 LatexCommand label
\r
36884 name "sub:Upright-small-Greek"
\r
36889 \begin_inset Index idx
\r
36892 \begin_layout Plain Layout
\r
36893 Greek letters ! upright
\r
36901 \begin_layout Standard
\r
36902 Most of the math fonts only provide italic small Greek letters.
\r
36903 But for symbols of elementary particles like pions and neutrinos, upright
\r
36904 Greek letters are needed.
\r
36910 \begin_inset Foot
\r
36913 \begin_layout Plain Layout
\r
36918 is part of the LaTeX-package
\r
36923 \begin_inset Index idx
\r
36926 \begin_layout Plain Layout
\r
36931 \begin_layout Plain Layout
\r
36951 \begin_inset Index idx
\r
36954 \begin_layout Plain Layout
\r
36955 Packages ! upgreek
\r
36960 that is loaded with the LaTeX-preamble line
\r
36963 \begin_layout Standard
\r
36968 usepackage{upgreek}
\r
36971 \begin_layout Standard
\r
36977 \begin_layout Plain Layout
\r
36987 \begin_inset Note Note
\r
36990 \begin_layout Plain Layout
\r
36991 The following table will only be displayed when the LaTeX-package
\r
37000 They are created when the command for a small Greek letter is started with
\r
37006 For example the command
\r
37013 \begin_inset Formula $\uptau$
\r
37019 \begin_layout Standard
\r
37020 With these commands reactions of elementary particles can be typeset:
\r
37021 \begin_inset Formula
\r
37023 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
\r
37031 \begin_layout Standard
\r
37032 The upright letters are more bold and wider than the italic ones.
\r
37033 They should therefore not be used for units like
\r
37034 \begin_inset Quotes eld
\r
37038 \begin_inset Quotes erd
\r
37044 \begin_layout Standard
\r
37048 \begin_layout Plain Layout
\r
37058 \begin_inset Note Note
\r
37061 \begin_layout Plain Layout
\r
37062 The following will be displayed when the LaTeX-package
\r
37066 is not installed:
\r
37074 \begin_layout Standard
\r
37075 You need to install the LaTeX-package
\r
37079 to see the rest of this subsection in the output.
\r
37082 \begin_layout Standard
\r
37086 \begin_layout Plain Layout
\r
37098 \begin_layout Subsection
\r
37099 Text Characters in Formulas
\r
37100 \begin_inset CommandInset label
\r
37101 LatexCommand label
\r
37102 name "sub:Text-Characters-in"
\r
37107 \begin_inset Index idx
\r
37110 \begin_layout Plain Layout
\r
37111 Text ! in formulas
\r
37119 \begin_layout Standard
\r
37120 In some cases you might want to insert text characters directly into formulas.
\r
37121 When for example the centered dot · is often used in formulas like
\r
37122 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
\r
37125 , one would have to insert the command
\r
37132 \begin_inset Foot
\r
37135 \begin_layout Plain Layout
\r
37137 \begin_inset CommandInset ref
\r
37139 reference "sub:Binary-Operators"
\r
37148 all the time, because this character is defined in all encodings as text
\r
37150 But the encoding can be changed by this LaTeX-preamble line:
\r
37153 \begin_layout Standard
\r
37158 Declare Inputtext{183}{
\r
37166 textperiodcentered
\r
37168 f\SpecialChar \textcompwordmark{}
\r
37172 \begin_layout Standard
\r
37173 The character encoding (menu
\r
37175 Document\SpecialChar \menuseparator
\r
37176 Settings\SpecialChar \menuseparator
\r
37179 ) specifies what character appears when a keyboard key is pressed.
\r
37180 When the key for the character '·' is pressed, internally the command
\r
37184 textperiodcentered
\r
37187 But this command is not available in a formula so that you would get LaTeX-erro
\r
37189 With the changed encoding the right command is chosen automatically, depending
\r
37190 on if the character was inserted into a formula or not.
\r
37193 \begin_layout Standard
\r
37194 The encoding of several characters is saved in definition files.
\r
37195 For example the encoding
\r
37199 is defined in the file
\r
37203 which is in the installation folder of LaTeX.
\r
37204 Encodings should only be changed via the LaTeX-preamble and not in the
\r
37205 definition files.
\r
37206 Otherwise documents could not be edited by other LyX users working on other
\r
37210 \begin_layout Standard
\r
37211 \begin_inset VSpace medskip
\r
37214 Besides the centered dot, in this document the degree sign ° is defined
\r
37215 with the following LaTeX-preamble line so that it can be directly inserted
\r
37219 \begin_layout Standard
\r
37224 DeclareInputtext{176}{
\r
37234 f\SpecialChar \textcompwordmark{}
\r
37238 \begin_layout Standard
\r
37239 \begin_inset Newpage newpage
\r
37245 \begin_layout Section
\r
37246 \start_of_appendix
\r
37247 Typographic Advice
\r
37248 \begin_inset Index idx
\r
37251 \begin_layout Plain Layout
\r
37252 Typographic advice
\r
37260 \begin_layout Standard
\r
37261 This section is a summary of the most important typographic rules, listed
\r
37263 \begin_inset Foot
\r
37266 \begin_layout Plain Layout
\r
37267 This collection was partly taken from the German semi-official dictionary
\r
37269 \begin_inset Quotes eld
\r
37273 \begin_inset Quotes erd
\r
37277 \begin_inset CommandInset citation
\r
37278 LatexCommand cite
\r
37283 that lists some of the ISO rules.
\r
37284 More rules are listed in
\r
37285 \begin_inset CommandInset citation
\r
37286 LatexCommand cite
\r
37299 \begin_layout Itemize
\r
37300 Physical units are
\r
37305 \begin_inset Foot
\r
37308 \begin_layout Plain Layout
\r
37309 done with font styles, see
\r
37310 \begin_inset CommandInset ref
\r
37312 reference "sub:Font-Styles"
\r
37321 , no matter if they appear in italic text: 30
\r
37322 \begin_inset space \thinspace{}
\r
37326 \begin_inset Newline newline
\r
37329 Between the value and the unit is the smallest space, see
\r
37330 \begin_inset CommandInset ref
\r
37332 reference "sub:Predefined-Space"
\r
37337 \begin_inset Newline newline
\r
37340 This convention is automatically fulfilled when the command
\r
37347 When it is entered to a formula, two boxes appear.
\r
37348 In the first one the value is inserted, in the second one the unit, and
\r
37349 one gets as above:
\r
37350 \begin_inset Formula $\unit[30]{km/h}$
\r
37354 \begin_inset space \thinspace{}
\r
37364 is not a real LaTeX command but the command
\r
37368 unit[value]{unit}
\r
37370 , therefore you cannot use it in TeX code.
\r
37373 \begin_layout Itemize
\r
37374 Percent and perthousand signs are set like physical units:
\r
37375 \begin_inset Newline newline
\r
37379 \begin_inset space \thinspace{}
\r
37382 ‰ alcohol in blood
\r
37385 \begin_layout Itemize
\r
37386 The degree sign follows directly on the value: 15°, but not when it is used
\r
37388 \begin_inset space \thinspace{}
\r
37394 \begin_layout Itemize
\r
37395 In numbers with more than four digits the smallest space is inserted before
\r
37396 every third digit to group them:
\r
37406 \begin_inset space \thinspace{}
\r
37410 \begin_inset space \thinspace{}
\r
37416 \begin_layout Itemize
\r
37417 For dimensions like 120×90×40
\r
37418 \begin_inset space \thinspace{}
\r
37421 cm the multiplication sign
\r
37422 \begin_inset Quotes eld
\r
37426 \begin_inset Quotes erd
\r
37430 It is available either via the command
\r
37438 Insert\SpecialChar \menuseparator
\r
37439 Special Character\SpecialChar \menuseparator
\r
37445 \begin_layout Itemize
\r
37446 Functions with names consisting of several letters are set upright to avoid
\r
37448 \begin_inset CommandInset ref
\r
37450 reference "sub:Predefined-Functions"
\r
37457 \begin_layout Itemize
\r
37458 Indices consisting of several letters, are set upright:
\r
37459 \begin_inset Formula $E_{\mathrm{kin}}$
\r
37463 \begin_inset Newline newline
\r
37466 Components of matrices are set italic:
\r
37467 \begin_inset Formula $\hat{H}_{kl}$
\r
37473 \begin_layout Itemize
\r
37474 The differentiation/integration operator 'd', the Euler's number 'e' and
\r
37475 the imaginary unit 'i' should be set upright, to avoid mixing them up with
\r
37479 \begin_layout Itemize
\r
37480 The character that denotes a
\r
37484 transformation is inserted either by the command
\r
37492 \begin_layout Plain Layout
\r
37505 Insert\SpecialChar \menuseparator
\r
37506 Special Character\SpecialChar \menuseparator
\r
37507 Symbols\SpecialChar \menuseparator
\r
37509 \begin_inset space ~
\r
37515 \begin_inset Formula $\mathscr{F}$
\r
37521 \begin_layout Standard
\r
37522 \begin_inset Newpage newpage
\r
37528 \begin_layout Section
\r
37530 \begin_inset Index idx
\r
37533 \begin_layout Plain Layout
\r
37542 \begin_layout Standard
\r
37543 Some characters and symbols can be created with several commands.
\r
37544 Here is a list of the synonym commands:
\r
37547 \begin_layout Standard
\r
37548 \begin_inset VSpace bigskip
\r
37552 \begin_inset space \hfill{}
\r
37556 \begin_inset Tabular
\r
37557 <lyxtabular version="3" rows="12" columns="2">
\r
37558 <features rotate="0" tabularvalignment="middle">
\r
37559 <column alignment="center" valignment="top" width="0pt">
\r
37560 <column alignment="center" valignment="top" width="0pt">
\r
37562 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
37563 \begin_inset Text
\r
37565 \begin_layout Plain Layout
\r
37571 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
37572 \begin_inset Text
\r
37574 \begin_layout Plain Layout
\r
37576 \begin_inset Note Note
\r
37579 \begin_layout Plain Layout
\r
37586 is only used as spacer.
\r
37598 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
37599 \begin_inset Text
\r
37601 \begin_layout Plain Layout
\r
37609 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
37610 \begin_inset Text
\r
37612 \begin_layout Plain Layout
\r
37616 \begin_layout Plain Layout
\r
37620 raisebox{-1.2mm}{
\r
37629 \begin_layout Plain Layout
\r
37643 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
37644 \begin_inset Text
\r
37646 \begin_layout Plain Layout
\r
37654 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
37655 \begin_inset Text
\r
37657 \begin_layout Plain Layout
\r
37667 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
37668 \begin_inset Text
\r
37670 \begin_layout Plain Layout
\r
37678 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
37679 \begin_inset Text
\r
37681 \begin_layout Plain Layout
\r
37691 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
37692 \begin_inset Text
\r
37694 \begin_layout Plain Layout
\r
37702 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
37703 \begin_inset Text
\r
37705 \begin_layout Plain Layout
\r
37713 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
37714 \begin_inset Text
\r
37716 \begin_layout Plain Layout
\r
37724 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
37725 \begin_inset Text
\r
37727 \begin_layout Plain Layout
\r
37735 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
37736 \begin_inset Text
\r
37738 \begin_layout Plain Layout
\r
37746 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
37747 \begin_inset Text
\r
37749 \begin_layout Plain Layout
\r
37759 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
37760 \begin_inset Text
\r
37762 \begin_layout Plain Layout
\r
37770 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
37771 \begin_inset Text
\r
37773 \begin_layout Plain Layout
\r
37783 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
37784 \begin_inset Text
\r
37786 \begin_layout Plain Layout
\r
37794 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
37795 \begin_inset Text
\r
37797 \begin_layout Plain Layout
\r
37807 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
37808 \begin_inset Text
\r
37810 \begin_layout Plain Layout
\r
37818 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
37819 \begin_inset Text
\r
37821 \begin_layout Plain Layout
\r
37831 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
37832 \begin_inset Text
\r
37834 \begin_layout Plain Layout
\r
37842 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
37843 \begin_inset Text
\r
37845 \begin_layout Plain Layout
\r
37853 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
37854 \begin_inset Text
\r
37856 \begin_layout Plain Layout
\r
37864 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
37865 \begin_inset Text
\r
37867 \begin_layout Plain Layout
\r
37879 \begin_inset space \hfill{}
\r
37883 \begin_inset Tabular
\r
37884 <lyxtabular version="3" rows="12" columns="2">
\r
37885 <features rotate="0" tabularvalignment="middle">
\r
37886 <column alignment="center" valignment="top" width="0pt">
\r
37887 <column alignment="center" valignment="top" width="0pt">
\r
37889 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\r
37890 \begin_inset Text
\r
37892 \begin_layout Plain Layout
\r
37898 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\r
37899 \begin_inset Text
\r
37901 \begin_layout Plain Layout
\r
37909 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
37910 \begin_inset Text
\r
37912 \begin_layout Plain Layout
\r
37920 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
37921 \begin_inset Text
\r
37923 \begin_layout Plain Layout
\r
37935 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\r
37936 \begin_inset Text
\r
37938 \begin_layout Plain Layout
\r
37946 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\r
37947 \begin_inset Text
\r
37949 \begin_layout Plain Layout
\r
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38175 \begin_inset space \hfill{}
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38181 \begin_layout Standard
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38202 The LaTeX Companion
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38205 Addison Wesley, 2004
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38210 LatexCommand bibitem
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38216 \begin_inset CommandInset href
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38217 LatexCommand href
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38218 name "Description"
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38219 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
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38223 of LaTeX's math abilities
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38226 \begin_layout Bibliography
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38228 LatexCommand bibitem
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38236 name "Description"
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38237 target "http://mirrors.ctan.org/macros/latex/required/amslatex/math/amsldoc.pdf"
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38266 LatexCommand href
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38268 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
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38272 of all symbols available with LaTeX-packages
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38275 \begin_layout Bibliography
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38285 name "Documentation"
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38286 target "http://mirrors.ctan.org/macros/latex/contrib/cancel/cancel.pdf"
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38290 of the LaTeX-package
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38299 Packages ! cancel
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38309 LatexCommand bibitem
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38315 \begin_inset CommandInset href
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38316 LatexCommand href
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38317 name "Documentation"
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38318 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
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38322 of the LaTeX-package
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38331 Packages ! hyperref
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38349 name "Documentation"
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38350 target "http://www.ctan.org/tex-archive/macros/latex/contrib/mhchem/mhchem.pdf"
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38354 of the LaTeX-package
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38363 Packages ! mhchem
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38381 name "Description"
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38382 target "http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf"
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38393 \begin_inset CommandInset ref
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38395 reference "sub:Operator-Limits"
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38400 \begin_inset Index idx
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38427 Auflage, Duden 2001
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38430 \begin_layout Bibliography
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38432 LatexCommand bibitem
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38438 \begin_inset CommandInset href
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38439 LatexCommand href
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38440 name "Check list"
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38441 target "http://physics.nist.gov/Document/checklist.pdf"
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38445 for reviewing manuscripts
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38448 \begin_layout Standard
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38449 \begin_inset CommandInset index_print
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38450 LatexCommand printindex
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projects / lyx.git / blob