\documentclass[11pt]{article} \usepackage[breakable]{tcolorbox} \usepackage{parskip} % Stop auto-indenting (to mimic markdown behaviour) \usepackage{iftex} \ifPDFTeX \usepackage[T1]{fontenc} \usepackage{mathpazo} \else \usepackage{fontspec} \fi % Basic figure setup, for now with no caption control since it's done % automatically by Pandoc (which extracts ![](path) syntax from Markdown). \usepackage{graphicx} % Maintain compatibility with old templates. Remove in nbconvert 6.0 \let\Oldincludegraphics\includegraphics % Ensure that by default, figures have no caption (until we provide a % proper Figure object with a Caption API and a way to capture that % in the conversion process - todo). \usepackage{caption} \DeclareCaptionFormat{nocaption}{} \captionsetup{format=nocaption,aboveskip=0pt,belowskip=0pt} \usepackage[Export]{adjustbox} % Used to constrain images to a maximum size \adjustboxset{max size={0.9\linewidth}{0.9\paperheight}} \usepackage{float} \floatplacement{figure}{H} % forces figures to be placed at the correct location \usepackage{xcolor} % Allow colors to be defined \usepackage{enumerate} % Needed for markdown enumerations to work \usepackage{geometry} % Used to adjust the document margins \usepackage{amsmath} % Equations \usepackage{amssymb} % Equations \usepackage{textcomp} % defines textquotesingle % Hack from http://tex.stackexchange.com/a/47451/13684: \AtBeginDocument{% \def\PYZsq{\textquotesingle}% Upright quotes in Pygmentized code } \usepackage{upquote} % Upright quotes for verbatim code \usepackage{eurosym} % defines \euro \usepackage[mathletters]{ucs} % Extended unicode (utf-8) support \usepackage{fancyvrb} % verbatim replacement that allows latex \usepackage{grffile} % extends the file name processing of package graphics % to support a larger range \makeatletter % fix for grffile with XeLaTeX \def\Gread@@xetex#1{% \IfFileExists{"\Gin@base".bb}% {\Gread@eps{\Gin@base.bb}}% {\Gread@@xetex@aux#1}% } \makeatother % The hyperref package gives us a pdf with properly built % internal navigation ('pdf bookmarks' for the table of contents, % internal cross-reference links, web links for URLs, etc.) \usepackage{hyperref} % The default LaTeX title has an obnoxious amount of whitespace. By default, % titling removes some of it. It also provides customization options. \usepackage{titling} \usepackage{longtable} % longtable support required by pandoc >1.10 \usepackage{booktabs} % table support for pandoc > 1.12.2 \usepackage[inline]{enumitem} % IRkernel/repr support (it uses the enumerate* environment) \usepackage[normalem]{ulem} % ulem is needed to support strikethroughs (\sout) % normalem makes italics be italics, not underlines \usepackage{mathrsfs} % Colors for the hyperref package \definecolor{urlcolor}{rgb}{0,.145,.698} \definecolor{linkcolor}{rgb}{.71,0.21,0.01} \definecolor{citecolor}{rgb}{.12,.54,.11} % ANSI colors \definecolor{ansi-black}{HTML}{3E424D} \definecolor{ansi-black-intense}{HTML}{282C36} \definecolor{ansi-red}{HTML}{E75C58} \definecolor{ansi-red-intense}{HTML}{B22B31} \definecolor{ansi-green}{HTML}{00A250} \definecolor{ansi-green-intense}{HTML}{007427} \definecolor{ansi-yellow}{HTML}{DDB62B} \definecolor{ansi-yellow-intense}{HTML}{B27D12} \definecolor{ansi-blue}{HTML}{208FFB} \definecolor{ansi-blue-intense}{HTML}{0065CA} \definecolor{ansi-magenta}{HTML}{D160C4} \definecolor{ansi-magenta-intense}{HTML}{A03196} \definecolor{ansi-cyan}{HTML}{60C6C8} \definecolor{ansi-cyan-intense}{HTML}{258F8F} \definecolor{ansi-white}{HTML}{C5C1B4} \definecolor{ansi-white-intense}{HTML}{A1A6B2} \definecolor{ansi-default-inverse-fg}{HTML}{FFFFFF} \definecolor{ansi-default-inverse-bg}{HTML}{000000} % commands and environments needed by pandoc snippets % extracted from the output of `pandoc -s` \providecommand{\tightlist}{% \setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}} \DefineVerbatimEnvironment{Highlighting}{Verbatim}{commandchars=\\\{\}} % Add ',fontsize=\small' for more characters per line \newenvironment{Shaded}{}{} \newcommand{\KeywordTok}[1]{\textcolor[rgb]{0.00,0.44,0.13}{\textbf{{#1}}}} \newcommand{\DataTypeTok}[1]{\textcolor[rgb]{0.56,0.13,0.00}{{#1}}} \newcommand{\DecValTok}[1]{\textcolor[rgb]{0.25,0.63,0.44}{{#1}}} \newcommand{\BaseNTok}[1]{\textcolor[rgb]{0.25,0.63,0.44}{{#1}}} \newcommand{\FloatTok}[1]{\textcolor[rgb]{0.25,0.63,0.44}{{#1}}} \newcommand{\CharTok}[1]{\textcolor[rgb]{0.25,0.44,0.63}{{#1}}} \newcommand{\StringTok}[1]{\textcolor[rgb]{0.25,0.44,0.63}{{#1}}} \newcommand{\CommentTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textit{{#1}}}} \newcommand{\OtherTok}[1]{\textcolor[rgb]{0.00,0.44,0.13}{{#1}}} \newcommand{\AlertTok}[1]{\textcolor[rgb]{1.00,0.00,0.00}{\textbf{{#1}}}} \newcommand{\FunctionTok}[1]{\textcolor[rgb]{0.02,0.16,0.49}{{#1}}} \newcommand{\RegionMarkerTok}[1]{{#1}} \newcommand{\ErrorTok}[1]{\textcolor[rgb]{1.00,0.00,0.00}{\textbf{{#1}}}} \newcommand{\NormalTok}[1]{{#1}} % Additional commands for more recent versions of Pandoc \newcommand{\ConstantTok}[1]{\textcolor[rgb]{0.53,0.00,0.00}{{#1}}} \newcommand{\SpecialCharTok}[1]{\textcolor[rgb]{0.25,0.44,0.63}{{#1}}} \newcommand{\VerbatimStringTok}[1]{\textcolor[rgb]{0.25,0.44,0.63}{{#1}}} \newcommand{\SpecialStringTok}[1]{\textcolor[rgb]{0.73,0.40,0.53}{{#1}}} \newcommand{\ImportTok}[1]{{#1}} \newcommand{\DocumentationTok}[1]{\textcolor[rgb]{0.73,0.13,0.13}{\textit{{#1}}}} \newcommand{\AnnotationTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textbf{\textit{{#1}}}}} \newcommand{\CommentVarTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textbf{\textit{{#1}}}}} \newcommand{\VariableTok}[1]{\textcolor[rgb]{0.10,0.09,0.49}{{#1}}} \newcommand{\ControlFlowTok}[1]{\textcolor[rgb]{0.00,0.44,0.13}{\textbf{{#1}}}} \newcommand{\OperatorTok}[1]{\textcolor[rgb]{0.40,0.40,0.40}{{#1}}} \newcommand{\BuiltInTok}[1]{{#1}} \newcommand{\ExtensionTok}[1]{{#1}} \newcommand{\PreprocessorTok}[1]{\textcolor[rgb]{0.74,0.48,0.00}{{#1}}} \newcommand{\AttributeTok}[1]{\textcolor[rgb]{0.49,0.56,0.16}{{#1}}} \newcommand{\InformationTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textbf{\textit{{#1}}}}} \newcommand{\WarningTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textbf{\textit{{#1}}}}} % Define a nice break command that doesn't care if a line doesn't already % exist. \def\br{\hspace*{\fill} \\* } % Math Jax compatibility definitions \def\gt{>} \def\lt{<} \let\Oldtex\TeX \let\Oldlatex\LaTeX \renewcommand{\TeX}{\textrm{\Oldtex}} \renewcommand{\LaTeX}{\textrm{\Oldlatex}} % Document parameters % Document title \title{Sage and Latex interaction} \author{Sebastiano Tronto - \texttt{sebastiano.tronto@uni.lu}} \date{2021-05-07} % Pygments definitions \makeatletter \def\PY@reset{\let\PY@it=\relax \let\PY@bf=\relax% \let\PY@ul=\relax \let\PY@tc=\relax% \let\PY@bc=\relax \let\PY@ff=\relax} \def\PY@tok#1{\csname PY@tok@#1\endcsname} \def\PY@toks#1+{\ifx\relax#1\empty\else% \PY@tok{#1}\expandafter\PY@toks\fi} \def\PY@do#1{\PY@bc{\PY@tc{\PY@ul{% \PY@it{\PY@bf{\PY@ff{#1}}}}}}} \def\PY#1#2{\PY@reset\PY@toks#1+\relax+\PY@do{#2}} \expandafter\def\csname PY@tok@w\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.73,0.73}{##1}}} \expandafter\def\csname PY@tok@c\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}} \expandafter\def\csname PY@tok@cp\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.74,0.48,0.00}{##1}}} \expandafter\def\csname PY@tok@k\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}} \expandafter\def\csname PY@tok@kp\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}} \expandafter\def\csname PY@tok@kt\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.69,0.00,0.25}{##1}}} \expandafter\def\csname PY@tok@o\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}} \expandafter\def\csname PY@tok@ow\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.67,0.13,1.00}{##1}}} \expandafter\def\csname PY@tok@nb\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}} \expandafter\def\csname PY@tok@nf\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.00,1.00}{##1}}} \expandafter\def\csname PY@tok@nc\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.00,1.00}{##1}}} \expandafter\def\csname PY@tok@nn\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.00,1.00}{##1}}} \expandafter\def\csname PY@tok@ne\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.82,0.25,0.23}{##1}}} \expandafter\def\csname PY@tok@nv\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.10,0.09,0.49}{##1}}} \expandafter\def\csname PY@tok@no\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.53,0.00,0.00}{##1}}} \expandafter\def\csname PY@tok@nl\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.63,0.63,0.00}{##1}}} \expandafter\def\csname PY@tok@ni\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.60,0.60,0.60}{##1}}} \expandafter\def\csname PY@tok@na\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.49,0.56,0.16}{##1}}} \expandafter\def\csname PY@tok@nt\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}} \expandafter\def\csname PY@tok@nd\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.67,0.13,1.00}{##1}}} \expandafter\def\csname PY@tok@s\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}} \expandafter\def\csname PY@tok@sd\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}} \expandafter\def\csname PY@tok@si\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.73,0.40,0.53}{##1}}} \expandafter\def\csname PY@tok@se\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.73,0.40,0.13}{##1}}} \expandafter\def\csname PY@tok@sr\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.40,0.53}{##1}}} \expandafter\def\csname PY@tok@ss\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.10,0.09,0.49}{##1}}} \expandafter\def\csname PY@tok@sx\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}} \expandafter\def\csname PY@tok@m\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}} \expandafter\def\csname PY@tok@gh\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.00,0.50}{##1}}} \expandafter\def\csname PY@tok@gu\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.50,0.00,0.50}{##1}}} \expandafter\def\csname PY@tok@gd\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.63,0.00,0.00}{##1}}} \expandafter\def\csname PY@tok@gi\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.63,0.00}{##1}}} \expandafter\def\csname PY@tok@gr\endcsname{\def\PY@tc##1{\textcolor[rgb]{1.00,0.00,0.00}{##1}}} \expandafter\def\csname PY@tok@ge\endcsname{\let\PY@it=\textit} \expandafter\def\csname PY@tok@gs\endcsname{\let\PY@bf=\textbf} \expandafter\def\csname PY@tok@gp\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.00,0.50}{##1}}} \expandafter\def\csname PY@tok@go\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.53,0.53,0.53}{##1}}} \expandafter\def\csname PY@tok@gt\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.27,0.87}{##1}}} \expandafter\def\csname PY@tok@err\endcsname{\def\PY@bc##1{\setlength{\fboxsep}{0pt}\fcolorbox[rgb]{1.00,0.00,0.00}{1,1,1}{\strut ##1}}} \expandafter\def\csname PY@tok@kc\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}} \expandafter\def\csname PY@tok@kd\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}} \expandafter\def\csname PY@tok@kn\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}} \expandafter\def\csname PY@tok@kr\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}} \expandafter\def\csname PY@tok@bp\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}} \expandafter\def\csname PY@tok@fm\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.00,1.00}{##1}}} \expandafter\def\csname PY@tok@vc\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.10,0.09,0.49}{##1}}} \expandafter\def\csname PY@tok@vg\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.10,0.09,0.49}{##1}}} \expandafter\def\csname PY@tok@vi\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.10,0.09,0.49}{##1}}} \expandafter\def\csname PY@tok@vm\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.10,0.09,0.49}{##1}}} \expandafter\def\csname PY@tok@sa\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}} \expandafter\def\csname PY@tok@sb\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}} \expandafter\def\csname PY@tok@sc\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}} \expandafter\def\csname PY@tok@dl\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}} \expandafter\def\csname PY@tok@s2\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}} \expandafter\def\csname PY@tok@sh\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}} \expandafter\def\csname PY@tok@s1\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}} \expandafter\def\csname PY@tok@mb\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}} \expandafter\def\csname PY@tok@mf\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}} \expandafter\def\csname PY@tok@mh\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}} \expandafter\def\csname PY@tok@mi\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}} \expandafter\def\csname PY@tok@il\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}} \expandafter\def\csname PY@tok@mo\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}} \expandafter\def\csname PY@tok@ch\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}} \expandafter\def\csname PY@tok@cm\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}} \expandafter\def\csname PY@tok@cpf\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}} \expandafter\def\csname PY@tok@c1\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}} \expandafter\def\csname PY@tok@cs\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}} \def\PYZbs{\char`\\} \def\PYZus{\char`\_} \def\PYZob{\char`\{} \def\PYZcb{\char`\}} \def\PYZca{\char`\^} \def\PYZam{\char`\&} \def\PYZlt{\char`\<} \def\PYZgt{\char`\>} \def\PYZsh{\char`\#} \def\PYZpc{\char`\%} \def\PYZdl{\char`\$} \def\PYZhy{\char`\-} \def\PYZsq{\char`\'} \def\PYZdq{\char`\"} \def\PYZti{\char`\~} % for compatibility with earlier versions \def\PYZat{@} \def\PYZlb{[} \def\PYZrb{]} \makeatother % For linebreaks inside Verbatim environment from package fancyvrb. \makeatletter \newbox\Wrappedcontinuationbox \newbox\Wrappedvisiblespacebox \newcommand*\Wrappedvisiblespace {\textcolor{red}{\textvisiblespace}} \newcommand*\Wrappedcontinuationsymbol {\textcolor{red}{\llap{\tiny$\m@th\hookrightarrow$}}} \newcommand*\Wrappedcontinuationindent {3ex } \newcommand*\Wrappedafterbreak {\kern\Wrappedcontinuationindent\copy\Wrappedcontinuationbox} % Take advantage of the already applied Pygments mark-up to insert % potential linebreaks for TeX processing. % {, <, #, %, $, ' and ": go to next line. % _, }, ^, &, >, - and ~: stay at end of broken line. % Use of \textquotesingle for straight quote. \newcommand*\Wrappedbreaksatspecials {% \def\PYGZus{\discretionary{\char`\_}{\Wrappedafterbreak}{\char`\_}}% \def\PYGZob{\discretionary{}{\Wrappedafterbreak\char`\{}{\char`\{}}% \def\PYGZcb{\discretionary{\char`\}}{\Wrappedafterbreak}{\char`\}}}% \def\PYGZca{\discretionary{\char`\^}{\Wrappedafterbreak}{\char`\^}}% \def\PYGZam{\discretionary{\char`\&}{\Wrappedafterbreak}{\char`\&}}% \def\PYGZlt{\discretionary{}{\Wrappedafterbreak\char`\<}{\char`\<}}% \def\PYGZgt{\discretionary{\char`\>}{\Wrappedafterbreak}{\char`\>}}% \def\PYGZsh{\discretionary{}{\Wrappedafterbreak\char`\#}{\char`\#}}% \def\PYGZpc{\discretionary{}{\Wrappedafterbreak\char`\%}{\char`\%}}% \def\PYGZdl{\discretionary{}{\Wrappedafterbreak\char`\$}{\char`\$}}% \def\PYGZhy{\discretionary{\char`\-}{\Wrappedafterbreak}{\char`\-}}% \def\PYGZsq{\discretionary{}{\Wrappedafterbreak\textquotesingle}{\textquotesingle}}% \def\PYGZdq{\discretionary{}{\Wrappedafterbreak\char`\"}{\char`\"}}% \def\PYGZti{\discretionary{\char`\~}{\Wrappedafterbreak}{\char`\~}}% } % Some characters . , ; ? ! / are not pygmentized. % This macro makes them "active" and they will insert potential linebreaks \newcommand*\Wrappedbreaksatpunct {% \lccode`\~`\.\lowercase{\def~}{\discretionary{\hbox{\char`\.}}{\Wrappedafterbreak}{\hbox{\char`\.}}}% \lccode`\~`\,\lowercase{\def~}{\discretionary{\hbox{\char`\,}}{\Wrappedafterbreak}{\hbox{\char`\,}}}% \lccode`\~`\;\lowercase{\def~}{\discretionary{\hbox{\char`\;}}{\Wrappedafterbreak}{\hbox{\char`\;}}}% \lccode`\~`\:\lowercase{\def~}{\discretionary{\hbox{\char`\:}}{\Wrappedafterbreak}{\hbox{\char`\:}}}% \lccode`\~`\?\lowercase{\def~}{\discretionary{\hbox{\char`\?}}{\Wrappedafterbreak}{\hbox{\char`\?}}}% \lccode`\~`\!\lowercase{\def~}{\discretionary{\hbox{\char`\!}}{\Wrappedafterbreak}{\hbox{\char`\!}}}% \lccode`\~`\/\lowercase{\def~}{\discretionary{\hbox{\char`\/}}{\Wrappedafterbreak}{\hbox{\char`\/}}}% \catcode`\.\active \catcode`\,\active \catcode`\;\active \catcode`\:\active \catcode`\?\active \catcode`\!\active \catcode`\/\active \lccode`\~`\~ } \makeatother \let\OriginalVerbatim=\Verbatim \makeatletter \renewcommand{\Verbatim}[1][1]{% %\parskip\z@skip \sbox\Wrappedcontinuationbox {\Wrappedcontinuationsymbol}% \sbox\Wrappedvisiblespacebox {\FV@SetupFont\Wrappedvisiblespace}% \def\FancyVerbFormatLine ##1{\hsize\linewidth \vtop{\raggedright\hyphenpenalty\z@\exhyphenpenalty\z@ \doublehyphendemerits\z@\finalhyphendemerits\z@ \strut ##1\strut}% }% % If the linebreak is at a space, the latter will be displayed as visible % space at end of first line, and a continuation symbol starts next line. % Stretch/shrink are however usually zero for typewriter font. \def\FV@Space {% \nobreak\hskip\z@ plus\fontdimen3\font minus\fontdimen4\font \discretionary{\copy\Wrappedvisiblespacebox}{\Wrappedafterbreak} {\kern\fontdimen2\font}% }% % Allow breaks at special characters using \PYG... macros. \Wrappedbreaksatspecials % Breaks at punctuation characters . , ; ? ! and / need catcode=\active \OriginalVerbatim[#1,codes*=\Wrappedbreaksatpunct]% } \makeatother % Exact colors from NB \definecolor{incolor}{HTML}{303F9F} \definecolor{outcolor}{HTML}{D84315} \definecolor{cellborder}{HTML}{CFCFCF} \definecolor{cellbackground}{HTML}{F7F7F7} % prompt \makeatletter \newcommand{\boxspacing}{\kern\kvtcb@left@rule\kern\kvtcb@boxsep} \makeatother \newcommand{\prompt}[4]{ \ttfamily\llap{{\color{#2}[#3]:\hspace{3pt}#4}}\vspace{-\baselineskip} } % Prevent overflowing lines due to hard-to-break entities \sloppy % Setup hyperref package \hypersetup{ breaklinks=true, % so long urls are correctly broken across lines colorlinks=true, urlcolor=urlcolor, linkcolor=linkcolor, citecolor=citecolor, } % Slightly bigger margins than the latex defaults \geometry{verbose,tmargin=1in,bmargin=1in,lmargin=1in,rmargin=1in} \begin{document} \maketitle It can happen that you need to include the results of your Sage computations and/or Sage code inside a LaTeX document. Luckily Sage provides some functions to translate its objects into LaTeX, and the listings package for LaTeX can be used to include any code (Sage, Python or any other language) in a LaTeX document. In this document we will describe some of these interactions between LaTeX and Sage. \hypertarget{the-show-command}{% \section{\texorpdfstring{The \texttt{show()} command}{The show() command}}\label{the-show-command}} \textbf{Reference:} {[}\href{https://doc.sagemath.org/html/en/reference/repl/sage/repl/display/pretty_print.html}{1}{]} (\texttt{show()} is just an alternative name for \texttt{pretty\_print()}). With this command Sage will generate a picture displaying the object. The result depends on the object itself: most of them will be typeset in Latex, but for example graphics primitives (such as plots) will be displayed as pictures. You can see it as an alternative to \texttt{print()}. \begin{tcolorbox}[breakable, size=fbox, boxrule=1pt, pad at break*=1mm,colback=cellbackground, colframe=cellborder] \prompt{In}{incolor}{4}{\boxspacing} \begin{Verbatim}[commandchars=\\\{\}] \PY{n}{s} \PY{o}{=} \PY{p}{(}\PY{n}{e}\PY{o}{\PYZca{}}\PY{n}{x}\PY{p}{)}\PY{o}{.}\PY{n}{series}\PY{p}{(}\PY{n}{x}\PY{o}{==}\PY{l+m+mi}{0}\PY{p}{,} \PY{l+m+mi}{4}\PY{p}{)} \PY{n}{M} \PY{o}{=} \PY{n}{matrix}\PY{p}{(}\PY{p}{[}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{,}\PY{l+m+mi}{3}\PY{p}{]}\PY{p}{,}\PY{p}{[}\PY{l+m+mi}{4}\PY{p}{,}\PY{l+m+mi}{5}\PY{p}{,}\PY{l+m+mi}{6}\PY{p}{]}\PY{p}{,}\PY{p}{[}\PY{l+m+mi}{8}\PY{p}{,}\PY{l+m+mi}{9}\PY{p}{,}\PY{l+m+mi}{10}\PY{p}{]}\PY{p}{]}\PY{p}{)} \PY{n+nb}{print}\PY{p}{(}\PY{n}{s}\PY{p}{)} \PY{n}{show}\PY{p}{(}\PY{n}{s}\PY{p}{)} \PY{n+nb}{print}\PY{p}{(}\PY{n}{M}\PY{p}{)} \PY{n}{show}\PY{p}{(}\PY{n}{M}\PY{p}{)} \PY{n+nb}{print}\PY{p}{(}\PY{n}{pi}\PY{p}{)} \PY{n}{show}\PY{p}{(}\PY{n}{pi}\PY{p}{)} \end{Verbatim} \end{tcolorbox} \begin{Verbatim}[commandchars=\\\{\}] 1 + 1*x + 1/2*x\^{}2 + 1/6*x\^{}3 + Order(x\^{}4) \end{Verbatim} \begin{math} \newcommand{\Bold}[1]{\mathbf{#1}}1 + 1 x + \frac{1}{2} x^{2} + \frac{1}{6} x^{3} + \mathcal{O}\left(x^{4}\right) \end{math} \begin{Verbatim}[commandchars=\\\{\}] [ 1 2 3] [ 4 5 6] [ 8 9 10] \end{Verbatim} \begin{math} \newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrr} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 8 & 9 & 10 \end{array}\right) \end{math} \begin{Verbatim}[commandchars=\\\{\}] pi \end{Verbatim} \begin{math} \newcommand{\Bold}[1]{\mathbf{#1}}\pi \end{math} In a Jupyter notebook, the results above are displayed using \href{https://www.mathjax.org/}{MathJax}. If you are running this code in an interactive console (terminal) instead of a Jupyter notebook, you will get the Latex source code for those objects. You can force this behavior by using the \texttt{latex()} command. \hypertarget{the-latex-command}{% \section{\texorpdfstring{The \texttt{latex()} command}{The latex() command}}\label{the-latex-command}} \textbf{Reference:} {[}\href{https://doc.sagemath.org/html/en/reference/misc/sage/misc/latex.html}{2}{]} This command is potentially very useful if you need to include the results of Sage computations in a Latex file, especially with complex objects like matrices or very large polynomials. Technically, this is a function that returns a string, so you need to \texttt{print()} it to see the result. \begin{tcolorbox}[breakable, size=fbox, boxrule=1pt, pad at break*=1mm,colback=cellbackground, colframe=cellborder] \prompt{In}{incolor}{5}{\boxspacing} \begin{Verbatim}[commandchars=\\\{\}] \PY{n+nb}{print}\PY{p}{(}\PY{n}{latex}\PY{p}{(}\PY{n}{s}\PY{p}{)}\PY{p}{)} \PY{n+nb}{print}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+se}{\PYZbs{}n}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)} \PY{n+nb}{print}\PY{p}{(}\PY{n}{latex}\PY{p}{(}\PY{n}{M}\PY{p}{)}\PY{p}{)} \end{Verbatim} \end{tcolorbox} \begin{Verbatim}[commandchars=\\\{\}] 1 + 1 x + \textbackslash{}frac\{1\}\{2\} x\^{}\{2\} + \textbackslash{}frac\{1\}\{6\} x\^{}\{3\} + \textbackslash{}mathcal\{O\}\textbackslash{}left(x\^{}\{4\}\textbackslash{}right) \textbackslash{}left(\textbackslash{}begin\{array\}\{rrr\} 1 \& 2 \& 3 \textbackslash{}\textbackslash{} 4 \& 5 \& 6 \textbackslash{}\textbackslash{} 8 \& 9 \& 10 \textbackslash{}end\{array\}\textbackslash{}right) \end{Verbatim} Interestingly, Sage can use matplotlib's PGF backend to generate Latex code for a plot. (PGF is the graphics language underlying TikZ, like TeX is the language underlying Latex). \begin{tcolorbox}[breakable, size=fbox, boxrule=1pt, pad at break*=1mm,colback=cellbackground, colframe=cellborder] \prompt{In}{incolor}{15}{\boxspacing} \begin{Verbatim}[commandchars=\\\{\}] \PY{c+c1}{\PYZsh{}latex(plot(x\PYZca{}2)) \PYZsh{} The output is more than 20 pages long} \end{Verbatim} \end{tcolorbox} It is probably easier to just generate the picture and include that in your Latex document with \texttt{\textbackslash{}includegraphics}. \hypertarget{a-latex-name-for-your-variables}{% \subsection{A Latex name for your variables}\label{a-latex-name-for-your-variables}} \textbf{Reference:} {[}\href{https://doc.sagemath.org/html/en/reference/calculus/sage/calculus/var.html}{3}{]} Sometimes you might want to use variables and functions that have, for example, a Greek letter as a name. You can tell Sage that you want them displayed this way when you declare them: \begin{tcolorbox}[breakable, size=fbox, boxrule=1pt, pad at break*=1mm,colback=cellbackground, colframe=cellborder] \prompt{In}{incolor}{16}{\boxspacing} \begin{Verbatim}[commandchars=\\\{\}] \PY{n}{var}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{epsilon}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{latex\PYZus{}name}\PY{o}{=}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+se}{\PYZbs{}\PYZbs{}}\PY{l+s+s2}{varepsilon}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)} \PY{n}{function}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{phi1}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{latex\PYZus{}name}\PY{o}{=}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+se}{\PYZbs{}\PYZbs{}}\PY{l+s+s2}{phi\PYZus{}1}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)} \PY{n+nb}{print}\PY{p}{(}\PY{n}{phi1}\PY{p}{(}\PY{n}{epsilon}\PY{p}{)}\PY{p}{)} \PY{n}{show}\PY{p}{(}\PY{n}{phi1}\PY{p}{(}\PY{n}{epsilon}\PY{p}{)} \PY{o}{+} \PY{n}{e}\PY{o}{\PYZca{}}\PY{n}{epsilon}\PY{p}{)} \PY{n}{latex}\PY{p}{(}\PY{n}{phi1}\PY{p}{(}\PY{n}{epsilon}\PY{p}{)} \PY{o}{+} \PY{n}{e}\PY{o}{\PYZca{}}\PY{n}{epsilon}\PY{p}{)} \end{Verbatim} \end{tcolorbox} \begin{Verbatim}[commandchars=\\\{\}] phi1(epsilon) \end{Verbatim} \begin{math} \newcommand{\Bold}[1]{\mathbf{#1}}e^{{\varepsilon}} + \phi_1\left({\varepsilon}\right) \end{math} \begin{tcolorbox}[breakable, size=fbox, boxrule=.5pt, pad at break*=1mm, opacityfill=0] \prompt{Out}{outcolor}{16}{\boxspacing} \begin{Verbatim}[commandchars=\\\{\}] e\^{}\{\{\textbackslash{}varepsilon\}\} + \textbackslash{}phi\_1\textbackslash{}left(\{\textbackslash{}varepsilon\}\textbackslash{}right) \end{Verbatim} \end{tcolorbox} \textbf{Warning:} You need to use two backspaces \texttt{\textbackslash{}\textbackslash{}}. The reason is that in Python (like in many other programming languages) the backslash symbol inside a string is used to print special characters, such as a newline \texttt{\textbackslash{}n}. \hypertarget{from-jupyter-to-latex}{% \section{From Jupyter to Latex}\label{from-jupyter-to-latex}} \textbf{Reference:} {[}\href{https://nbconvert.readthedocs.io/en/latest/}{4}{]} From the Jupyter menu \texttt{File\ \textgreater{}\ Download\ as} you can choose to download your work in many formats, among which there are also Latex and pdf. Personally I prefer downloading the .tex file, so then I can change the title, add an author name and make any other change I like before compiling it into a pdf file. If you choose to download the pdf file, you might need to install some extra packages. For example I had to install \href{https://pandoc.org/}{\texttt{pandoc}}, \texttt{texlive-XeTeX} and \texttt{texlive-Xdvi}, but this depends on your operating system and Latex distribution. \hypertarget{sagetex}{% \section{SageTex}\label{sagetex}} \textbf{Reference:} {[}\href{https://doc.sagemath.org/html/en/tutorial/sagetex.html}{5}{]} With SageTex it is possible to run Sage commands directly inside Latex, using the \texttt{\textbackslash{}sage\{\}} command. In this way you don't need to run your Sage code first and then copy the results in Latex. It can be useful especially for short Sage commands. You might need to take some extra steps to make this work on your system, see the link above. \hypertarget{the-latex-listings-package}{% \section{\texorpdfstring{The Latex \texttt{listings} package}{The Latex listings package}}\label{the-latex-listings-package}} \textbf{References:} {[}\href{https://en.wikibooks.org/wiki/LaTeX/Source_Code_Listings}{6}{]} and {[}\href{https://ftp.snt.utwente.nl/pub/software/tex/macros/latex/contrib/listings/listings.pdf}{7}{]} If you want to include some code (Sage, Python or anything else) in a Latex document you can use the listings package. \begin{verbatim} \usepackage{listings} ... \begin{lstlisting}[language=Python] for i in range(0,100): if i%5 == 0: print("Multiple of 5!") \end{lstlisting} \end{verbatim} You need to specify the language you are using with the \texttt{language=} option. This option can also be set at the beginning of the document using the \texttt{\textbackslash{}lstset\{language=Python\}} command. As an alternative, you can include a file directly without copying the code into the tex file, like you would do for a picture: \begin{verbatim} \lstinputlisting[language=Python]{file.py} \end{verbatim} It is technically possible to include Latex listings in a markdown cell of the Jupyter notebook using \href{https://jupyter-contrib-nbextensions.readthedocs.io/en/latest/nbextensions/latex_envs/README.html}{this package}, but it does not make much sense. So we will move to a Latex editor for the examples. \begin{tcolorbox}[breakable, size=fbox, boxrule=1pt, pad at break*=1mm,colback=cellbackground, colframe=cellborder] \prompt{In}{incolor}{ }{\boxspacing} \begin{Verbatim}[commandchars=\\\{\}] \end{Verbatim} \end{tcolorbox} % Add a bibliography block to the postdoc \end{document}