Added files

1 files changed, 634 insertions, 0 deletions

diff --git a/src/Lecture6/notebook/9-SageLatex.tex b/src/Lecture6/notebook/9-SageLatex.tex
new file mode 100644
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--- /dev/null
+++ b/src/Lecture6/notebook/9-SageLatex.tex
@@ -0,0 +1,634 @@
+\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}