\begin{frame}{\LARGE 6. An Implementation of $\Gamma$.}
If I didn't implement I wouldn't believe myself.
\vskip 2mm
Written in Mathematica~\cite{Wolfram:Mathematica}, available as the notebook {\tt Gamma.nb} at \url{http://drorbn.net/mo21/ap}. Code lines are highlighted in grey, demo lines are plain.
We start with canonical forms for quadratics with rational function coefficients:

\noindent\nbpdfInput{Snips/Gamma/1.pdf}

\end{frame}
\begin{frame}\null
Multiplying and comparing $\Gamma$ objects:

\noindent\nbpdfInput{Snips/Gamma/2.pdf}

No rules for linear operations!
\end{frame}
\begin{frame}\null
Contractions:

\noindent\nbpdfInput{Snips/Gamma/3.pdf}

\end{frame}
\begin{frame}\null
The crossings and the point:

\noindent\nbpdfInput{Snips/Gamma/4.pdf}

\noindent\nbpdfInput{Snips/Gamma/5.pdf}

\end{frame}
\begin{frame}\null
Automatic intelligent contractions:

\noindent\nbpdfInput{Snips/Gamma/6.pdf}

\end{frame}
\begin{frame}\null
Conversions $\calA\leftrightarrow\Gamma$:

\noindent\nbpdfInput{Snips/Gamma/7.pdf}

The conversions are inverses of each other:

\noindent\nbpdfInput{Snips/Gamma/8.pdf}

\noindent\nbpdfOutput{Snips/Gamma/9.pdf}

The conversions commute with contractions:

\noindent\nbpdfInput{Snips/Gamma/10.pdf}

\noindent\nbpdfOutput{Snips/Gamma/11.pdf}

\end{frame}

\begin{frame} {\large The Naik-Stanford Double Delta Move (again)}
\[ \scalebox{0.8}{\input{figs/NaikStanford.pdf_t}} \]

\noindent\nbpdfInput{Snips/Gamma/12.pdf}

\noindent\nbpdfOutput{Snips/Gamma/13.pdf}

\end{frame}

\begin{frame}{\large Conway's Third Identity}
\[ \input{figs/C3.pdf_t} \]

Sorry, $\Gamma$ has nothing to say about that...'
\end{frame}