\frametitle {I started Sage in 2005 \hfill \includegraphics [height=.07\textheight ]{graphics/python}\hspace {1em}\includegraphics [height=.07\textheight ]{graphics/pari}}\begin {block}{SAGE}
\underline{S}oftware for \underline{A}rithmetic \underline{G}eometry \underline{E}xperimentation
\end{block}
\begin{itemize}
\item I needed an {\em open source} alternative to Magma.
David Joyner (coding theorist) had similar concerns.
\item SAGE in 2005 -- number theory (PARI) and coding theory (GAP) -- no
symbolic calculus or numerical computation.
\end{itemize}
\begin{block}{Number theory \& Coding theory: started out very technical}
\begin{lstlisting}[]
sage: E = EllipticCurve('389a'); E
Elliptic Curve defined by y^2 + y = x^3 + x^2 - 2*x
sage: E.gens()
[(-1 : 1 : 1), (0 : -1 : 1)]
sage: G = matrix(GF(5), 4, 7, [1,1,1,0,0,0,0,1,0,0,1,1,...
sage: C = LinearCode(G); C
Linear code of length 7, dimension 4 over Finite Field ...
sage: C.minimum_distance()
3
\end{lstlisting}
\end{block}