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\noindent{}SAGE is a project that the PI launched 
in January 2005 to create a software
environment for research and experimentation in 
algebra, geometry, number theory,
cryptography, and  numerical computation.
This involves creating the free open 
software SAGE, which is a distribution of mathematics software
that provides  new functionality and is able to create and work with 
objects defined in a wide range of mathematical software packages,
including Axiom, Maple, Mathematica, Macaulay2, Magma, MATLAB,
Octave, Maxima, Singular, and PARI/GP. 

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\noindent{\bf Intellectual Merit:}

\mypar{}SAGE provides powerful tools for advanced 
research mathematics, and
work on SAGE will result in practical implementations
of new algorithms, especially for research in number theory
and cryptography.  The creation of SAGE also
requires solving fundamental problems so that numerous
mathematics programs can be used together.

% When reading a paper that cites
%computations done using SAGE, in many cases readers will 
%be able to verify and extend the results of the 
%computations, and the exact version of SAGE used in the paper
%will always be freely available.


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\noindent{\bf Broader Impact:}
\mypar{}SAGE features a uniform interface to many different 
aspects of computation, which may help unify mathematical
software, and gives researchers
convenient access to a range of different software.
Also, instead of researchers having to pay 
to buy mathematics software, they
will in many cases have the option to use SAGE for free.
At many institutions, purchasing computer software is a significant burden,
and SAGE may help address this problem.
Moreover, because SAGE is free, it is available to undergraduates, high school students, and non-mathematicians, all of whom have contributed
greatly to SAGE development.
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