alphaCertified: Software for certifying solutions to polynomial systems.

Author: Frank Sottile
Author: Jonathon D Hauenstein

Smale's \alpha-theory provides computable certificates that,
for a square system of polynomial equations, Newton iterations
beginning at a given point will converge quadratically, doubling
the precision at each step, to a solution to the system.  
In theory, this may be used to certify the output of a numerical
solver, including certifying that all solutions have been found,
that two numerically computed solutions are distinct, and that
a numerically computed solution is real.

   alphaCertified is a stand-alone software package with a MAPLE 
interface that uses \alpha-theory to compute certificates for
solutions to systems of polynomial equations.

   This talk will briefly recall the main points of Smale's 
\alpha-theory and describe the functionality of alphaCertified.  
It will also include some examples of the application of these 
algorithms to questions that arise in our research, for alphaCertified 
was written as a tool for our work.