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Conclusions and Future Developments

PHC is a general-purpose solver for polynomial systems that features recent research advances in root-counting methods. The software package is portable via the gnu-ada compiler. Practical evidence for the performance of its black-box solver has been given on a large set of applications.

A recent new exciting development concerns homotopies that solve problems in enumerative geometry, see [Sottile 1997] and  [Huber, Sottile and Sturmfels 1998].

The author acknowledges
the technical assistance, usage of PHC, con...
 ...for many helpful comments
and useful suggestions on the first version.\end{acks}

Jan Verschelde