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Section: New Results

Decision procedures for polynomials

Participant : Yves Bertot.

Following up on the work in previous years around Bernstein Polynomials, we implemented a decision procedure for guaranteeing the sign of a polynomial function inside an interval, using Bernstein polynomials and dichotomy. In the long run, we hope to explore two approaches, one based on the off-line computation of certificates for sub-intervals (these certificates are easy to verify), and one based on implementing computational reflection. This approach should also generalize quite easily to multi-variate polynomials.