Quantifier Elimination over Algebraically Closed Fields in a Proof Assistant using a Computer Algebra System

Authors:
David Delahaye;Micaela Mayero
Affiliations:
CPR (CEDRIC), CNAM, Paris, France;LCR (LIPN), Université Paris Nord (Paris 13), Villetaneuse, France
Venue:
Electronic Notes in Theoretical Computer Science (ENTCS)
Year:
2006

Citing 8
Cited 1

Quantifier elimination in the theory of an algebraically-closed field

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Abstract

We propose a decision procedure for algebraically closed fields based on a quantifier elimination method. The procedure is intended to build proofs for systems of polynomial equations and inequations. We describe how this procedure can be carried out in a proof assistant using a Computer Algebra system in a purely skeptical way. We present an implementation in the particular framework of Coq and Maple giving some details regarding the interface between the two tools. This allows us to show that a Computer Algebra system can be used not only to bring additional computational power to a proof assistant but also to enhance the automation of such tools.