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0?’, where 
{=,>,<}. An implementation of the procedure in Maple and PVS exploits the existing Maple, PVS and QEPCAD connections. It is at present limited to those twice differentiable functions whose derivatives are rational functions (rationally differentiable). This procedure is particularly applicable to the analysis of control systems in determining important properties such as stability.
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doi:10.1016/j.entcs.2005.11.023 
Copyright © 2006 Elsevier B.V. All rights reserved.
Quantifier Elimination over Algebraically Closed Fields in a Proof Assistant using a Computer Algebra System
Available online 11 March 2006.
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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.
Keywords: Theorem Proving; Computer Algebra; Algebraically Closed Fields; Coq; Maple
