New Opportunities for the Formal Proof of Computational Real Geometry? (Extended Abstract)

The purpose of this paper is to explore the question "to what extent could we produce formal, machine-verifiable, proofs in real algebraic geometry?" The question has been asked before but as yet the leading algorithms for answering such questions have not been formalised. We present a thesis that a new algorithm for ascertaining satisfiability of formulae over the reals via Cylindrical Algebraic Coverings [Abraham, Davenport, England, Kremer, \emph{Deciding the Consistency of Non-Linear Real Arithmetic Constraints with a Conflict Driver Search Using Cylindrical Algebraic Coverings}, 2020] might provide trace and outputs that allow the results to be more susceptible to machine verification than those of competing algorithms.

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