Deciding Univariate Polynomial Problems Using Untrusted Certificates in Isabelle/HOL06 Sep 2017
We present a proof procedure for univariate real polynomial problems in Isabelle/HOL. The core mathematics of our procedure is based on univariate cylindrical algebraic decomposition. We follow the approach of untrusted certiﬁcates, separating solving from verifying: eﬃcient external tools perform expensive real algebraic computations, producing evidence that is formally checked within Isabelle’s logic. This allows us to exploit highly-tuned computer algebra systems like Mathematica to guide our procedure without impacting the correctness of its results. We present experiments demonstrating the eﬃcacy of this approach, in many cases yielding orders of magnitude improvements over previous methods.