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Alex Bortolotti

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Preprint Sep 2026

Ideal Membership in Polynomial Calculus: Complexity and Reductions

The Ideal Membership Problem (IMP) asks whether a polynomial f belongs to an idealof Q[x_1, ..., x_n]. Polynomial Calculus (PC) certifies membership by deriving f from the generators, and a degree-d derivation needs at most n^O(d) steps. We write PC-IMPd for the problem of producing a degree-bounded PC certificate, and...

Alex Bortolotti, M. Mastrolilli · 0 citations

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