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Ideal Membership in Polynomial Calculus: Complexity and Reductions
The Ideal Membership Problem (IMP) asks whether a polynomial f belongs to an ideal of 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
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