Ideal Membership in Polynomial Rings over the Integers

@inproceedings{Aschenbrenner2004IdealMI,
title={Ideal Membership in Polynomial Rings over the Integers},
author={Matthias Aschenbrenner and Grete Hermann},
year={2004}
}

We present a new approach to the ideal membership problem for polynomial rings over the integers: given polynomials f0, f1, . . . , fn ∈ Z[X], where X = (X1, . . . , XN ) is an N -tuple of indeterminates, are there g1, . . . , gn ∈ Z[X] such that f0 = g1f1 + · · · + gnfn? We show that the degree of the polynomials g1, . . . , gn can be bounded by (2d)2 O(N log(N+1)) (h+1) where d is the maximum total degree and h the maximum height of the coefficients of f0, . . . , fn. Some related questions… CONTINUE READING

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