# Some Complexity Results for Polynomial Ideals

@article{Mayr1997SomeCR, title={Some Complexity Results for Polynomial Ideals}, author={Ernst W. Mayr}, journal={J. Complex.}, year={1997}, volume={13}, pages={303-325} }

In this paper, we survey some of our new results on the complexity of a number of problems related to polynomial ideals. We consider multivariate polynomials over some ring, like the integers or the rationals. For instance, a polynomial ideal membership problem is a (w+ 1)-tupleP= (f,g1,g2, ?gwwherefand thegiare multivariate polynomials, and the problem is to determine whetherfis in the ideal generated by thegi. For polynomials over the integers or rationals, this problem is known to be…

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