On Polynomial Ideals, Their Complexity, and Applications

@inproceedings{Mayr1995OnPI,
  title={On Polynomial Ideals, Their Complexity, and Applications},
  author={Ernst W. Mayr},
  booktitle={FCT},
  year={1995}
}
  • E. Mayr
  • Published in FCT 22 August 1995
  • Mathematics
A polynomial ideal membership problem is a (w+1)-tuple P=(f, g1,g2, ..., g w ) where f and the g i are multivariate polynomials over some ring, and the problem is to determine whether f is in the ideal generated by the g i . For polynomials over the integers or rationals, it is known that this problem is exponential space complete. We discuss complexity results known for a number of problems related to polynomial ideals, like the word problem for commutative semigroups, a quantitative version… 
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