A polynomial ideal membership problem is an (n+l)-tuple P = (P, P l ,P2 , . . . ,P,~) where p and the Pl are multivariate polynomials over some ring, and the problem is to determine whether p is in the ideal generated by the pi. For polynomials over the integers or rationals, it is known that this problem is exponential space hard. Here, we show that the… (More)