Journal of Symbolic Computation 13 (1992): 209-220.
The Inverse of an Automorphism in Polynomial Time
Matthew T. Dickerson
Abstract
In this paper we present a polynomial time algorithm for computing the inverse of an automorphism over the polynomial ring K[X] (where X=x1,x2,...,xn). The algorithm works over any commutative ring K, and in the case when K is a field, provides an exponential time solution to the problem of determining when an endomorphism is invertible.