In this paper we present a polynomial time algorithm for computing the inverse of an automorphism over a polynomial ring K[x]. 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. © 1991, Academic Press Limited. All rights reserved.
Dickerson, M. (1992). The inverse of an automorphism in polynomial time. Journal of Symbolic Computation, 13(2), 209–220. https://doi.org/10.1016/S0747-7171(08)80090-9