Computing Polynomial Composition Factors and Inverses of Automorphisms in Polynomial Time
Dickerson, Matthew T.
The problem of determining when an endomorphism on a polynomial ring is an automorphism and, when it is, the problem of computing its inverse are long standing problems which have received much attention both recently and in the past [BCW], [N], [NS], [SS]. There has also been much attention given recently to various problems relating to the functional decomposition of polynomials [AT], [BZ], [D], [G1], [G2], [GKL], [KL]. In this paper, we present the first polynomial time algorithm for computing the left composition factor of a multivariate polynomial decomposition and we use that result in the first polynomial time algorithm for computing the inverse of an automorphism on a polynomial ring. Finally, we show how these algorithms can be used to determine when an endomorphism is an automorphism.
computer science; technical report
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