High order derivatives and decomposition of multivariate polynomials

Abstract

In this paper, we present an improved method for decomposing multivariate polynomials. This problem, also known as the Functional Decomposition Problem (FDP) [17, 9, 27], is classical in computer algebra (e.g. [17, 18, 19, 23, 24, 7, 25]). Here, we propose to use high order partial derivatives to improve the algorithm described in [14]. Our new approach is more simple, and in some sense more natural. From a practical point of view, this new approach will lead to more efficient algorithms. The complexity of our algorithms will depend of the degree of the input polynomials, and the ratio n/u between the number of variables/polynomials. Copyright 2009 ACM.