Computation, on Macsyma, of the minimal differential representation of noncommutative polynomials

Abstract

We present here a package of Macsyma programs, allowing the manipulation of words, and noncommutative power series over a finite alphabet. On the basis of the works of Fliess and Reutenauer concerning the local minimal realization of analytical systems, we present an algorithm allowing the computation of the local minimal realization of finite generating power series. We describe that algorithm in the algebraic computation language, Macsyma.