Computing the characteristic polynomial of multivariate polynomial matrices given by straight-line programs Original Research Article

In this paper, we present algorithms for representing and computing with multivariate polynomials and multivariate polynomial matrices, which are given by straight-line programs that are implemented as arithmetic circuits. This data structure allows the representation and evaluation of the characteristic polynomials of these matrices for problems that otherwise could not be done because of intermediate expression swell. The computations are possible even when the total degree, the number of variables, or monomial terms makes handling the polynomials unmanageable by the usual methods employed in traditional computer algebra systems. To present a clear picture how this technique works in a computer algebra system, we introduce some results from the prototype system TERA.