MASSIVELY-PARALLEL COMPUTATIONS ON MANY-VARIABLE POLYNOMIALS

We show that a multivariate homogeneous polynomial can be represented on a hypercube in such a way that sums, products and partial derivativ es can be performed by massively parallel computers. This representati on is derived from the theoretical results of Beauzamy-Bombieri-Enflo- Montgomery [1]. The norm associated with it, denoted by [.], is itself a very efficient tool: when products of polynomials are performed, th e best constant in inequalities of the form [PQ] greater than or equal to C[P][Q] are provided, and the extremal pairs (that is, the pairs o f polynomials for which the product is as small as possible) can be id entified.