Sparse Polynomial Powering Using Heaps

Abstract

Abstract. We modify an old algorithm for expanding powers of dense polynomials to make it work for sparse polynomials, by using a heap to sort monomials. It has better complexity and lower space requirements than other sparse powering algorithms for dense polynomials. We show how to parallelize the method, and compare its performance on a series of benchmark problems to other methods and the Magma and Singular computer algebra systems.

Nemo/Hecke

“…We make use of variants of the sparse algorithms described by Monagan and Pearce for heap-based multiplication [20], exact division and division with remainder [19] and powering [21]. For powering of polynomials with few terms, we make use of the multinomial formula.…”