We present a high performance algorithm for multiplying sparse distributed polynomials using a multicore processor. Each core uses a heap of pointers to multiply parts of the polynomials using itsâ€¦ (More)

A common way of implementing multivariate polynomial multiplication and division is to represent polynomials as linked lists of terms sorted in a term ordering and to use repeated merging. Thisâ€¦ (More)

We present a parallel algorithm for exact division of sparse distributed polynomials on a multicore processor. This is a problem with significant data dependencies, so our solution requiresâ€¦ (More)

We present a new algorithm for pseudo-division of sparse multivariate polynomials with integer coefficients. It uses a heap of pointers to simultaneously merge the dividend and partial products,â€¦ (More)

In 1974, Johnson showed how to multiply and divide sparse polynomials using a binary heap. This paper introduces a new algorithm that uses a heap to divide with the same complexity as multiplication.â€¦ (More)

We demonstrate new routines for sparse multivariate polynomial multiplication and division over the integers that we have integrated into Maple 14 through the expand and divide commands. Theseâ€¦ (More)

We present two algorithms for simplifying rational expressions modulo an ideal of the polynomial ring <i>k[x</i><sub>1</sub>, . . . , <i>x<sub>n</sub></i>]. The first method generates the set ofâ€¦ (More)

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 requirementsâ€¦ (More)

We present a compact and parallel C implementation of the F4 algorithm for computing GrÃ¶bner bases which uses Cilk. We give an easy way to parallelize the sparse linear algebra which is the main costâ€¦ (More)