The MAGMA algebra system I: the user language
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
Algebraic and symbolic manipulation of Poisson series
Journal of Symbolic Computation
Comparing the speed of programs for sparse polynomial multiplication
ACM SIGSAM Bulletin
Communications of the ACM - Designing for the mobile device
Parallel sparse polynomial multiplication using heaps
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Parallel operations of sparse polynomials on multicores: I. multiplication and Poisson bracket
Proceedings of the 4th International Workshop on Parallel and Symbolic Computation
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We present a high performance algorithm for the parallel multiplication of sparse multivariate polynomials on modern computer architectures. The algorithm is built on three main concepts: a cache-friendly hash table implementation for the storage of polynomial terms in distributed form, a statistical method for the estimation of the size of the multiplication result, and the use of Kronecker substitution as a homomorphic hash function. The algorithm achieves high performance by promoting data access patterns that favour temporal and spatial locality of reference. We present benchmarks comparing our algorithm to routines of other computer algebra systems, both in sequential and parallel mode.