The Altran system for rational function manipulation — a survey
Communications of the ACM
A lisp-language Mathematica-to-lisp translator
ACM SIGSAM Bulletin
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
Parallel sparse polynomial division using heaps
Proceedings of the 4th International Workshop on Parallel and Symbolic Computation
TRIP: a computer algebra system dedicated to celestial mechanics and perturbation series
ACM Communications in Computer Algebra
Sparse polynomial multiplication and division in Maple 14
ACM Communications in Computer Algebra
Sparse polynomial division using a heap
Journal of Symbolic Computation
Development of TRIP: fast sparse multivariate polynomial multiplication using burst tries
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part II
On the bit-complexity of sparse polynomial and series multiplication
Journal of Symbolic Computation
Parallel sparse polynomial multiplication on modern hardware architectures
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
Practical Gröbner basis computation
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
On the complexity of multivariate blockwise polynomial multiplication
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
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How should one design and implement a program for the multiplication of sparse polynomials? This is a simple question, necessarily addressed by the builders of any computer algebra system (CAS). To examine a few options we start with a single easily-stated computation which we believe represents a useful benchmark of "medium difficulty" for CAS designs. We describe a number of design options and their effects on performance. We also examine the performance of a variety of commercial and freely-distributed systems. Important considerations include the cost of high-precision (exact) integer arithmetic and the effective use of cache memory.