The Balance Multiprocessor System
IEEE Micro
Guide to parallel programming on Sequent computer systems: 2nd edition
Guide to parallel programming on Sequent computer systems: 2nd edition
Elements of computer algebra with applications
Elements of computer algebra with applications
GCDHEU: Heuristic polynomial GCD algorithm based on integer GCD computation
Journal of Symbolic Computation
Parallel univariate polynomial factorization on shared-memory multiprocessors
ISSAC '90 Proceedings of the international symposium on Symbolic and algebraic computation
Parallel univariate p-adic lifting on shared-memory multiprocessors
ISSAC '92 Papers from the international symposium on Symbolic and algebraic computation
Subresultants and Reduced Polynomial Remainder Sequences
Journal of the ACM (JACM)
On Euclid's Algorithm and the Computation of Polynomial Greatest Common Divisors
Journal of the ACM (JACM)
On Euclid's Algorithm and the Theory of Subresultants
Journal of the ACM (JACM)
Computer Algebra and Parallelism
Computer Algebra and Parallelism
Improved Sparse Multivariate Polynomial Interpolation Algorithms
ISAAC '88 Proceedings of the International Symposium ISSAC'88 on Symbolic and Algebraic Computation
Computer Algebra: Past and Future
EUROCAL '85 Invited Lectures from the European Conference on Computer Algebra-Volume I - Volume I
Evaluation of "performance enhancements" in algebraic manipulation systems
Evaluation of "performance enhancements" in algebraic manipulation systems
On computing greatest common divisors with polynomials given by black boxes for their evaluations
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
Algorithms for the non-monic case of the sparse modular GCD algorithm
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Component-level parallelization of triangular decompositions
Proceedings of the 2007 international workshop on Parallel symbolic computation
On sparse interpolation over finite fields
ACM Communications in Computer Algebra
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Reported are experiences and practical results from parallelizing the modular GCD algorithm for sparse multivariate polynomials. The strategy is to identify key computation steps in the sequential algorithm and implement them in parallel. The two major steps of the sequential algorithm—computing the GCD modulo several primes and applying the Chinese Remainder Algorithm on the integer coefficients—are easily partitioned into independent subtasks. The subtask of computing the GCD modulo one prime can be subdivided further. Several parallel strategies for the multivariate GCD modulo a prime are presented. Actual timings on a Sequent Balance with 26 processors are presented.