A parallel implementation of the cylindrical algebraic decomposition algorithm
ISSAC '89 Proceedings of the ACM-SIGSAM 1989 international symposium on Symbolic and algebraic computation
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Multivariate Polynomial Factorization
Journal of the ACM (JACM)
On the Efficiency of a Polynomial Irreducibility Test
Journal of the ACM (JACM)
Computer Algebra and Parallelism
Computer Algebra and Parallelism
Early detection of true factors in univariate polynominal factorization
EUROCAL '83 Proceedings of the European Computer Algebra Conference on Computer Algebra
Implementing a polynomial factorization and GCD package
SYMSAC '81 Proceedings of the fourth ACM symposium on Symbolic and algebraic computation
ACM SIGSAM Bulletin
On the multi-threaded computation of integral polynomial greatest common divisors
ISSAC '91 Proceedings of the 1991 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
ISSAC '94 Proceedings of the international symposium on Symbolic and algebraic computation
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Using parallelism afforded by shared-memory multiprocessors to speed up systems for polynomial factorization is discussed. The approach is to take the fastest known factoring algorithm for practical purposes and parallelize key parts of it. The univariate factoring algorithm consists of two major tasks (a) factoring modulo small integer primes and (b) EEZ lifting and recovery of true factors. A C coded system PFACTOR that implements (a) in parallel is described in detail. PFACTOR is a stand-alone parallel factorizer that can take input from a file, a pipe or a socket connection over a network. It can also be used interactively as a UNIX command. PFACTOR consists of parallel selection of primes, automatic balancing of work, parallel Berlekamp algorithm, and parallel reconciliation of degrees of factors modulo different primes. Actual timings on the Encore Multimax show the effectiveness of the approach. Work on part (b) is still on going.