GCDHEU: Heuristic polynomial GCD algorithm based on integer GCD computation
Journal of Symbolic Computation
The computation of polynomial greatest common divisors over an algebraic number field
Journal of Symbolic Computation
Computing GCDs of polynomials over algebraic number fields
Journal of Symbolic Computation
On bivariate Hensel and its parallelization
ISSAC '98 Proceedings of the 1998 international symposium on Symbolic and algebraic computation
On the genericity of the modular polynomial GCD algorithm
ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
On Euclid's Algorithm and the Computation of Polynomial Greatest Common Divisors
Journal of the ACM (JACM)
In-place Arithmetic for Polinominals over Zn
DISCO '92 Proceedings of the International Symposium on Design and Implementation of Symbolic Computation Systems
Heuristic Methods for Operations With Algebraic Numbers. (Extended Abstract)
ISAAC '88 Proceedings of the International Symposium ISSAC'88 on Symbolic and Algebraic Computation
Probabilistic algorithms for sparse polynomials
EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
ACM SIGSAM Bulletin
A modular GCD algorithm over number fields presented with multiple extensions
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Algorithms for polynomial GCD computation over algebraic function fields
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
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We study the design and implementation of the dense modular GCD algorithm of Brown applied to bivariate polynomial GCDs over the integers and number fields. We present an improved design of Brown's algorithm and compare it asymptotically with Brown's original algorithm, with GCD-HEU, the heuristic GCD algorithm, and with the EEZGCD algorithm. We also make an empirical comparison based on Maple implementations of the algorithms. Our findings show that a careful implementation of our improved version of Brown's algorithm is much better than the other algorithms in theory and in practice.