The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Subresultants and Reduced Polynomial Remainder Sequences
Journal of the ACM (JACM)
On Euclid's Algorithm and the Theory of Subresultants
Journal of the ACM (JACM)
The Exact Solution of Systems of Linear Equations with Polynomial Coefficients
Journal of the ACM (JACM)
Algorithms for rational function arithmetic operations
STOC '72 Proceedings of the fourth annual ACM symposium on Theory of computing
Symbolic mathematical computation—introduction and overview
SYMSAC '71 Proceedings of the second ACM symposium on Symbolic and algebraic manipulation
Modular arithmetic and finite field theory: A tutorial
SYMSAC '71 Proceedings of the second ACM symposium on Symbolic and algebraic manipulation
Algebraic simplification a guide for the perplexed
SYMSAC '71 Proceedings of the second ACM symposium on Symbolic and algebraic manipulation
Arrangement computation for planar algebraic curves
Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation
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This paper examines the computation of polynomial greatest common divisors by various generalizations of Euclid's algorithm. The phenomenon of coefficient growth is described, and the history of successful efforts first to control it and then to eliminate it is related. The recently developed modular algorithm is presented in careful detail, with special attention to the case of multivariate polynomials. The computing times for the subresultant PRS algorithm, which is essentially the best of its kind, and for the modular algorithm are analyzed, and it is shown that the modular algorithm is markedly superior. In fact, the modular algorithm can obtain a GCD in less time than is required to verify it by classical division.