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)
The Calculation of Multivariate Polynomial Resultants
Journal of the ACM (JACM)
Integer Arithmetic Algorithms for Polynomial Real Zero Determination
Journal of the ACM (JACM)
Modular arithmetic and finite field theory: A tutorial
SYMSAC '71 Proceedings of the second ACM symposium on Symbolic and algebraic manipulation
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This paper describes a set of algorithms for isolating the real zeros of a univariate polynomial with integer coefficients. The algorithms employ congruence (modular, finite field) arithmetic and are analogous to a set of integer arithmetic algorithms described by the author in a recent paper. The algorithms are analyzed to bound their computing times and these computing times are compared to the computing times of the integer arithmetic algorithms. Some empirical computing times are reported.