A modular greatest common divisor algorithm for gaussian polynomials

Authors:
B. F. Caviness;Michael Rothstein
Affiliations:
-;-
Venue:
ACM '75 Proceedings of the 1975 annual conference
Year:
1975

Citing 1
Cited 1

On Euclid's Algorithm and the Computation of Polynomial Greatest Common Divisors

Journal of the ACM (JACM)

On the genericity of the modular polynomial GCD algorithm

ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation

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Abstract

In this paper the Brown-Collins modular greatest common divisor algorithm for polynomials in Z[x1,...,xv], where Z denotes the ring of rational integers, is generalized to apply to polynomials in G[x1,...,xv], where G denotes the ring of Gaussian integers, i.e., complex numbers of the form a + ib where a, b are in Z Under certain simplifying assumptions, a function is found that dominates the maximum computing time of the new god algorithm.