The computation of polynomial greatest common divisors over an algebraic number field

Lars Langemyr; Scott McCallum

doi:10.1016/S0747-7171(89)80053-7

The computation of polynomial greatest common divisors over an algebraic number field

Lars Langemyr^*, Scott McCallum

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

18 Citations (Scopus)

Abstract

We present a modular algorithm for computing the greatest common divisor of two polynomials over an algebraic number field. Our algorithm is an application of ideas of Brown and Collins. We use the Weinberger-Rothschild homomorphic scheme with the important change that we avoid factoring the modular image of the minimal polynomial. We perform a computing time analysis and report some empirical computing times.

Original language	English
Pages (from-to)	429-448
Number of pages	20
Journal	Journal of Symbolic Computation
Volume	8
Issue number	5
DOIs	https://doi.org/10.1016/S0747-7171(89)80053-7
Publication status	Published - 1 Jan 1989
Externally published	Yes

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AB - We present a modular algorithm for computing the greatest common divisor of two polynomials over an algebraic number field. Our algorithm is an application of ideas of Brown and Collins. We use the Weinberger-Rothschild homomorphic scheme with the important change that we avoid factoring the modular image of the minimal polynomial. We perform a computing time analysis and report some empirical computing times.

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The computation of polynomial greatest common divisors over an algebraic number field

Abstract

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