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Modular methods for computing the gcd of two univariate polynomials over an algebraic number field require <italic>a priori</italic> knowledge about the denominators of the rational numbers in the representation of the gcd. We derive a multiplicative bound for these denominators without assuming that the number generating the field is an algebraic integer.… (More)

Trager's nom-based algorithm for factoring univariate poly-Ilomials over algebraic number fields is improved by intro-(Iucing a device for reducing the number of combinations of modrdar factors ofthe norm that have to be examined in the trial-division phase of the algorithm. Empirical computing times show that using the device can result in a significant… (More)

The paper describes improved techniques for factoring univariate polynomials over the integers. The authors modify the usual linear method for lifting modular polynomial factorizations so that eecient early factor detection can be performed. The new lifting method is universally faster than the classical quadratic method, and is faster than a linear method… (More)

Trager's algorithm for factoringa univariate polynomialover an algebraic number field computes thenorm of the polynomial and then factors the norm over the integers. It has been observed by the author as well as others that the norm tends to factor modulo a prime into more irreducible factors than one would expect from a typical random polynomial, but no… (More)

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