Single-factor coefficient bounds

Authors:
George E. Collins
Affiliations:
1124 Climbing Rose Turn, Cary, NC 27511, United States
Venue:
Journal of Symbolic Computation
Year:
2004

Citing 2
Cited 2

Polynomial factorization: sharp bounds, efficient algorithms

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Improved techniques for factoring univariate polynomials

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Exact certification of global optimality of approximate factorizations via rationalizing sums-of-squares with floating point scalars

Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
Bounds on factors in Z[x]

Journal of Symbolic Computation

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Abstract

In a 1993 paper Beauzamy, Trevisan and Wang derived a single-factor coefficient bound, one which limits the max norm (height) of at least one irreducible factor of any univariate integral polynomial A. Their bound is a function of the degree and the weighted norm of A. In the conclusion of their paper they ask whether the max norm of A might already be a single-factor coefficient bound. In 1998 Knuth, citing these authors, asked instead whether there is a constant c such that c times the max norm of A is a single-factor coefficient bound. We present the results of extensive calculations relating to this question. We show that c, if it exists, must be greater than 2 and accrue evidence in support of a conjecture that the answer to Knuth's question is ''no''.