Some results on the defect

Authors:
R. Bradford
Affiliations:
School of Mathematical Sciences, University of Bath, Claverton Down, Bath BA2 7AY
Venue:
ISSAC '89 Proceedings of the ACM-SIGSAM 1989 international symposium on Symbolic and algebraic computation
Year:
1989

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Abstract

The defect of an algebraic number field (or, more correctly, of a presentation of the field) is the largest rational integer that divides the denominator of any algebraic integer in the field when written using that presentation. Knowing the defect, or estimating it accurately is extremely valuable in many algorithms, the factorization of polynomials over algebraic number fields being a prime example. We present a few results that are a move in the right direction.