Some results on the defect

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.

REFERENCES

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INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.1 SYMBOLIC AND ALGEBRAIC MANIPULATION

Additional Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS

General Terms:
Algorithms, Theory