16.15 DefectApproximation

DefectApproximation( L )

computes a multiple of the defect of the basis of L, given by the powers of the primitive element. The defect indicates, which denominator is necessary in the coefficients, to express algebraic integers in L as a linear combination of the base of L. DefectApproximation takes the maximal square in the discriminant as a first approximation, and then uses Berwicks and Hesses method (see Bra89) to improve this approximation. The number returned is not neccessarily the defect, but may be a proper multiple of it.

    gap> DefectApproximation(e);
    1

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GAP 3.4.4
April 1997