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Abstract : |
This paper investigates the arithmetic of fractional ideals of a purely cubic function eld and the infrastructure of the principal ideal class when the eld has unit rank one. First, we describe how irreducible polynomials decompose into prime ideals in the maximal order of the eld. We go on to compute so-called canonical bases of ideals; such bases are very suitable for computation. We state algorithms for ideal multiplication and, in the case of unit rank one and characteristic at least ve, ideal reduction. The paper concludes with an analysis of the infrastructure in the set of reduced fractional principal ideals of a purely cubic function eld of unit rank one and characteristic at least ve. 1, |
