Computation of the fundamental units and the regulator of a cyclic cubic function field.

Lee, Y.; Scheidler, R.; Yarrish, C.

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Ideal arithmetic and infrastructure in purely cubic function fields

Renate Scheidler (2001)

Journal de théorie des nombres de Bordeaux

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This paper investigates the arithmetic of fractional ideals of a purely cubic function field and the infrastructure of the principal ideal class when the field has unit rank one. First, we describe how irreducible polynomials decompose into prime ideals in the maximal order of the field. 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...