Papers › Computing the ideal class monoid of an order
Computing the ideal class monoid of an order
Stefano Marseglia
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There are well known algorithms to compute the class group of the maximal order 𝒪_K of a number field K and the group of invertible ideal classes of a non-maximal order R. In this paper we explain how to compute also the isomorphism classes of non-invertible ideals of an order R in a finite product of number fields K. In particular we also extend the above-mentioned algorithms to this more general setting. Moreover, we generalize a theorem of Latimer and MacDuffee providing a bijection between the conjugacy classes of integral matrices with given minimal and characteristic polynomials and the isomorphism classes of lattices in certain ℚ-algebras, which under certain assumptions can be explicitly described in terms of ideal classes.
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