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Title:
An effective version of the theorem by Latimer and MacDuffee for 2 by 2
integral matrices
Abstract: Two n by n integral matrices A and B are considered to be equivalent if B=S-1AS, for some n by n integral matrix S, with det S = 1. If we consider n by n integral matrices with a fixed characteristic polynomial that is irreducible over Q, it is well known from a result by Latimer and MacDuffee that the number of matrix classes (equivalence classes of matrices), is equal to the number of ideal classes of the ring obtained by adjoining a root of the characteristic polynomial to Z. We will give an effective version of this result for two by two matrices. |