The method rational_form for matrices just returns the class representative of the conjugacy class of a matrix by other rational matrices. A similar function PrimaryRationalForm in magma returns 3 things -- the class representative, a rational matrix which, when conjugated by the input, gives the representative, and a list of pairs: irreducible polynomial and multplicity. It would be nice if SAGE could return the same things as an option. The third one is easy to reconstruct from SAGE's output (since it outputs a subdivided matrix), but the second one isn't
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