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For elements of an order, the norm and trace are (mathematically) integers, but Sage returns Rationals. More generally, the charpoly and minpoly are returned as Rational polynomials when they are (mathematically) in ZZ[].
I would like this to change, as it led to some very inefficient behaviour until I discovered it, and now I am having to manually coerce norms and traces into ZZ.
Review of patch: the code looks just fine and appears to solve the problem raised. I only say "appears" as I'm travelling and not in a position to test it myself, but the added doctests give me sufficitne confidence to say: OK!
For elements of an order, the norm and trace are (mathematically) integers, but Sage returns Rationals. More generally, the charpoly and minpoly are returned as Rational polynomials when they are (mathematically) in ZZ[].
I would like this to change, as it led to some very inefficient behaviour until I discovered it, and now I am having to manually coerce norms and traces into ZZ.
Component: number theory
Keywords: orders, norm, trace
Issue created by migration from https://trac.sagemath.org/ticket/2653
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