Trace and Norm

Trace(x) : AlgEtQElt -> Any
Returns the trace of the element x of an étale algebra.
Norm(x) : AlgEtQElt -> Any
Returns the norm of the element x of an étale algebra.
AbsoluteTrace(x) : AlgEtQElt -> Any
Returns the absolute trace of the element x of an étale algebra. Since the étale algebra is over the rationals this is the same as Trace.
AbsoluteNorm(x) : AlgEtQElt -> Any
Returns the absolute norm of the element x of an étale algebra. Since the étale algebra is over the rationals this is the same as Norm.
TraceDualIdeal(I) : AlgEtQIdl -> AlgEtQIdl
Returns the trace dual ideal of the ideal I, that is, the set of elements x of the algebra such that Tr(x .I) is integer-valued.
TraceDualIdeal(O) : AlgEtQOrd -> AlgEtQIdl
Returns the trace dual ideal of an order in an étale algebra, that is, the set of elements x of the algebra such that Tr(x .O) is integer-valued.
V2.29, 21 October 2025