Totally Real and Positive

IsTotallyReal(a): AlgEtQElt -> BoolElt

Returns whether element \(a\) is totally real.

IsTotallyRealPositive(a): AlgEtQElt -> BoolElt

Returns whether the element \(a\) is totally positive, that is, totally real and with positive image in CC.

TotallyRealSubAlgebra(K): AlgEtQ -> AlgEtQ, Map

Given a CM algebra \(K\), returns the unique totally real subalgebra, with an embedding.

TotallyRealUnitGroup(S): AlgEtQOrd -> Grp

Given an order \(S\) in a CM étale algebra \(A\) returns the groups of totally real units of \(S\), as a subgroup of \(S^*\).

TotallyRealPositiveUnitGroup(S): AlgEtQOrd -> Grp

Given an order \(S\) in a CM étale algebra. Returns the groups of totally positive units of \(S\), as a subgroup of \(S^*\).