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 * .
V2.29, 21 October 2025