Picard Group

ResidueRingUnits(S, I) : AlgEtQOrd, AlgEtQIdl -> GrpAb,Map
Returns the group (S/I) * and a map (S/I) * -> S. The order S is required to be maximal.
IsPrincipal(I1) : AlgEtQIdl ->BoolElt, AlgAssElt
    GRH: BoolElt                        Default: false
Return if the argument is a principal ideal; if so the function returns also the generator. The optional parameter GRH decides whether the bound for the IsPrincipal test should be conditional. The default value is false.
PicardGroup(S) : AlgEtQOrd -> GrpAb, Map
    GRH: BoolElt                        Default: false
Return the PicardGroup of the order S, which is not required to be maximal, and a map from the Picard group to a set of representatives of the ideal classes. The optional parameter GRH decides the bound for the computations of the Class group and Unit group of the maximal order. The default value is false.
UnitGroup(S) : AlgEtQOrd -> GrpAb, Map
    GRH: BoolElt                        Default: false
Return the unit group of a order in a étale algebra. The optional parameter GRH decides the bound for the computation of the unit group of the maximal order. The default value is false.
IsIsomorphic(I, J) : AlgEtQIdl, AlgEtQIdl -> BoolElt, AlgAssElt
    GRH: BoolElt                        Default: false
Checks if I=x .J, for some x. If so, also x is returned. The optional parameter GRH decides whether the bound for the IsPrincipal test should be conditional. The default value is false.
V2.29, 26 September 2025