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Quaternionic Orders

The following intrinsics which take an argument of type AlgAssVOrd, AlgAssVOrdElt, or AlgAssVOrdIdl, apply only to associative orders of quaternion algebras and are documented in that chapter, Chapter QUATERNION ALGEBRAS.

MaximalOrder(O) : AlgAssVOrd[RngOrd] -> AlgAssVOrd
pMaximalOrder(O, p) : AlgAssVOrd, RngOrdIdl -> AlgAssVOrd, RngIntElt
IsMaximal(O) : AlgAssVOrd -> BoolElt
IspMaximal(O, p) : AlgAssVOrd, RngOrdIdl -> BoolElt
pMatrixRing(O, p) : AlgAssVOrd, RngOrdIdl -> AlgQuat, Map, Map
Embed(Oc, O) : RngOrd, AlgAssVOrd -> AlgAssVOrdElt, Map
LeftIdealClasses(S) : AlgAssVOrd[RngOrd] -> [AlgAssVOrdIdl]
RightIdealClasses(S) : AlgAssVOrd[RngOrd] -> [AlgAssVOrdIdl]
TwoSidedIdealClasses(S) : AlgAssVOrd[RngOrd] -> [AlgAssVOrdIdl]
TwoSidedIdealClassGroup(S) : AlgAssVOrd[RngOrd] -> GrpAb, Map
OptimizedRepresentation(O) : AlgAssVOrd -> AlgQuat, Map
OptimisedRepresentation(O) : AlgAssVOrd -> AlgQuat, Map
Units(S) : AlgAssVOrd -> SeqEnum
MultiplicativeGroup(S) : AlgAssVOrd -> GrpPerm, Map
UnitGroup(S) : AlgAssVOrd[RngOrd] -> GrpPC, Map
Conjugate(x) : AlgAssVOrdElt -> AlgAssVOrdElt
Enumerate(O, A, B) : AlgAssVOrd[RngOrd], RngElt, RngElt -> [AlgAssVOrdElt]
Enumerate(O, B) : AlgAssVOrd[RngOrd], RngElt -> [AlgAssVOrdElt]
Enumerate(O, B) : AlgAssVOrd[RngOrd], [RngElt] -> [AlgAssVOrdElt]
Enumerate(I, B) : AlgAssVOrdIdl[RngOrd], [RngElt] -> [AlgAssVOrdElt]
ReducedBasis(O) : AlgAssVOrd[RngOrd] -> [AlgAssVElt]
ReducedBasis(I) : AlgAssVOrdIdl[RngOrd] -> [AlgAssVOrdElt]
IsIsomorphic(I, J) : AlgAssVOrdIdl[RngOrd], AlgAssVOrdIdl[RngOrd] -> BoolElt, AlgQuatElt
IsLeftIsomorphic(I, J) : AlgAssVOrdIdl[RngOrd], AlgAssVOrdIdl[RngOrd] -> BoolElt, AlgQuatElt
IsRightIsomorphic(I, J) : AlgAssVOrdIdl[RngOrd], AlgAssVOrdIdl[RngOrd] -> BoolElt, AlgQuatElt
IsPrincipal(I) : AlgAssVOrdIdl[RngOrd] -> BoolElt, AlgQuatElt

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Version: V2.19 of Mon Dec 17 14:40:36 EST 2012