- Introduction
- Creation of Quaternion Algebras
- QuaternionAlgebra< K | a, b > : Rng, RngElt, RngElt -> AlgQuat
- AssignNames(~A, S) : AlgQuat, [MonStgElt] ->
- Example AlgQuat_Quaternion_Constructor (H93E1)
- Example AlgQuat_Quaternion_Constructor_char2 (H93E2)
- QuaternionAlgebra(N) : RngIntElt -> AlgQuat
- QuaternionAlgebra(N) : RngUPolElt -> AlgQuat
- QuaternionAlgebra(I) : RngOrdIdl -> AlgQuat
- QuaternionAlgebra(I, S) : RngOrdIdl, [PlcNumElt] -> AlgQuat
- QuaternionAlgebra(S) : [PlcNumElt] -> AlgQuat
- Example AlgQuat_Quaternion_Constructor_Over_NumberField (H93E3)
- QuaternionAlgebra(D1, D2, T) : RngIntElt, RngIntElt, RngIntElt -> AlgQuat
- Example AlgQuat_Quaternion_Constructor_over_Rationals (H93E4)
- Creation of Quaternion Orders
- Elements of Quaternion Algebras
- Attributes of Quaternion Algebras
- Hilbert Symbols and Embeddings
- HilbertSymbol(a, b, p) : FldRatElt, FldRatElt, RngIntElt -> RngIntElt
- IsRamified(p, A) : RngElt, AlgQuat -> BoolElt
- Example AlgQuat_Hilbert_Symbols (H93E12)
- pMatrixRing(A, p) : AlgQuat, RngOrdIdl -> AlgMat, Map, Map
- IsSplittingField(K, A) : Fld, AlgQuat -> BoolElt, AlgQuatElt, Map
- Embed(K, A) : Fld, AlgQuat -> AlgQuatElt, Map
- Embed(Oc, O) : RngOrd, AlgAssVOrd -> AlgAssVOrdElt, Map
- Example AlgQuat_Embed (H93E13)
- Predicates on Algebras
- Recognition Functions
- Attributes of Orders
- Predicates of Orders
- IsMaximal(O) : AlgAssVOrd -> BoolElt
- IspMaximal(O, p) : AlgAssVOrd, RngOrdIdl -> BoolElt
- IsEichler(O) : AlgAssVOrd -> BoolElt, AlgAssVOrd, AlgAssVOrd
- IsEichler(O, p) : AlgAssVOrd , RngOrdIdl -> BoolElt, AlgAssVOrd, AlgAssVOrd
- EichlerInvariant(O, p) : AlgAssVOrd , RngOrdIdl -> RngIntElt
- IsHereditary(O) : AlgAssVOrd -> BoolElt
- IsHereditary(O, p) : AlgAssVOrd , RngOrdIdl -> BoolElt
- IsGorenstein(O) : AlgAssVOrd -> BoolElt, .
- IsGorenstein(O, p) : AlgAssVOrd , RngOrdIdl -> BoolElt, RngIntElt
- IsBass(O) : AlgAssVOrd -> BoolElt
- IsBass(O, p) : AlgAssVOrd , RngOrdIdl -> BoolElt
- IsSameType(O1, O2) : AlgAssVOrd , AlgAssVOrd -> BoolElt
- Operations with Orders
- Ideal Theory of Orders
- Norm Spaces and Basis Reduction
- NormSpace(A) : AlgQuat -> ModTupFld, Map
- NormSpace(S) : AlgQuatOrd -> ModTupRng, Map
- GramMatrix(S) : AlgQuatOrd -> AlgMatElt
- ReducedGramMatrix(S) : AlgQuatOrd[RngInt] -> AlgMatElt
- ReducedBasis(S) : AlgQuatOrd[RngInt] -> SeqEnum
- Example AlgQuat_Basis_Reduction (H93E22)
- ReducedGramMatrix(S) : AlgQuatOrd[RngUPol] -> AlgMatElt, SeqEnum
- ReducedBasis(O) : AlgAssVOrd[RngOrd] -> [AlgAssVElt]
- OptimizedRepresentation(O) : AlgAssVOrd -> AlgQuat, Map
- OptimizedRepresentation(A) : AlgQuat -> AlgQuat, Map
- Enumerate(O, A, B) : AlgQuatOrd[RngInt], RngIntElt, RngIntElt -> [AlgQuatOrdElt]
- Enumerate(O, A, B) : AlgAssVOrd[RngOrd], RngElt, RngElt -> [AlgAssVOrdElt]
- Isomorphisms
- Isomorphisms of Algebras
- Isomorphisms of Orders
- Isomorphisms of Ideals
- IsIsomorphic(I, J) : AlgAssVOrdIdl, AlgAssVOrdIdl -> BoolElt, AlgAssVElt
- IsPrincipal(I) : AlgAssVOrdIdl -> BoolElt, AlgQuatElt
- IsLeftIsomorphic(I, J) : AlgQuatOrdIdl, AlgQuatOrdIdl -> BoolElt, Map, AlgQuatElt
- IsLeftIsomorphic(I, J) : AlgAssVOrdIdl[RngOrd], AlgAssVOrdIdl[RngOrd] -> BoolElt, AlgQuatElt
- LeftIsomorphism(I, J) : AlgQuatOrdIdl, AlgQuatOrdIdl -> Map, AlgQuatElt
- RightIsomorphism(I, J) : AlgQuatOrdIdl, AlgQuatOrdIdl -> Map, AlgQuatElt
- Examples
- Units and Unit Groups
- Bibliography
V2.28, 13 July 2023