Associative Algebras
- Introduction
- Construction of Associative Algebras
- Construction of an Associative Structure Constant Algebra
AssociativeAlgebra< R, n | Q : parameters >: Rng, RngIntElt, SeqEnum → AlgAssAssociativeAlgebra< M | Q : parameters >: ModTupRng, SeqEnum → AlgAssAssociativeAlgebra< R, n | T : parameters >: Rng, RngIntElt, SeqEnum → AlgAssAssociativeAlgebra(A): AlgGen → AlgAssChangeBasis(A, B): AlgAss, {[AlgAssElt]} → AlgAssChangeBasis(A, B): AlgAss, {[ModTupFldElt]} → AlgAssChangeBasis(A, B): AlgAss, Mtrx → AlgAss
- Associative Structure Constant Algebras from other Algebras
- Operations on Algebras and their Elements
- Operations on Algebras
Centre(A): AlgAss → AlgAssCentralizer(A, S): AlgAss, AlgAss → AlgAssCentraliser(A, S): AlgAss, AlgAss → AlgAssIdealizer(A, B: parameters): AlgAss, AlgAss → AlgAssIdealiser(A, B: parameters): AlgAss, AlgAss → AlgAssLieAlgebra(A): AlgAss → AlgGen, MapCommutatorModule(A, B): AlgAss, AlgAss → ModTupRngCommutatorIdeal(A, B): AlgAss, AlgAss → AlgAssLeftAnnihilator(A, B): AlgAss, AlgAss → AlgAss, AlgAssRightAnnihilator(A, B): AlgAss, AlgAss → AlgAss, AlgAssExample: liealgRestrictionOfScalars(A): AlgAss[FldAlg] → AlgAss, MapRestrictionOfScalars(A): AlgAss[FldFun] → AlgAss, MapRestrictionOfScalars(A, F): AlgAss[FldAlg], Fld → AlgAss, MapRestrictionOfScalars(A, F): AlgAss[FldFun], FldFunG → AlgAss, MapExample: restrict
- Operations on Elements
Centralizer(A, s): AlgAss, AlgAssElt → AlgAssCentraliser(A, s): AlgAss, AlgAssElt → AlgAssLieBracket(a, b): AlgAssElt, AlgAssElt → AlgAssElt(a, b): AlgAssElt, AlgAssElt → AlgAssEltIsScalar(a): AlgAssElt → BoolElt, RngEltRepresentationMatrix(a, M : parameters): AlgAssElt, AlgAss → AlgMatElt
- Representations
- Decomposition of an Algebra
- Orders
- Construction of Orders
Order(R, S): Rng, SeqEnum[AlgAssVElt] → AlgAssVOrdOrder(R, S): RngFunOrd, SeqEnum[AlgAssVElt[FldFunG]] → AlgAssVOrdOrder(S): SeqEnum[AlgAssVElt[FldAlg]] → AlgAssVOrdOrder(S): SeqEnum[AlgAssVElt[FldFun]] → AlgAssVOrdOrder(S, I): SeqEnum[AlgAssVElt[FldAlg]], SeqEnum[RngOrdFracIdl] → AlgAssVOrdOrder(S, I): SeqEnum[AlgAssVElt[FldFunG]], SeqEnum[RngFunOrdIdl] → AlgAssVOrdOrder(A, m, I): AlgAssV[FldOrd], AlgMatElt[FldOrd], SeqEnum[RngOrdFracIdl] → AlgAssVOrdOrder(A, m, I): AlgAssV[FldNum], AlgMatElt[FldNum], SeqEnum[RngOrdFracIdl] → AlgAssVOrd, MapOrder(A, m, I): AlgAssV[FldFun], AlgMatElt[FldFun], SeqEnum[RngFunOrdIdl] → AlgAssVOrdOrder(A, pm): AlgAssV[FldOrd], PMat → AlgAssVOrdOrder(A, pm): AlgAssV[FldNum], PMat → AlgAssVOrd, MapOrder(A, pm): AlgAssV[FldFun], PMat → AlgAssVOrdExample: Ord Creat CycExample: Ord Creat CycMaximalOrder(A): AlgAssV[FldRat] → AlgAssVOrdMaximalOrder(A): AlgAssV[FldAlg] → AlgAssVOrdMaximalOrder(O): AlgAssVOrd[RngInt] → AlgAssVOrdMaximalOrder(O): AlgAssVOrd[RngOrd] → AlgAssVOrdMaximalOrderFinite(A): AlgAssV[FldFunRat] → AlgAssVOrdMaximalOrderInfinite(A): AlgAssV[FldFunRat] → AlgAssVOrdMaximalOrderFinite(A): AlgAssV[FldFun] → AlgAssVOrdMaximalOrderInfinite(A): AlgAssV[FldFun] → AlgAssVOrdMaximalOrder(O): AlgAssVOrd[RngUPol] → AlgAssVOrdMaximalOrder(O): AlgAssVOrd[RngVal] → AlgAssVOrdMaximalOrder(O): AlgAssVOrd[RngFunOrd] → AlgAssVOrdExample: Max OrdExample: Max Ord AlgRestrictionOfScalars(O): AlgAssVOrd[RngOrd] → AlgAssVOrd, MapRestrictionOfScalars(O): AlgAssVOrd[RngFunOrd] → AlgAssVOrd, MapRestrictionOfScalars(O, C): AlgAssVOrd[RngOrd], Rng → AlgAssVOrd, MapRestrictionOfScalars(O, C): AlgAssVOrd[RngFunOrd], Rng → AlgAssVOrd, MapExample: restrict
- Attributes
- Bases of Orders
- Predicates
- Operations with Orders
- Elements of Orders
- Ideals of Orders
- Construction of Ideals
lideal<O | E>: AlgAssVOrd, [AlgAssVOrdElt] → AlgAssVOrdIdlrideal<O | E>: AlgAssVOrd, [AlgAssVOrdElt] → AlgAssVOrdIdlideal<O | E>: AlgAssVOrd, [AlgAssVOrdElt] → AlgAssVOrdIdllideal<O | M>: AlgAssVOrd, PMat → AlgAssVOrdIdllideal<O | M>: AlgAssVOrd, Mtrx → AlgAssVOrdIdlrideal<O | M>: AlgAssVOrd, PMat → AlgAssVOrdIdlrideal<O | M>: AlgAssVOrd, Mtrx → AlgAssVOrdIdlideal<O | M>: AlgAssVOrd, PMat → AlgAssVOrdIdlideal<O | M>: AlgAssVOrd, Mtrx → AlgAssVOrdIdlO * e: AlgAssVOrd, RngElt → AlgAssVOrdIdle * O: RngElt, AlgAssVOrd → AlgAssVOrdIdl
- Attributes of Ideals
Order(I): AlgAssVOrdIdl → AlgAssVOrdAlgebra(I): AlgAssVOrdIdl → AlgAssVLeftOrder(I): AlgAssVOrdIdl → AlgAssVOrdRightOrder(I): AlgAssVOrdIdl → AlgAssVOrdArithmeticRadical(O, p): AlgAssVOrd[RngOrd], RngOrdIdl → AlgAssVOrdIdlArithmeticRadical(O, p): AlgQuat, RngElt → AlgQuatOrdIdlRadicalIdealizer(O, p): AlgAssVOrd[RngOrd], RngOrdIdl → AlgAssVOrdRadicalIdealizer(O, p): AlgQuat, RngElt → AlgQuatNeighbors(I, p): AlgAssVOrdIdl, RngOrdIdl → SeqEnum[AlgAssVOrdIdl]Neighbors(I, p): AlgQuatOrdIdl, RngInt → SeqEnum[AlgQuatOrdIdl]ElementsOfNorm(I, n): AlgAssVOrdIdl, RngElt → SeqEnum
- Bases of Ideals
Denominator(I): AlgAssVOrdIdl → RngEltPseudoBasis(I): AlgAssVOrdIdl[RngOrd] → SeqEnumPseudoMatrix(I): AlgAssVOrdIdl[RngOrd] → PMatPseudoMatrix(I): AlgAssVOrdIdl[RngFunOrd] → PMatBasis(I): AlgAssVOrdIdl → SeqEnumBasisMatrix(I): AlgAssVOrdIdl → AlgMatEltZBasis(I): AlgAssVOrdIdl[RngOrd] → [AlgAssVOrdElt]Generators(I): AlgAssVOrdIdl[RngOrd] → [AlgAssVOrdElt]LocalBasis(I, p): AlgAssVOrdIdl, RngOrdIdl → [AlgAssElt]PseudoBasis(I, R): AlgAssVOrdIdl[RngOrd], Str → SeqEnumPseudoMatrix(I, R): AlgAssVOrdIdl[RngOrd], Str → PMatBasis(I, R): AlgAssVOrdIdl, Str → SeqEnumBasisMatrix(I, R): AlgAssVOrdIdl, Str → AlgMatElt
- Arithmetic for Ideals
I + J: AlgAssVOrdIdl, AlgAssVOrdIdl → AlgAssVOrdIdlI * J: AlgAssVOrdIdl, AlgAssVOrdIdl → AlgAssVOrdIdl, AlgAssVOrdIdlI * J: AlgAssVOrdIdl[RngOrd], AlgAssVOrdIdl[RngOrd] → AlgAssVOrdIdl, AlgAssVOrdIdla * I: RngElt, AlgAssVOrdIdl → AlgAssVOrdIdlI * a: AlgAssVOrdIdl, RngElt → AlgAssVOrdIdla * I: RngElt, AlgQuatOrdIdl → AlgQuatOrdIdlI * a: AlgQuatOrdIdl, RngElt → AlgQuatOrdIdlA * I: RngOrdFracIdl, AlgAssVOrdIdl[RngOrd]) → AlgAssVOrdIdlI * A: RngOrdFracIdl, AlgAssVOrdIdl[RngOrd]) → AlgAssVOrdIdlColon(J, I): AlgAssVOrdIdl[RngOrd], AlgAssVOrdIdl[RngOrd] → PMatMultiplicatorRing(I): AlgAssVOrdIdl → AlgAssVOrd
- Predicates on Ideals
- Other Operations on Ideals
