- Introduction
- Construction
- Attributes
- Homomorphisms
- Elements
- Parent(x) : AlgEtQElt -> AlgEtQ
- Components(x) : AlgEtQElt -> SeqEnum
- AbsoluteCoordinates(x) : AlgEtQElt -> SeqEnum
- AbsoluteCoordinates(x, S) : AlgEtQElt, AlgEtQOrd -> SeqEnum
- IsCoercible(A, x) : AlgEtQ, Any -> BoolElt, AlgEtQElt
- A ! x : AlgEtQ, Any) -> AlgEtQElt
- One(A) : AlgEtQ -> AlgEtQElt
- Zero(A) : AlgEtQ -> AlgEtQElt
- IsUnit(x) : AlgEtQElt -> BoolElt
- IsZeroDivisor(x) : AlgEtQElt -> BoolElt
- Random(A, bd) : AlgEtQ, RngIntElt -> AlgEtQElt
- Random(A) : AlgEtQ -> AlgEtQElt
- RandomUnit(A, bd) : AlgEtQ, RngIntElt -> AlgEtQElt
- x1 eq x2 : AlgEtQElt, AlgEtQElt -> BoolElt
- Inverse(x) : AlgEtQElt -> AlgEtQElt
- &+ seq : SeqEnum[AlgEtQElt] -> AlgEtQElt
- &* seq : SeqEnum[AlgEtQElt] -> AlgEtQElt
- DotProduct(a, b) : SeqEnum, SeqEnum -> Any
- Example AlgEtQ_DotProductExample (H42E4)
- MinimalPolynomial(x) : AlgEtQElt -> RngUPolElt
- MinimalPolynomial(x, F) : AlgEtQElt, Rng -> RngUPolElt
- AbsoluteMinimalPolynomial(x) : AlgEtQElt -> RngUPolElt
- IsIntegral(x) : AlgEtQElt -> BoolElt
- Evaluate(f, a) : RngUPolElt, AlgEtQElt -> AlgEtQElt
- PrimitiveElement(A) : AlgEtQ -> AlgEtQElt
- PowerBasis(A) : AlgEtQ -> SeqEnum[AlgEtQElt]
- Basis(A) : AlgEtQ -> SeqEnum
- AbsoluteBasis(A) : AlgEtQ -> SeqEnum
- A . i : AlgEtQ, RngIntElt -> AlgEtQElt
- AbsoluteCoordinates(seq, basis) : SeqEnum[AlgEtQElt], SeqEnum[AlgEtQElt] -> SeqEnum
- OrthogonalIdempotents(A) : AlgEtQ -> SeqEnum
- Idempotents(A) : AlgEtQ -> SeqEnum
- Orders of Algebras
- IsCoercible(S, x) : AlgEtQOrd, Any -> BoolElt, AlgEtQElt
- Order(gens) : SeqEnum[AlgEtQElt] -> AlgEtQOrd
- Order(A, orders) : AlgEtQ, Tup -> AlgEtQOrd
- Algebra(S) : AlgEtQOrd -> AlgEtQ
- ZBasis(S) : AlgEtQOrd -> SeqEnum[AlgEtQElt]
- Generators(S) : AlgEtQOrd ->SeqEnum[AlgEtQElt]
- O1 eq O2 : AlgEtQOrd, AlgEtQOrd -> BoolElt
- x in O : AlgEtQElt, AlgEtQOrd -> BoolElt
- AbsoluteCoordinates(seq, O) : SeqEnum[AlgEtQElt], AlgEtQOrd -> SeqEnum
- One(S) : AlgEtQOrd -> AlgEtQElt
- Zero(S) : AlgEtQOrd -> AlgEtQElt
- Random(O, bd) : AlgEtQOrd, RngIntElt -> AlgEtQElt
- Random(O) : AlgEtQOrd -> AlgEtQElt
- IsKnownOrder(~R) : AlgEtQOrd ->
- EquationOrder(A) : AlgEtQ -> AlgEtQOrd
- ProductOfEquationOrders(A) : AlgEtQ -> AlgEtQOrd
- MaximalOrder(A) : AlgEtQ -> AlgEtQOrd
- IsMaximal(S) : AlgEtQOrd -> BoolElt
- IsProductOfOrders(O) : AlgEtQOrd -> BoolElt, Tup
- IsProductOfOrdersInComponents(O) : AlgEtQOrd -> BoolElt, Tup
- IsProductOfOrdersInFactorAlgebras(S) : AlgEtQOrd -> BoolElt, SeqEnum[AlgEtQElt]
- Example AlgEtQ_OrdersFactorAlgebras (H42E5)
- Index(T) : AlgEtQOrd -> FldRatElt
- Index(S, T) : AlgEtQOrd, AlgEtQOrd -> FldRatElt
- O1 subset O2 : AlgEtQOrd, AlgEtQOrd -> BoolElt
- O1 * O2 : AlgEtQOrd, AlgEtQOrd -> AlgEtQOrd
- O1 meet O2 : AlgEtQOrd, AlgEtQOrd -> AlgEtQOrd
- MultiplicatorRing(R) : AlgEtQOrd -> AlgEtQOrd
- Ideals
- Ideal(S, gens) : AlgEtQOrd, SeqEnum -> AlgEtQIdl
- Ideal(S, idls) : AlgEtQOrd, Tup -> AlgEtQIdl
- Ideal(S, gen) : AlgEtQOrd, Any -> AlgEtQIdl
- T !! I : AlgEtQOrd, AlgEtQIdl -> AlgEtQIdl
- Algebra(I) : AlgEtQIdl -> AlgEtQ
- Order(I) : AlgEtQIdl -> AlgEtQOrd
- ZBasis(I) : AlgEtQIdl -> SeqEnum[AlgEtQElt]
- Generators(I) : AlgEtQIdl -> SeqEnum[AlgEtQElt]
- I eq J : AlgEtQIdl, AlgEtQIdl -> BoolElt
- I eq S : AlgEtQIdl, AlgEtQOrd -> BoolElt
- AbsoluteCoordinates(x, I) : AlgEtQElt, AlgEtQIdl -> SeqEnum
- AbsoluteCoordinates(seq, I) : SeqEnum[AlgEtQElt], AlgEtQIdl -> SeqEnum
- x in I : AlgEtQElt, AlgEtQIdl -> BoolElt
- S subset I : AlgEtQOrd, AlgEtQIdl -> BoolElt
- I subset S : AlgEtQIdl, AlgEtQOrd -> BoolElt
- I1 subset I2 : AlgEtQIdl, AlgEtQIdl -> BoolElt
- Index(T) : AlgEtQIdl -> FldRatElt
- Index(J, I) : AlgEtQIdl, AlgEtQIdl -> Any
- Index(S, I) : AlgEtQOrd, AlgEtQIdl -> Any
- OneIdeal(S) : AlgEtQOrd -> AlgEtQIdl
- Conductor(O) : AlgEtQOrd -> AlgEtQOrdIdl
- I + J : AlgEtQIdl, AlgEtQIdl -> AlgEtQIdl
- I * J : AlgEtQIdl, AlgEtQIdl -> AlgEtQIdl
- I * x : AlgEtQIdl, AlgEtQElt -> AlgEtQIdl
- I ^ n : AlgEtQIdl, RngIntElt) -> AlgEtQIdl
- I meet S : AlgEtQIdl, AlgEtQOrd -> AlgEtQIdl
- I meet J : AlgEtQIdl, AlgEtQIdl -> AlgEtQIdl
- &+ seq : SeqEnum[AlgEtQIdl] -> AlgEtQIdl
- ColonIdeal(I, J) : AlgEtQIdl, AlgEtQIdl -> AlgEtQIdl
- ColonIdeal(O, J) : AlgEtQOrd, AlgEtQIdl -> AlgEtQIdl
- ColonIdeal(I, O) : AlgEtQIdl, AlgEtQOrd -> AlgEtQIdl
- IsInvertible(I) : AlgEtQIdl -> BoolElt
- Inverse(I) : AlgEtQIdl -> AlgEtQIdl
- MultiplicatorRing(I) : AlgEtQIdl -> AlgEtQOrd
- IsProductOfIdeals(I) : AlgEtQIdl -> BoolElt, Tup
- Random(I, bd) : AlgEtQIdl, RngIntElt -> AlgEtQElt
- Random(I) : AlgEtQIdl -> AlgEtQElt
- IsCoprime(I, J) : AlgEtQIdl, AlgEtQIdl -> BoolElt
- IsIntegral(I) : AlgEtQIdl -> BoolElt
- MakeIntegral(I) : AlgEtQIdl -> AlgEtQIdl, RngIntElt
- MinimalInteger(I) : AlgEtQIdl -> RngIntElt
- CoprimeRepresentative(I, J) : AlgEtQIdl, AlgEtQIdl -> AlgEtQElt, AlgEtQIdl
- ZBasisLLL(~S) : AlgEtQOrd ->
- Quotients
- Quotient(I, zbJ) : AlgEtQIdl, SeqEnum[AlgEtQElt] -> GrpAb, Map
- Quotient(I, J) : AlgEtQIdl, AlgEtQIdl -> GrpAb, Map
- Quotient(S, zbJ) : AlgEtQOrd, SeqEnum[AlgEtQElt] -> GrpAb, Map
- ResidueRing(S, I) : AlgEtQOrd, AlgEtQIdl -> GrpAb , Map
- ResidueField(P) : AlgEtQIdl -> FldFin, Map
- PrimitiveElementResidueField(P) : AlgEtQIdl->AlgEtQElt
- QuotientVS(I, J, P) : AlgEtQOrd, AlgEtQOrd, AlgEtQIdl -> ModRng, Map
- Example AlgEtQ_QuotientsResidues (H42E6)
- QuotientVS(I, J, P) : AlgEtQOrd, AlgEtQIdl, AlgEtQIdl -> ModRng, Map
- QuotientVS(I, J, P) : AlgEtQIdl, AlgEtQOrd, AlgEtQIdl -> ModRng, Map
- QuotientVS(I, J, P) : AlgEtQIdl, AlgEtQIdl, AlgEtQIdl -> ModRng, Map
- Over Orders
- Over Order Graph
- Trace and Norm
- Completion
- Intermediate Ideals
- IntermediateIdeals(I, J) : AlgEtQIdl, AlgEtQIdl -> SetIndx[AlgEtQIdl]
- IntermediateIdeals(I, J, O) :AlgEtQIdl, AlgEtQIdl, AlgEtQOrd -> SetIndx[AlgEtQIdl]
- IntermediateIdeals(I, J, N) : AlgEtQIdl, AlgEtQIdl, RngIntElt->SetIndx[AlgEtQIdl]
- Ideals of Index
- IdealsOfIndex(O, N) : RngOrd, RngIntElt -> SeqEnum[RngOrdIdl]
- IdealsOfIndex(I, N) : RngOrdIdl, RngIntElt -> SeqEnum[RngOrdIdl]
- IdealsOfIndex(I, N) : RngOrdFracIdl, RngIntElt -> SeqEnum[RngOrdFracIdl]
- IdealsOfIndex(I, N) : AlgEtQIdl, RngIntElt -> SeqEnum[AlgEtQIdl]
- IdealsOfIndex(O, N) : AlgEtQOrd, RngIntElt -> SeqEnum[AlgEtQIdl]
- Short Element and Small Representative
- Minimal Generators
- Chinese Remainder Theorem
- Picard Group
- ResidueRingUnits(S, I) : AlgEtQOrd, AlgEtQIdl -> GrpAb,Map
- ResidueRingUnits(I) : AlgEtQIdl -> GrpAb,Map
- ResidueRingUnitsSubgroupGenerators(F) : AlgEtQIdl -> SeqEnum[AlgEtQElt]
- IsPrincipal(I1) : AlgEtQIdl ->BoolElt, AlgAssElt
- PicardGroup(S) : AlgEtQOrd -> GrpAb, Map
- ExtensionHomPicardGroups(S, T) : AlgEtQOrd, AlgEtQOrd -> Map
- UnitGroup(S) : AlgEtQOrd -> GrpAb, Map
- Example AlgEtQ_PicardAndUnits (H42E10)
- IsIsomorphic(I, J) : AlgEtQIdl, AlgEtQIdl -> BoolElt, AlgAssElt
- Factorization and Primes
- Low Cohen Macauley Type
- Weak Classes
- Weak Testing
- Ideal Class Monoid
- Complex Conjugation
- Complex Multiplication
- Totally Real and Positive
- Printing and Saving
- Bibliography
V2.29, 28 November 2025