- Introduction
- Number Field Lattices
- Creation of Number Field Lattices
- NumberFieldLattice(K, d) : FldNum, RngIntElt -> LatNF
- NumberFieldLattice(S) : [ModTupFldElt] -> LatNF
- NumberFieldLattice(D) : ModDed -> LatNF
- NumberFieldLatticeWithGram(F) : Mtrx -> LatNF
- Module(L) : LatNF -> ModDed
- sub<L | RHS> : LatNF, Any -> LatNF, Map
- ext<L | RHS> : LatNF, Any -> LatNF, Map
- A + B : LatNF, LatNF -> LatNF
- A meet B : LatNF, LatNF -> LatNF
- r * L : RngElt, LatNF -> LatNF
- InnerProductScaling(L, r) : LatNF, RngElt -> LatNF
- J * L : RngOrdFracIdl, LatNF -> LatNF
- T * L : Mtrx, LatNF -> LatNF
- TJ * L : PMat, LatNF -> LatNF
- L * T : LatNF, Mtrx -> LatNF
- DirectSum(A, B) : LatNF, LatNF -> LatNF
- OrthogonalComplement(L, v) : LatNF, LatNFElt -> LatNF
- Dual(L) : LatNF -> LatNF
- SimpleLattice(L) : LatNF -> LatNF
- MaximalSublattices(L, p) : LatNF, RngOrdIdl -> [LatNF], [RngIntElt]
- MaximalIntegralLattice(Q) : Mtrx -> LatNF
- MaximalIntegralLattice(L) : LatNF -> LatNF
- Example LatNF_creation-examples (H32E1)
- Attributes of Number Field Lattices
- Basis(L) : LatNF -> [ModTupFldElt]
- LocalBasis(L, p) : LatNF, RngOrdIdl -> [ModTupFldElt]
- PseudoBasis(L) : LatNF -> [ModTupFldElt]
- PseudoMatrix(L) : LatNF -> PMat
- CoefficientIdeals(L) : LatNF -> SeqEnum
- Generators(L) : LatNF -> SeqEnum
- InnerProductMatrix(L) : LatNF -> Mtrx
- MakeAmbientInnerProduct(~L, IP) : LatNF ->
- GramMatrix(L) : LatNF -> Mtrx
- PseudoGramMatrix(L) : LatNF -> Mtrx
- Rank(L) : LatNF -> RngIntElt
- Degree(L) : LatNF -> RngIntElt
- BaseRing(L) : LatNF -> FldNum
- Determinant(L) : LatNF -> FldNumElt
- Discriminant(L) : LatNF -> RngOrdFracIdl
- Norm(L) : LatNF -> RngOrdFracIdl
- Scale(L) : LatNF -> RngOrdFracIdl
- BadPrimes(L) : LatNF -> Set
- JordanDecomposition(L, p) : LatNF, RndOrdIdl -> List, List, SeqEnum
- MaximalNormSplitting(L, p) : LatNF, RngOrdIdl -> SeqEnum, List
- GoodBasisOfNormGenerators(L, p) : LatNF, RngOrdIdl -> SeqEnum, SeqEnum
- GenusSymbol(L, p) : LatNF, RngOrdIdl -> SeqEnum, Any
- HasseInvariant(L, p) : LatNF, RngOrdIdl -> RngIntElt
- WittInvariant(L, p) : LatNF, RngOrdIdl -> RngIntElt
- SpinorNorm(L, p) : LatNF, RngOrdIdl -> ModTupFld, Map, BoolElt
- Mass(L) : LatNF -> FldRatElt
- Neighbours(L, p) : LatNF, RngOrdIdl -> [LatNF], [RngIntElt]
- IteratedNeighbours(L, p) : LatNF, RngOrdIdl -> [LatNF]
- GenusRepresentatives(L) : LatNF -> [LatNF]
- Example LatNF_attr-examples (H32E2)
- Predicates on Number Field Lattices
- IsSimple(L) : LatNF -> BoolElt
- IsFree(L) : LatNF -> BoolElt
- IsZero(L) : LatNF -> BoolElt
- IsTotallyPositiveDefinite(L) : LatNF -> BoolElt
- IsDefinite(L) : LatNF -> BoolElt, RngOrdElt
- A eq B : LatNF, LatNF -> BoolElt
- IsIdentical(A, B) : LatNF, LatNF -> BoolElt
- IsSublattice(S, L) : LatNF, LatNF -> BoolElt, Mtrx
- IsMaximal(L) : LatNF -> BoolElt, LatNF
- IsMaximalIntegral(L) : LatNF -> BoolElt, LatNF
- IsModular(L) : LatNF -> BoolElt, RngOrdFracIdl
- IsModular(L, p) : LatNF, RngOrdIdl -> BoolElt, RngIntElt
- IsIsotropic(L, p) : LatNF, RngOrdIdl -> BoolElt nosigIsIsotropic(L, p) : LatNF, PlcNumElt -> BoolElt
- IsLocallyIsometric(L1, L2, p) : LatNF, LatNF, RngOrdIdl -> BoolElt
- IsSameGenus(L1, L2) : LatNF, LatNF -> BoolElt
- IsRationallyEquivalent(L1, L2, p) : LatNF, LatNF, RngOrdIdl -> BoolElt
- IsRationallyEquivalent(L1, L2) : LatNF, LatNF -> BoolElt
- Totally Positive Definite Lattices
- AutomorphismGroup(L) : LatNF -> GrpMat
- IsIsometric(A, B) : LatNF, LatNF -> BoolElt, Mtrx
- IsSimilar(A, B) : LatNF, LatNF -> BoolElt, Mtrx, FldNumElt
- Sphere(L, e) : LatNF, RngElt -> Setq
- IsRepresented(L::LatNF, e) : LatNF, RngElt -> BoolElt, LatNFElt
- Number Field Lattice Elements
- Creation
- Parent and Element Relations
- Arithmetic
- v + w : LatNFElt, LatNFElt -> LatNFElt
- s * v : RngElt, LatNFElt -> LatNFElt
- T * v : Mtrx, LatNFElt -> LatNFElt
- v * T : LatNFElt, Mtrx -> LatNFElt
- v ^ M : LatNFElt, Mtrx -> LatNFElt
- v ^ G : LatNFElt, GrpMat -> Setq[LatNFElt]
- Stabilizer(G, v) : GrpMat, LatNFElt -> GrpMat
- Norm(v) : LatNFElt -> FldNumElt
- InnerProduct(v, w) : LatNFElt, LatNFElt -> FldNumElt
- Example LatNF_nflatelt-ex (H32E3)
- Access Functions
- Examples
- Lorentzian Lattices
- Special Intrinsics
- IsLorentzian(L) : LatNF -> BoolElt, ModTupFldElt, RngIntElt
- IsTimelike(v): LatNFElt -> BoolElt
- AutomorphismGroup(L, v) : LatNF, LatNFElt -> GrpMat, GrpMat
- IsIsometric(L, v, w) : LatNF, LatNFElt, LatNFElt -> BoolElt, Mtrx
- Example LatNF_simple-lorentz-lat-ex (H32E9)
- Bibliography
V2.28, 13 July 2023