Introduction
Creation Functions
Creation of Structures BinaryQuadraticForms(D) : RngIntElt -> QuadBin
Creation of Forms Identity(Q) : QuadBin -> QuadBinElt Q ! [a, b, c] : QuadBin, RngIntElt, RngIntElt, RngIntElt -> QuadBinElt PrimeForm(Q, p) : QuadBin, RngIntElt -> QuadBinElt
Basic Invariants Discriminant(f) : QuadBinElt -> RngIntElt Discriminant(Q) : QuadBin -> RngIntElt IsDiscriminant(D) : RngIntElt -> BoolElt FundamentalDiscriminant(D) : RngIntElt -> RngIntElt IsFundamentalDiscriminant(D) : RngIntElt -> BoolElt Conductor(Q) : QuadBin -> RngIntElt
Operations on Forms
Arithmetic Conjugate(f) : QuadBinElt -> QuadBinElt f * g : QuadBinElt, QuadBinElt -> QuadBinElt f ^ n : QuadBinElt, RngIntElt -> QuadBinElt Reduction(f) : QuadBinElt -> QuadBinElt, Mtrx ReductionStep(f) : QuadBinElt -> QuadBinElt ReductionOrbit(f) : QuadBinElt -> SeqEnum[QuadBinElt] Order(f) : QuadBinElt -> RngIntElt
Attribute Access Eltseq(f) : QuadBinElt -> SeqEnum[RngIntElt]
Boolean Operations f in Q : QuadBinElt, QuadBin -> BoolElt f eq g : QuadBinElt, QuadBinElt -> BoolElt IsIdentity(f) : QuadBinElt -> BoolElt IsReduced(f) : QuadBinElt -> BoolElt IsEquivalent(f, g) : QuadBinElt, QuadBinElt -> BoolElt, AlgMatElt
Related Structures QuadraticOrder(Q) : QuadBin -> RngQuad Ideal(f) : QuadBinElt -> RngQuadIdl
Class Group ReducedForms(Q) : QuadBin -> [ QuadBinElt ] ReducedOrbits(Q) : QuadBin -> [ {@ QuadBinElt @} ] ClassNumber(Q: parameters) : QuadBin -> RngIntElt ClassGroup(Q: parameters) : QuadBin -> GrpAb, Map ClassGroupStructure(Q: parameters) : QuadBin -> [ RngIntElt ] AmbiguousForms(Q) : QuadBin -> SeqEnum TwoTorsionSubgroup(Q) : QuadBin -> GrpAb, Map Example QuadBin_Forms (H30E1)
Class Group Coercions FundamentalQuotient(Q) : QuadBin -> Map QuotientMap(Q1, Q2) : QuadBin, QuadBin -> Map Q ! f : QuadBin, QuadBinElt -> QuadBinElt
Discrete Logarithms Log(b, x): QuadBinElt, QuadBinElt -> RngIntElt Log(b, x, t): QuadBinElt, QuadBinElt, RngIntElt -> RngIntElt
Elliptic and Modular Invariants Lattice(f) : QuadBinElt -> Lat GramMatrix(f) : QuadBinElt -> AlgMatElt ThetaSeries(f, n) : QuadBinElt, RngIntElt -> RngSerElt RepresentationNumber(f, n) : QuadBinElt, RngIntElt -> RngIntElt jInvariant(f) : QuadBinElt -> RngSerElt Eisenstein(k, f) : RngIntElt, QuadBinElt -> RngSerElt WeierstrassSeries(z, f) : RngSerElt, QuadBinElt -> RngSerElt Example QuadBin_ell_mod (H30E2)
Class Invariants HilbertClassPolynomial(D) : RngIntElt -> RngUPolElt WeberClassPolynomial(D) : RngIntElt -> RngUPolElt
Matrix Action on Forms
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