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
      IsFundamental(D) : RngIntElt -> BoolElt
      FundamentalDiscriminant(D) : RngIntElt -> RngIntElt
      Conductor(Q) : QuadBin -> RngIntElt

 
Operations on Forms

      Arithmetic
            Conjugate(f) : QuadBinElt -> QuadBinElt
            f * g : QuadBinElt, QuadBinElt -> QuadBinElt
            f ^ n : QuadBinElt, RngIntElt -> QuadBinElt

      Matrix Action
            f * M : QuadBinElt, GrpMatElt -> QuadBinElt

      Reduction
            Reduction(f) : QuadBinElt -> QuadBinElt, Mtrx
            ReductionStep(f) : QuadBinElt -> QuadBinElt
            ReductionOrbit(f) : QuadBinElt -> {@ QuadBinElt @}
            Order(f) : QuadBinElt -> RngIntElt

      Attribute Access
            f[i] : QuadBinElt, RngIntElt -> RngIntElt
            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

      Maps of Forms
            FundamentalQuotient(Q) : QuadBin -> Map
            QuotientMap(Q1, Q2) : QuadBin, QuadBin -> Map
            Q ! f : QuadBin, QuadBinElt -> QuadBinElt

      Related Structures
            QuadraticOrder(Q) : QuadBin -> RngQuad
            Ideal(f) : QuadBinElt -> RngQuadIdl

 
Reduced Forms
      ReducedForms(Q) : QuadBin -> [ QuadBinElt ]
      ReducedOrbits(Q) : QuadBin -> [ {@ QuadBinElt @} ]

 
Class Groups
      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 (H35E1)

 
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 (H35E2)

 
Class Invariants

 
Bibliography

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