Introduction

      Representation

 
Creation of Structures
      QuadraticField(m) : RngIntElt -> FldQuad
      EquationOrder(F) : FldQuad -> RngQuad
      MaximalOrder(F) : FldQuad -> RngQuad
      NumberField(O) : RngQuad -> FldQuad
      sub< O | f > : RngQuad, RngIntElt ->
      IsQuadratic(K) : FldNum -> BoolElt, FldQuad
      Example FldQuad_creation (H37E1)
      Example FldQuad_hom (H37E2)

 
Operations on Structures
      AssignNames(~F, [s]) : FldQuad, [ MonStgElt ]) ->
      Name(F, 1) : FldQuad, RngIntElt -> FldQuadElt
      FundamentalUnit(K) : FldQuad -> FldQuadElt
      Discriminant(K) : FldQuad -> RngIntElt
      Conductor(K) : FldQuad -> RngIntElt, [RngIntElt]
      Conductor(O) : RngQuad -> RngIntElt

      Ideal Class Group
            ClassGroup(K) : FldQuad -> GrpAb, Map
            ClassNumber(K) : FldQuad -> RngIntElt
            PicardGroup(O) : RngQuad -> GrpAb, Map
            Example FldQuad_quad_sieve (H37E3)
            QuadraticClassGroupTwoPart(K) : FldQuad -> GrpAb, Map
            Example FldQuad_qcgtp (H37E4)

      Norm Equations
            NormEquation(F, m) : FldQuad, RngIntElt -> BoolElt, SeqEnum
            Example FldQuad_norm-equation (H37E5)

 
Special Element Operations

      Division Algorithm
            a div b : RngQuadElt, RngQuadElt -> RngQuadElt
            a mod b : RngQuadElt, RngQuadElt -> RngQuadElt
            GreatestCommonDivisor(a, b) : RngQuadElt, RngQuadElt -> RngQuadElt
            LeastCommonMultiple(a, b) : RngQuadElt, RngQuadElt -> RngQuadElt
            Modexp(a, e, n) : RngQuadElt, RngInt, RngQuadElt -> RngQuadElt

      Factorization
            Factorization(n) : RngQuadElt -> SeqEnum, Tup
            TrialDivision(n, B) : RngQuadElt, RngIntElt -> SeqEnum, SeqEnum, Tup

      Conjugates
            ComplexConjugate(a) : FldQuadElt -> FldQuadElt
            Conjugate(a) : FldQuadElt -> FldQuadElt

      Other Element Functions
            BiquadraticResidueSymbol(a, b) : RngQuadElt, RngQuadElt -> RngQuadElt
            Primary(a) : RngQuadElt -> RngQuadElt
            Example FldQuad_Represent (H37E6)

 
Special Functions for Ideals
      Content(I) : RngQuadFracIdl -> RngQuadFracIdl
      Conjugate(I) : RngQuadFracIdl -> RngQuadFracIdl
      Discriminant(I) : RngQuadFracIdl -> RngIntElt
      QuadraticForm(I) : RngQuadFracIdl -> QuadBinElt
      Ideal(f) : QuadBinElt -> RngQuadIdl
      Reduction(I) : RngQuadFracIdl -> RngQuadFracIdl

 
Bibliography

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