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 (H32E1) Example FldQuad_hom (H32E2)
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 QuadraticClassGroupTwoPart(K) : FldQuad -> GrpAb, Map Example FldQuad_qcgtp (H32E3)
Norm Equations NormEquation(F, m) : FldQuad, RngIntElt -> BoolElt, SeqEnum Example FldQuad_norm-equation (H32E4)
Special Element Operations a mod b : RngQuadElt, RngQuadElt -> RngQuadElt
Greatest Common Divisors Gcd(a, b) : RngQuadElt, RngQuadElt -> RngQuadElt Lcm(a, b) : RngQuadElt, RngQuadElt -> RngQuadElt
Modular Arithmetic 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 (H32E5)
Special Functions for Ideals Content(I) : RngQuadFracIdl -> RngQuadFracIdl Conjugate(I) : RngQuadFracIdl -> RngQuadFracIdl Discriminant(I) : RngQuadFracIdl -> RngIntElt QuadraticForm(I) : RngQuadFracIdl -> QuadBinElt Ideal(f) : QuadBinElt -> RngQuadIdl
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