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 (H35E1)
Example FldQuad_hom (H35E2)
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 (H35E3)
QuadraticClassGroupTwoPart(K) : FldQuad -> GrpAb, Map
Example FldQuad_qcgtp (H35E4)
Norm Equations
NormEquation(F, m) : FldQuad, RngIntElt -> BoolElt, SeqEnum
Example FldQuad_norm-equation (H35E5)
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 (H35E6)
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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Version: V2.19 of
Mon Dec 17 14:40:36 EST 2012