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
IsFundamental(D) : RngIntElt -> BoolElt
Conductor(Q) : QuadBin -> RngIntElt
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
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
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 (H33E1)
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 (H33E2)
Class Invariants
HilbertClassPolynomial(D) : RngIntElt -> RngUPolElt
WeberClassPolynomial(D) : RngIntElt -> RngUPolElt
Matrix Action on Forms
f * M : QuadBinElt, GrpMatElt -> QuadBinElt
Bibliography
[Next][Prev] [Right] [____] [Up] [Index] [Root]
Version: V2.19 of
Mon Dec 17 14:40:36 EST 2012