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Magma
Computer • algebra
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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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V2.28, 28 February 2025