Rational Curve and Conic Creation
Conic(coeffs) : [RngElt] -> CrvCon
Conic(M) : Mtrx -> CrvCon
Conic(X, f) : Prj, RngMPolElt -> CrvCon
IsConic(S) : Sch -> BoolElt, CrvCon
RationalCurve(X, f) : Prj, RngMPolElt -> CrvRat
IsRationalCurve(S) : Sch -> BoolElt, CrvRat
Example CrvCon_ConicCreation (H119E1)
Access Functions
DefiningPolynomial(C) : Crv -> RngMPolElt
DefiningIdeal(C) : Crv -> RngMPol
Rational Curve and Conic Examples
Example CrvCon_RationalCurveExample (H119E2)
Example CrvCon_ConicCurve (H119E3)
Example CrvCon_ConicAccess (H119E4)
Elementary Invariants
Discriminant(C) : CrvCon -> FldElt
Alternative Defining Polynomials
LegendrePolynomial(C) : CrvCon -> RngMPolElt, ModMatRngElt
ReducedLegendrePolynomial(C) : CrvCon -> RngMPolElt, ModMatRngElt
Alternative Models
LegendreModel(C) : CrvCon -> CrvCon, MapIsoSch
ReducedLegendreModel(C) : CrvCon -> CrvCon, MapIsoSch
Other Functions on Conics
MinimalModel(C) : CrvCon -> CrvCon, Map
Example CrvCon_ConicMinimalModel (H119E5)
Local Conditions for Conics
BadPrimes(C) : CrvCon -> SeqEnum
Norm Residue Symbol
NormResidueSymbol(a, b, p) : FldRatElt, FldRatElt, RngIntElt -> RngIntElt
HilbertSymbol(a, b, p : parameters) : FldRatElt, FldRatElt, RngIntElt -> RngIntElt
Example CrvCon_LocalGlobal (H119E6)
Finding Points
HasRationalPoint(C) : CrvCon -> BoolElt, Pt
RationalPoint(C) : CrvCon -> Pt
Random(C : parameters) : CrvCon -> Pt
Points(C : parameters) : CrvCon -> SetIndx
Example CrvCon_rational-point-enum (H119E7)
Point Reduction
IsReduced(p) : Pt -> BoolElt
Reduction(p) : Pt -> Pt
Example CrvCon_PointReduction (H119E8)
Example CrvCon_PointFinding (H119E9)
Isomorphisms with Standard Models
Conic(C) : Crv -> MapSch
Example CrvCon_ (H119E10)
ParametrizationMatrix(C) : CrvCon -> ModMatRngElt
Example CrvCon_ (H119E11)
Parametrization(C) : CrvCon -> MapSch
Example CrvCon_RationalParametrization (H119E12)
Automorphisms of Rational Curves
Automorphism(C, S, T) : CrvRat, SetIndx, SetIndx -> MapIsoSch
Automorphisms of Conics
QuaternionAlgebra(C) : CrvCon-> AlgQuat
Automorphism(C, a) : CrvCon, AlgQuatElt -> MapIsoSch
Example CrvCon_ConicAutomorphisms (H119E13)
Bibliography
[Next][Prev] [Right] [____] [Up] [Index] [Root]
Version: V2.19 of
Mon Dec 17 14:40:36 EST 2012