Skip to content

Latest commit

 

History

History
209 lines (164 loc) · 8.2 KB

intrinsics.md

File metadata and controls

209 lines (164 loc) · 8.2 KB
Raw

Exported intrinsics

Invariants

Genus 2

intrinsic IgusaInvariants(f::RngUPolElt, h::RngUPolElt :
    extend := false, normalize := false) -> SeqEnum, SeqEnum
intrinsic IgusaInvariants(f::RngUPolElt :
    Quick  := false, extend := false, normalize := false) -> SeqEnum, SeqEnum
intrinsic IgusaInvariants(f::RngMPolElt :
    Quick  := false, extend := false, normalize := false) -> SeqEnum, SeqEnum
intrinsic IgusaInvariants(f::RngUPolElt, p::RngIntElt :
    Quick  := false, extend := false, normalize := false) -> SeqEnum, SeqEnum
intrinsic IgusaInvariants(f::RngMPolElt, p::RngIntElt :
    Quick  := false, extend := false, normalize := false) -> SeqEnum, SeqEnum
intrinsic IgusaInvariants(C::CrvHyp :
    Quick := false, extend := false, normalize := false) -> SeqEnum, SeqEnum

intrinsic IgusaInvariantsEqual(JI1::SeqEnum, JI2::SeqEnum) -> BoolElt
intrinsic DiscriminantFromIgusaInvariants(JI::SeqEnum) -> .
intrinsic IgusaAlgebraicRelations(JI::SeqEnum) -> SeqEnum

intrinsic G2Invariants(X::CrvHyp) -> SeqEnum
intrinsic IgusaToG2Invariants(JI::SeqEnum) -> SeqEnum
intrinsic G2ToIgusaInvariants(GI::SeqEnum) -> SeqEnum

Genus 3

intrinsic ShiodaInvariants(f::RngUPolElt, p::RngIntElt :
    normalize := false, PrimaryOnly := false, IntegralNormalization := false, degmax := Infinity(), degmin := 1) -> SeqEnum, SeqEnum
intrinsic ShiodaInvariants(f::RngMPolElt, p::RngIntElt :
    normalize := false, PrimaryOnly := false, IntegralNormalization := false, degmax := Infinity(), degmin := 1) -> SeqEnum, SeqEnum
intrinsic ShiodaInvariants(f::RngUPolElt :
    normalize := false, PrimaryOnly := false, IntegralNormalization := false, degmax := Infinity(), degmin := 1) -> SeqEnum, SeqEnum
intrinsic ShiodaInvariants(f::RngMPolElt :
    normalize := false, PrimaryOnly := false, IntegralNormalization := false, degmax := Infinity(), degmin := 1) -> SeqEnum, SeqEnum
intrinsic ShiodaInvariants(fh::SeqEnum :
    normalize := false, PrimaryOnly := false, IntegralNormalization := false, degmax := Infinity(), degmin := 1) -> SeqEnum, SeqEnum
intrinsic ShiodaInvariants(C::CrvHyp :
    normalize := false, PrimaryOnly := false, IntegralNormalization := false, degmax := Infinity(), degmin := 1) -> SeqEnum, SeqEnum

intrinsic ShiodaInvariantsEqual(JI1::SeqEnum, JI2::SeqEnum) -> BoolElt
intrinsic DiscriminantFromShiodaInvariants(JI::SeqEnum) -> .
intrinsic ShiodaAlgebraicInvariants(PrimaryInvariants::SeqEnum :
    ratsolve := true) -> SeqEnum

intrinsic MaedaInvariants(f::RngUPolElt) -> SeqEnum
intrinsic MaedaInvariants(C::CrvHyp) -> SeqEnum

Reconstruct curve from invariants

Genus 2

intrinsic HyperellipticCurveFromIgusaInvariants(II::SeqEnum :
    RationalModel := false, minimize := true) -> CrvHyp, GrpPerm
intrinsic HyperellipticCurveFromG2Invariants(GI::SeqEnum :
    RationalModel := false, minimize := true) -> CrvHyp, GrpPerm

Genus 3

intrinsic HyperellipticCurveFromShiodaInvariants(JI::SeqEnum :
    RationalModel := true, minimize := true) -> CrvHyp, GrpPerm
intrinsic HyperellipticPolynomialFromShiodaInvariants(JI::SeqEnum :
    RationalModel := true, minimize := true) -> SeqEnum, GrpPerm
intrinsic HyperellipticPolynomialsFromShiodaInvariants(JI::SeqEnum :
    RationalModel := true, minimize := true) -> SeqEnum, GrpPerm

Isomorphisms

Genus 1

intrinsic GeometricAutomorphismGroup(Ec::CrvEll) -> GrpPerm

Genus 2

intrinsic GeometricAutomorphismGroupFromIgusaInvariants(II::SeqEnum) -> GrpPerm
intrinsic GeometricAutomorphismGroupGenus2Classification(FF::FldFin) -> SeqEnum, SeqEnum

Genus 3

intrinsic GeometricAutomorphismGroupFromShiodaInvariants(JI::SeqEnum) -> GrpPerm
intrinsic GeometricAutomorphismGroupGenus3Classification(FF::FldFin) -> SeqEnum, SeqEnum

Any genus

intrinsic IsIsomorphicHyperellipticCurves(X1::CrvHyp, X2::CrvHyp :
    geometric := false, covariant := true, commonfield := true) ->  BoolElt, List
intrinsic IsIsomorphicHyperellipticCurves(f1::RngUPolElt, f2::RngUPolElt :
    geometric := false, covariant := true, commonfield := true) ->  BoolElt, List

intrinsic IsomorphismsOfHyperellipticCurves(X1::CrvHyp, X2::CrvHyp :
    geometric := false, covariant := true, commonfield := true) ->  List
intrinsic IsomorphismsOfHyperellipticCurves(f1::RngUPolElt, f2::RngUPolElt :
    geometric := false, covariant := true, commonfield := true) -> List

intrinsic AutomorphismsOfHyperellipticCurve(X::CrvHyp :
    geometric := false, commonfield := true, covariant := true) -> List
intrinsic AutomorphismsOfHyperellipticCurve(f::RngUPolElt :
    geometric := false, commonfield := true, covariant := true) -> List

intrinsic AutomorphismGroupOfHyperellipticCurve(X::CrvHyp, Autos::List :
    explicit := false) -> GrpPerm, Map
intrinsic AutomorphismGroupOfHyperellipticCurve(f::RngUPolElt, Autos::List :
    explicit := false) -> GrpPerm, Map

intrinsic AutomorphismGroupOfHyperellipticCurve(X::CrvHyp :
    geometric := false, explicit := false) -> GrpPerm, Map
intrinsic AutomorphismGroupOfHyperellipticCurve(f::RngUPolElt :
    geometric := false, explicit := false) -> GrpPerm, Map

intrinsic GeometricAutomorphismGroup(Ec::CrvEll) -> GrpPerm
    {Compute the geometric automorphism group of an elliptic curve.}
intrinsic GeometricAutomorphismGroup(X::CrvHyp) -> GrpPerm
    {Compute the geometric automorphism group of an hyperelliptic curve.}

Reduced isomorphisms

intrinsic IsGL2EquivalentExtended(f1::RngUPolElt, f2::RngUPolElt, deg::RngIntElt :
    geometric := false, covariant := true, commonfield := false) -> BoolElt, List

intrinsic IsReducedIsomorphicHyperellipticCurves(X1::CrvHyp, X2::CrvHyp :
    geometric := false, covariant := true, commonfield := true) ->  BoolElt, List
intrinsic IsReducedIsomorphicHyperellipticCurves(f1::RngUPolElt, f2::RngUPolElt :
    geometric := false, covariant := true, commonfield := true) ->  BoolElt, List

intrinsic ReducedIsomorphismsOfHyperellipticCurves(X1::CrvHyp, X2::CrvHyp :
    geometric := false, covariant := true, commonfield := true) ->  List
intrinsic ReducedIsomorphismsOfHyperellipticCurves(f1::RngUPolElt, f2::RngUPolElt :
    geometric := false, covariant := true, commonfield := true) ->  List

intrinsic ReducedAutomorphismsOfHyperellipticCurve(X::CrvHyp :
    geometric := false, commonfield := true, covariant := true) -> List
intrinsic ReducedAutomorphismsOfHyperellipticCurve(f::RngUPolElt :
    geometric := false, commonfield := true, covariant := true) -> List

intrinsic ReducedAutomorphismGroupOfHyperellipticCurve(X::CrvHyp, Autos::List :
    explicit := false) -> GrpPerm, Map
intrinsic ReducedAutomorphismGroupOfHyperellipticCurve(f::RngUPolElt, Autos::List :
    explicit := false) -> GrpPerm, Map

intrinsic ReducedAutomorphismGroupOfHyperellipticCurve(X::CrvHyp :
    geometric := false, explicit := false) -> GrpPerm, Map
intrinsic ReducedAutomorphismGroupOfHyperellipticCurve(f::RngUPolElt :
    geometric := false, explicit := false) -> GrpPerm, Map

Twists

Genus 2

intrinsic TwistsFromIgusaInvariants(JI::SeqEnum[FldFinElt]) -> SeqEnum[CrvHyp], GrpPerm
intrinsic TwistsFromG2Invariants(II::SeqEnum[FldFinElt]) -> SeqEnum[CrvHyp], GrpPerm

Genus 3

intrinsic TwistsFromShiodaInvariants(JI::SeqEnum[FldFinElt]) -> SeqEnum[CrvHyp], GrpPerm
intrinsic TwistedHyperellipticPolynomialsFromShiodaInvariants(JI::SeqEnum[FldFinElt] :
    RationalModel := true, Deterministic := false) -> SeqEnum, GrpPerm

Any genus

intrinsic Twists(X::CrvHyp :
    AutomorphismGroup := false) -> SeqEnum[CrvHyp], GrpPerm
intrinsic TwistsOfHyperellipticPolynomials(f::RngUPolElt :
    AutomorphismGroup := false) -> SeqEnum[RngUPolElt], GrpPerm
intrinsic TwistsOfHyperellipticPolynomials(fh::SeqEnum[RngUPolElt] :
    AutomorphismGroup := false) -> SeqEnum, GrpPerm

General curves

intrinsic Twists(C::Crv, Autos::SeqEnum  :
    AutomorphismGroup := false) -> SeqEnum[Crv], GrpPerm

Weighted projective space toolbox

intrinsic WPSEnumInit(FF::FldFin, Wght::SeqEnum) -> Rec
intrinsic WPSEnumNext(~V, ~WPSCtxt::Rec)
intrinsic WPSEqual(Wght::SeqEnum, V1::SeqEnum, V2::SeqEnum) -> BoolElt
intrinsic WPSNormalize(Wght::SeqEnum, V::SeqEnum) -> SeqEnuminsic;
intrinsic WPSMultiply(Wght::SeqEnum, V::SeqEnum, lambda::.) -> SeqEnum
intrinsic WPSMinimize(Wght::SeqEnum, V::SeqEnum) -> SeqEnum