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HYPERGEOMETRIC MOTIVES

 
Acknowledgements
 
Introduction
 
Functionality
      Creation Functions
      Access Functions
      Functionality with L-series and Euler Factors
            Identification of Hypergeometric Data as Other Objects
      Associated Schemes and Curves
      Utility Functions
 
Examples
 
Bibliography







DETAILS

 
Introduction

 
Functionality

      Creation Functions
            HypergeometricData(A, B) : SeqEnum, SeqEnum -> HypGeomData
            HypergeometricData(G) : SeqEnum[RngIntElt] -> HypGeomData
            HypergeometricData(G) : List -> HypGeomData
            HypergeometricData(F, G) : SeqEnum[RngIntElt], SeqEnum[RngIntElt] -> HypGeomData
            HypergeometricData(E) : SeqEnum[SeqEnum] -> HypGeomData
            Twist(H) : HypGeomData -> HypGeomData
            PrimitiveData(H) : HypGeomData -> HypGeomData
            PossibleHypergeometricData(d) : RngIntElt -> SeqEnum

      Access Functions
            Weight(H) : HypGeomData -> RngIntElt
            Degree(H) : HypGeomData -> RngIntElt
            DefiningPolynomials(H) : HypGeomData -> RngUPolElt, RngUPolElt
            CyclotomicData(H) : HypGeomData -> SeqEnum, SeqEnum
            AlphaBetaData(H) : HypGeomData -> SeqEnum, SeqEnum
            MValue(H) : HypGeomData -> FldRatElt
            GammaArray(H) : HypGeomData -> SeqEnum
            GammaList(H) : HypGeomData -> List
            H1 eq H2 : HypGeomData, HypGeomDat -> BoolElt
            IsPrimitive(H) : HypGeomData -> BoolElt, RngIntElt

      Functionality with L-series and Euler Factors
            EulerFactor(H, t, p) : HypGeomData, FldRatElt, RngIntElt -> RngUPolElt
            LSeries(H, t) : HypGeomData, FldRatElt -> LSer

            Identification of Hypergeometric Data as Other Objects
                  ArtinRepresentation(H, t) : HypGeomData, FldRatElt -> ArtRep
                  EllipticCurve(H) : HypGeomData -> CrvEll
                  HyperellipticCurve(H) : HypGeomData -> CrvHyp
                  Identify(H, t) : HypGeomData, FldRatElt -> Any

      Associated Schemes and Curves
            CanonicalScheme(H) : HypGeomData -> Sch
            CanonicalCurve(H) : HypGeomData -> Crv

      Utility Functions
            HypergeometricMotiveSaveLimit(n) : RngIntElt -> Void

 
Examples
      Example HypGeomMot_hypergeom-mot-first-example (H126E1)
      Example HypGeomMot_hg-twist-example (H126E2)
      Example HypGeomMot_imprimitivity (H126E3)
      Example HypGeomMot_canonical-schemes-and-curves (H126E4)
      Example HypGeomMot_hg-siegel-modular-form (H126E5)
      Example HypGeomMot_hg-bad-reduction (H126E6)
      Example HypGeomMot_hg-quintic-3fold (H126E7)
      Example HypGeomMot_tame-primes (H126E8)
      Example HypGeomMot_hgm-speed-test (H126E9)

 
Bibliography

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Version: V2.19 of Wed Apr 24 15:09:57 EST 2013