Introduction

 
Functionality

      Creation Functions
            HypergeometricData(A, B) : SeqEnum, SeqEnum -> HypGeomData
            HypergeometricData(G) : SeqEnum[RngIntElt] -> HypGeomData
            HypergeometricData(L) : 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
            Bezoutian(H) : HypGeomData -> RngIntElt
            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
            HypergeometricTrace(H, t, q) : HypGeomData, RngQZElt, RngIntElt -> RngIntElt
            HypergeometricTraceK(A, B, t, q) : SeqEnum, SeqEnum, RngQZElt, RngIntElt -> FldPadElt
            EulerFactor(H, t, p) : HypGeomData, RngQZElt, RngIntElt -> RngUPolElt
            LSeries(H, t) : HypGeomData, RngQZElt -> LSer, LSer

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

      Associated Schemes and Curves
            CanonicalScheme(H) : HypGeomData -> Sch
            CanonicalCurve(H) : HypGeomData -> Crv
            AssociatedSchemes(H) : HypGeomData -> List, SeqEnum, RngIntElt

      Utility Functions
            HypergeometricMotiveSaveLimit(n) : RngIntElt ->
            pPart(H, p) : HypGeomMot, RngIntElt -> Tup

 
Examples
      Example HypGeomMot_hypergeom-mot-first-example (H138E1)
      Example HypGeomMot_hg-twist-example (H138E2)
      Example HypGeomMot_imprimitivity (H138E3)
      Example HypGeomMot_canonical-schemes-and-curves (H138E4)
      Example HypGeomMot_associated-schemes (H138E5)
      Example HypGeomMot_hg-siegel-modular-form (H138E6)
      Example HypGeomMot_hypergeometric-tracek (H138E7)
      Example HypGeomMot_hg-bad-reduction (H138E8)
      Example HypGeomMot_hg-quintic-3fold (H138E9)
      Example HypGeomMot_tame-primes (H138E10)
      Example HypGeomMot_more-tame-primes (H138E11)
      Example HypGeomMot_hgm-speed-test (H138E12)

      Special Hypergeometric Motives
            Example HypGeomMot_first-special-HGM-example (H138E13)

 
Jacobi Motives

      Background

      Kummer and Tate Twists

 
Jacobi Motive Functionality

      Creation Functions
            JacobiMotive(A, B) : SeqEnum, SeqEnum -> JacketMot
            JacketMotive(A, B, t, rho, j) : SeqEnum, SeqEnum, RngQZElt, RngQZElt, RngIntElt -> JacketMot
            KummerTwist(J, t, rho) : JacketMot, RngQZElt, RngQZElt -> JacketMot
            TateTwist(J, j) : JacketMot, RngIntElt -> JacketMot

      Operations
            J1 * J2 : JacketMot, JacketMot -> JacketMot
            J1 / J2 : JacketMot, JacketMot -> JacketMot
            J1 eq J2 : JacketMot, JacketMot -> JacketMot
            Scale(J, q) : JacketMot, RngQZElt -> JacketMot

      Attributes
            Field(J) : JacketMot -> FldNum
            Weight(J) : JacketMot -> RngIntElt
            EffectiveWeight(J) : JacketMot -> RngIntElt
            HodgeStructure(J) : JacketMot -> HodgeStruc

      L-function
            EulerFactor(J, p) : JacketMot, RngIntElt -> RngUPolElt
            ComplexEvaluation(J, P) : JacketMot, RngOrdIdl -> FldComElt
            Grossencharacter(J) : JacketMot -> GrossenChar

 
Jacobi Motive Examples
      Example HypGeomMot_jacobi-motive-first-example (H138E14)
      Example HypGeomMot_jacobi-motive7 (H138E15)
      Example HypGeomMot_jacobi-arith (H138E16)
      Example HypGeomMot_jacobi-same-overQ (H138E17)
      Example HypGeomMot_jacobi-relation-to-hypergeom (H138E18)

 
Bibliography

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