# Hypergeometric Motives

- [Introduction](Introduction.md)

- [Functionality](Functionality.md)

  - [Creation Functions](Functionality.md#creation-functions)

    - [`HypergeometricData(A, B): SeqEnum, SeqEnum → HypGeomData`](Functionality.md#function-hypergeometricdata-seqenum-seqenum)

    - [`HypergeometricData(F, G): RngUPolElt, RngUPolElt → HypGeomData`](Functionality.md#function-hypergeometricdata-rngupolelt-rngupolelt)

    - [`HypergeometricData(G): SeqEnum[RngIntElt] → HypGeomData`](Functionality.md#function-hypergeometricdata-seqenum-rngintelt)

    - [`HypergeometricData(L): List → HypGeomData`](Functionality.md#function-hypergeometricdata-list)

    - [`HypergeometricData(F, G): SeqEnum[RngIntElt], SeqEnum[RngIntElt] → HypGeomData`](Functionality.md#function-hypergeometricdata-seqenum-rngintelt-seqenum-rngintelt)

    - [`HypergeometricData(E): SeqEnum[SeqEnum] → HypGeomData`](Functionality.md#function-hypergeometricdata-seqenum-seqenum-2)

    - [`Twist(H): HypGeomData → HypGeomData`](Functionality.md#function-twist-hypgeomdata)

    - [`PrimitiveData(H): HypGeomData → HypGeomData`](Functionality.md#function-primitivedata-hypgeomdata)

    - [`PossibleHypergeometricData(d): RngIntElt → SeqEnum`](Functionality.md#function-possiblehypergeometricdata-rngintelt)

  - [Access Functions](Functionality.md#access-functions)

    - [`Weight(H): HypGeomData → RngIntElt`](Functionality.md#function-weight-hypgeomdata)

    - [`Degree(H): HypGeomData → RngIntElt`](Functionality.md#function-degree-hypgeomdata)

    - [`DefiningPolynomials(H): HypGeomData → RngUPolElt, RngUPolElt`](Functionality.md#function-definingpolynomials-hypgeomdata)

    - [`Bezoutian(H): HypGeomData → RngIntElt`](Functionality.md#function-bezoutian-hypgeomdata)

    - [`CyclotomicData(H): HypGeomData → SeqEnum, SeqEnum`](Functionality.md#function-cyclotomicdata-hypgeomdata)

    - [`AlphaBetaData(H): HypGeomData → SeqEnum, SeqEnum`](Functionality.md#function-alphabetadata-hypgeomdata)

    - [`MValue(H): HypGeomData → FldRatElt`](Functionality.md#function-mvalue-hypgeomdata)

    - [`GammaArray(H): HypGeomData → SeqEnum`](Functionality.md#function-gammaarray-hypgeomdata)

    - [`GammaList(H): HypGeomData → List`](Functionality.md#function-gammalist-hypgeomdata)

    - [`H1 eq H2: HypGeomData, HypGeomDat → BoolElt`](Functionality.md#operation-op-eq-hypgeomdata-hypgeomdat)

    - [`H1 ne H2: HypGeomData, HypGeomDat → BoolElt`](Functionality.md#operation-op-ne-hypgeomdata-hypgeomdat)

    - [`IsPrimitive(H): HypGeomData → BoolElt, RngIntElt`](Functionality.md#function-isprimitive-hypgeomdata)

  - [Functionality with $L$-series and Euler Factors](Functionality.md#functionality-with-l-series-and-euler-factors)

    - [`HypergeometricTrace(H, t, q): HypGeomData, RngQZElt, RngIntElt → RngIntElt`](Functionality.md#function-hypergeometrictrace-hypgeomdata-rngqzelt-rngintelt)

    - [`HypergeometricTraceK(A, B, t, q): SeqEnum, SeqEnum, RngQZElt, RngIntElt → FldPadElt`](Functionality.md#function-hypergeometrictracek-seqenum-seqenum-rngqzelt-rngintelt)

    - [`HypergeometricTraceK(A, B, t, q): SeqEnum, SeqEnum, FldPadElt, RngIntElt → FldPadElt`](Functionality.md#function-hypergeometrictracek-seqenum-seqenum-fldpadelt-rngintelt)

    - [`EulerFactor(H, t, p): HypGeomData, RngQZElt, RngIntElt → RngUPolElt`](Functionality.md#function-eulerfactor-hypgeomdata-rngqzelt-rngintelt)

    - [`LSeries(H, t): HypGeomData, RngQZElt → LSer, LSer`](Functionality.md#function-lseries-hypgeomdata-rngqzelt)

    - [Identification of Hypergeometric Data as Other Objects](Functionality.md#identification-of-hypergeometric-data-as-other-objects)

      - [`ArtinRepresentation(H, t): HypGeomData, RngQZElt → ArtRep`](Functionality.md#function-artinrepresentation-hypgeomdata-rngqzelt)

      - [`EllipticCurve(H): HypGeomData → CrvEll`](Functionality.md#function-ellipticcurve-hypgeomdata)

      - [`EllipticCurve(H, t): HypGeomData, RngQZElt → CrvEll`](Functionality.md#function-ellipticcurve-hypgeomdata-rngqzelt)

      - [`HyperellipticCurve(H): HypGeomData → CrvHyp`](Functionality.md#function-hyperellipticcurve-hypgeomdata)

      - [`HyperellipticCurve(H, t): HypGeomData, RngQZElt → CrvHyp`](Functionality.md#function-hyperellipticcurve-hypgeomdata-rngqzelt)

      - [`Identify(H, t): HypGeomData, RngQZElt → Any`](Functionality.md#function-identify-hypgeomdata-rngqzelt)

  - [Associated Schemes and Curves](Functionality.md#associated-schemes-and-curves)

    - [`CanonicalScheme(H): HypGeomData → Sch`](Functionality.md#function-canonicalscheme-hypgeomdata)

    - [`CanonicalScheme(H, t): HypGeomData, RngQZElt → Sch`](Functionality.md#function-canonicalscheme-hypgeomdata-rngqzelt)

    - [`CanonicalCurve(H): HypGeomData → Crv`](Functionality.md#function-canonicalcurve-hypgeomdata)

    - [`CanonicalCurve(H, t): HypGeomData, RngQZElt → Crv`](Functionality.md#function-canonicalcurve-hypgeomdata-rngqzelt)

    - [`AssociatedSchemes(H): HypGeomData → List, SeqEnum, RngIntElt`](Functionality.md#function-associatedschemes-hypgeomdata)

    - [`AssociatedSchemes(H, t): HypGeomData, RngElt → List, SeqEnum, RngIntElt`](Functionality.md#function-associatedschemes-hypgeomdata-rngelt)

  - [Utility Functions](Functionality.md#utility-functions)

    - [`HypergeometricMotiveSaveLimit(n): RngIntElt`](Functionality.md#function-hypergeometricmotivesavelimit-rngintelt)

    - [`HypergeometricMotiveClearTable()`](Functionality.md#function-hypergeometricmotivecleartable)

    - [`pPart(H, p): HypGeomMot, RngIntElt → Tup`](Functionality.md#function-ppart-hypgeommot-rngintelt)

    - [`pParts(H): HypGeomMot → List`](Functionality.md#function-pparts-hypgeommot)

- [Examples](hypergeom-examples.md)

  - [`Example: Hypergeom Mot First Example`](hypergeom-examples.md#example-ex-15319e)

  - [`Example: Hg Twist Example`](hypergeom-examples.md#example-ex-81c686)

  - [`Example: imprimitivity`](hypergeom-examples.md#example-ex-34ea1e)

  - [`Example: Canonical Schemes And Curves`](hypergeom-examples.md#example-ex-77d133)

  - [`Example: Associated Schemes`](hypergeom-examples.md#example-ex-c4df99)

  - [`Example: Hg Siegel Modular Form`](hypergeom-examples.md#example-ex-678dfc)

  - [`Example: Hypergeometric Tracek`](hypergeom-examples.md#example-ex-6d9b8f)

  - [`Example: Hg Bad Reduction`](hypergeom-examples.md#example-ex-bd0b5d)

  - [`Example: Hg Quintic 3fold`](hypergeom-examples.md#example-ex-87ce78)

  - [`Example: Tame Primes`](hypergeom-examples.md#example-ex-3f5d52)

  - [`Example: More Tame Primes`](hypergeom-examples.md#example-ex-00ce74)

  - [`Example: Hgm Speed Test`](hypergeom-examples.md#example-ex-1d8d1b)

  - [Special Hypergeometric Motives](hypergeom-examples.md#special-hypergeometric-motives)

    - [`Example: First Special HGM Example`](hypergeom-examples.md#example-ex-77313e)

- [Jacobi Motives](Jacobi_motives.md)

  - [Background](Jacobi_motives.md#background)

  - [Kummer and Tate Twists](Jacobi_motives.md#kummer-and-tate-twists)

- [Jacobi Motive Functionality](jacmot-functionality.md)

  - [Creation Functions](jacmot-functionality.md#creation-functions)

    - [`JacobiMotive(A, B): SeqEnum, SeqEnum → JacketMot`](jacmot-functionality.md#function-jacobimotive-seqenum-seqenum)

    - [`JacketMotive(A, B, t, rho, j): SeqEnum, SeqEnum, RngQZElt, RngQZElt, RngIntElt → JacketMot`](jacmot-functionality.md#function-jacketmotive-seqenum-seqenum-rngqzelt-rngqzelt-rngintelt)

    - [`KummerTwist(J, t, rho): JacketMot, RngQZElt, RngQZElt → JacketMot`](jacmot-functionality.md#function-kummertwist-jacketmot-rngqzelt-rngqzelt)

    - [`TateTwist(J, j): JacketMot, RngIntElt → JacketMot`](jacmot-functionality.md#function-tatetwist-jacketmot-rngintelt)

  - [Operations](jacmot-functionality.md#operations)

    - [`J1 * J2: JacketMot, JacketMot → JacketMot`](jacmot-functionality.md#operation-op-times-jacketmot-jacketmot)

    - [`J1 / J2: JacketMot, JacketMot → JacketMot`](jacmot-functionality.md#operation-op-div-jacketmot-jacketmot)

    - [`J1 eq J2: JacketMot, JacketMot → JacketMot`](jacmot-functionality.md#operation-op-eq-jacketmot-jacketmot)

    - [`J1 ne J2: JacketMot, JacketMot → JacketMot`](jacmot-functionality.md#operation-op-ne-jacketmot-jacketmot)

    - [`Scale(J, q): JacketMot, RngQZElt → JacketMot`](jacmot-functionality.md#function-scale-jacketmot-rngqzelt)

  - [Attributes](jacmot-functionality.md#attributes)

    - [`Field(J): JacketMot → FldNum`](jacmot-functionality.md#function-field-jacketmot)

    - [`Weight(J): JacketMot → RngIntElt`](jacmot-functionality.md#function-weight-jacketmot)

    - [`EffectiveWeight(J): JacketMot → RngIntElt`](jacmot-functionality.md#function-effectiveweight-jacketmot)

    - [`HodgeStructure(J): JacketMot → HodgeStruc`](jacmot-functionality.md#function-hodgestructure-jacketmot)

    - [`HodgeVector(J): JacketMot → HodgeStruc, RngIntElt`](jacmot-functionality.md#function-hodgevector-jacketmot)

    - [`EffectiveHodgeStructure(J): JacketMot → HodgeStruc`](jacmot-functionality.md#function-effectivehodgestructure-jacketmot)

  - [L-function](jacmot-functionality.md#l-function)

    - [`EulerFactor(J, p): JacketMot, RngIntElt → RngUPolElt`](jacmot-functionality.md#function-eulerfactor-jacketmot-rngintelt)

    - [`ComplexEvaluation(J, P): JacketMot, RngOrdIdl → FldComElt`](jacmot-functionality.md#function-complexevaluation-jacketmot-rngordidl)

    - [`Grossencharacter(J): JacketMot → GrossenChar`](jacmot-functionality.md#function-grossencharacter-jacketmot)

- [Jacobi Motive Examples](jacobi-examples.md)

  - [`Example: Jacobi Motive First Example`](jacobi-examples.md#example-ex-1aeb77)

  - [`Example: Jacobi Motive7`](jacobi-examples.md#example-ex-475839)

  - [`Example: Jacobi Arith`](jacobi-examples.md#example-ex-c0a387)

  - [`Example: Jacobi Same OverQ`](jacobi-examples.md#example-ex-46e756)

  - [`Example: Jacobi Relation To Hypergeom`](jacobi-examples.md#example-ex-b87008)