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Datasets:
roseking
/
openAI-math-dataset

Languages:
English
Chinese
Size:
100K<n<1M
Tags:
mathematics
mirror
lean
formal-proofs
License:
Dataset card Files
xet
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openAI-math-dataset
File size: 15,695 Bytes
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import OAI.Dynamics.EntropyCounterexample.AmbientPrediction
import OAI.Dynamics.EntropyCounterexample.AmbientRetraction
import OAI.Dynamics.EntropyCounterexample.AngularDerivative
import OAI.Dynamics.EntropyCounterexample.AngularExtension
import OAI.Dynamics.EntropyCounterexample.Assembly
import OAI.Dynamics.EntropyCounterexample.AttractionSupport
import OAI.Dynamics.EntropyCounterexample.C1Conjugacy
import OAI.Dynamics.EntropyCounterexample.C1CoordinatePullback
import OAI.Dynamics.EntropyCounterexample.C1Coordinates
import OAI.Dynamics.EntropyCounterexample.C1Retraction
import OAI.Dynamics.EntropyCounterexample.C1Support
import OAI.Dynamics.EntropyCounterexample.CircleClockDoubling
import OAI.Dynamics.EntropyCounterexample.CircleDoublingChains
import OAI.Dynamics.EntropyCounterexample.CircleWindingCocycle
import OAI.Dynamics.EntropyCounterexample.Clock
import OAI.Dynamics.EntropyCounterexample.ClockAtInfinity
import OAI.Dynamics.EntropyCounterexample.ClockCharts
import OAI.Dynamics.EntropyCounterexample.ClockDynamics
import OAI.Dynamics.EntropyCounterexample.ClockLift
import OAI.Dynamics.EntropyCounterexample.ClockLiftBridge
import OAI.Dynamics.EntropyCounterexample.ClockLocalExtension
import OAI.Dynamics.EntropyCounterexample.ClockModel
import OAI.Dynamics.EntropyCounterexample.ClockOrbit
import OAI.Dynamics.EntropyCounterexample.ClockPassage
import OAI.Dynamics.EntropyCounterexample.ClockPeriodization
import OAI.Dynamics.EntropyCounterexample.ClockPeriodizationCompatibility
import OAI.Dynamics.EntropyCounterexample.ClockPeriodizationLocal
import OAI.Dynamics.EntropyCounterexample.ClockPrediction
import OAI.Dynamics.EntropyCounterexample.ClockProfiles
import OAI.Dynamics.EntropyCounterexample.ClockQuotient
import OAI.Dynamics.EntropyCounterexample.ClockQuotientC1
import OAI.Dynamics.EntropyCounterexample.ClockRotation
import OAI.Dynamics.EntropyCounterexample.ClockSupport
import OAI.Dynamics.EntropyCounterexample.CompactLabels
import OAI.Dynamics.EntropyCounterexample.ConcreteContinuity
import OAI.Dynamics.EntropyCounterexample.ConcreteErasure
import OAI.Dynamics.EntropyCounterexample.ConcreteErasureLimit
import OAI.Dynamics.EntropyCounterexample.ConcreteInputRegularity
import OAI.Dynamics.EntropyCounterexample.Conjugacy
import OAI.Dynamics.EntropyCounterexample.CoordinateGoodCover
import OAI.Dynamics.EntropyCounterexample.Counterexample
import OAI.Dynamics.EntropyCounterexample.CounterexampleEntropy
import OAI.Dynamics.EntropyCounterexample.CylinderAttraction
import OAI.Dynamics.EntropyCounterexample.CylinderModels
import OAI.Dynamics.EntropyCounterexample.Definitions
import OAI.Dynamics.EntropyCounterexample.Development
import OAI.Dynamics.EntropyCounterexample.EigenpairBound
import OAI.Dynamics.EntropyCounterexample.Embedding
import OAI.Dynamics.EntropyCounterexample.EntropyBounds
import OAI.Dynamics.EntropyCounterexample.EntropyCoding
import OAI.Dynamics.EntropyCounterexample.EntropyLocalization
import OAI.Dynamics.EntropyCounterexample.EntropyNeighborhood
import OAI.Dynamics.EntropyCounterexample.EntropySection
import OAI.Dynamics.EntropyCounterexample.EntropySparseCover
import OAI.Dynamics.EntropyCounterexample.EntropySupport
import OAI.Dynamics.EntropyCounterexample.ExactSequenceSpectrum
import OAI.Dynamics.EntropyCounterexample.FiniteSpectrumBound
import OAI.Dynamics.EntropyCounterexample.FiniteTypeSupport
import OAI.Dynamics.EntropyCounterexample.GainCircle
import OAI.Dynamics.EntropyCounterexample.GainLocalExtension
import OAI.Dynamics.EntropyCounterexample.GainProfile
import OAI.Dynamics.EntropyCounterexample.GlobalEscape
import OAI.Dynamics.EntropyCounterexample.HomotopySpectrum
import OAI.Dynamics.EntropyCounterexample.ImageEntropy
import OAI.Dynamics.EntropyCounterexample.InfinityChart
import OAI.Dynamics.EntropyCounterexample.InputSeries
import OAI.Dynamics.EntropyCounterexample.LocalPredictionInput
import OAI.Dynamics.EntropyCounterexample.Map
import OAI.Dynamics.EntropyCounterexample.MapAmplification
import OAI.Dynamics.EntropyCounterexample.MapBoundedOrbit
import OAI.Dynamics.EntropyCounterexample.MapC1
import OAI.Dynamics.EntropyCounterexample.MapC1Complete
import OAI.Dynamics.EntropyCounterexample.MapClockComponent
import OAI.Dynamics.EntropyCounterexample.MapConcretePassage
import OAI.Dynamics.EntropyCounterexample.MapContinuity
import OAI.Dynamics.EntropyCounterexample.MapData
import OAI.Dynamics.EntropyCounterexample.MapEntropy
import OAI.Dynamics.EntropyCounterexample.MapEntropyComplete
import OAI.Dynamics.EntropyCounterexample.MapErasure
import OAI.Dynamics.EntropyCounterexample.MapFinalReduction
import OAI.Dynamics.EntropyCounterexample.MapFiniteOrbit
import OAI.Dynamics.EntropyCounterexample.MapGlobalEscape
import OAI.Dynamics.EntropyCounterexample.MapInfinity
import OAI.Dynamics.EntropyCounterexample.MapInfinityAttraction
import OAI.Dynamics.EntropyCounterexample.MapInputRegularity
import OAI.Dynamics.EntropyCounterexample.MapLocalEscape
import OAI.Dynamics.EntropyCounterexample.MapMainRegularity
import OAI.Dynamics.EntropyCounterexample.MapOrbitAlternatives
import OAI.Dynamics.EntropyCounterexample.MapOrbitLift
import OAI.Dynamics.EntropyCounterexample.MapPassage
import OAI.Dynamics.EntropyCounterexample.MapPassagePhase
import OAI.Dynamics.EntropyCounterexample.MapPassageSchedule
import OAI.Dynamics.EntropyCounterexample.MapPrediction
import OAI.Dynamics.EntropyCounterexample.MapPredictionAgreement
import OAI.Dynamics.EntropyCounterexample.MapPreparationRadius
import OAI.Dynamics.EntropyCounterexample.MapPreparationReset
import OAI.Dynamics.EntropyCounterexample.MapQuotientContinuity
import OAI.Dynamics.EntropyCounterexample.MapReadout
import OAI.Dynamics.EntropyCounterexample.MapRecoveredReadout
import OAI.Dynamics.EntropyCounterexample.MapRegisterRegularity
import OAI.Dynamics.EntropyCounterexample.MapRegularity
import OAI.Dynamics.EntropyCounterexample.MapSignal
import OAI.Dynamics.EntropyCounterexample.MapSignals
import OAI.Dynamics.EntropyCounterexample.MapTerminalEntropy
import OAI.Dynamics.EntropyCounterexample.ModelTransport
import OAI.Dynamics.EntropyCounterexample.MonotoneItineraries
import OAI.Dynamics.EntropyCounterexample.NormalizedPrediction
import OAI.Dynamics.EntropyCounterexample.OnePointSupport
import OAI.Dynamics.EntropyCounterexample.OrbitAttraction
import OAI.Dynamics.EntropyCounterexample.OrbitSupport
import OAI.Dynamics.EntropyCounterexample.OrderedIntervalLabels
import OAI.Dynamics.EntropyCounterexample.PassagePhase
import OAI.Dynamics.EntropyCounterexample.PassagePhaseInterval
import OAI.Dynamics.EntropyCounterexample.PeriodicDerivativeBound
import OAI.Dynamics.EntropyCounterexample.PeriodicEntropy
import OAI.Dynamics.EntropyCounterexample.PhaseAlignment
import OAI.Dynamics.EntropyCounterexample.PolarLabels
import OAI.Dynamics.EntropyCounterexample.PolarProductEntropy
import OAI.Dynamics.EntropyCounterexample.PolynomialSpectralBound
import OAI.Dynamics.EntropyCounterexample.PredictionClock
import OAI.Dynamics.EntropyCounterexample.PredictionDerivative
import OAI.Dynamics.EntropyCounterexample.PredictionInput
import OAI.Dynamics.EntropyCounterexample.PredictionModelBridge
import OAI.Dynamics.EntropyCounterexample.PredictionSeries
import OAI.Dynamics.EntropyCounterexample.PredictionSignal
import OAI.Dynamics.EntropyCounterexample.PredictionSupport
import OAI.Dynamics.EntropyCounterexample.PredictionTerm
import OAI.Dynamics.EntropyCounterexample.RadialOrbitRepresentation
import OAI.Dynamics.EntropyCounterexample.RadialRegisterEntropy
import OAI.Dynamics.EntropyCounterexample.RawBaseGoodCover
import OAI.Dynamics.EntropyCounterexample.RawInvariantInfinity
import OAI.Dynamics.EntropyCounterexample.RawInvariantSets
import OAI.Dynamics.EntropyCounterexample.RawSpectrumFactor
import OAI.Dynamics.EntropyCounterexample.ReadoutCover
import OAI.Dynamics.EntropyCounterexample.ReadoutLocalExtension
import OAI.Dynamics.EntropyCounterexample.RealAngularDerivative
import OAI.Dynamics.EntropyCounterexample.RealizedConstruction
import OAI.Dynamics.EntropyCounterexample.RealizedRegisterRegularity
import OAI.Dynamics.EntropyCounterexample.RegisterEmbedded
import OAI.Dynamics.EntropyCounterexample.RegisterEntropyCoding
import OAI.Dynamics.EntropyCounterexample.RegisterEntropySupport
import OAI.Dynamics.EntropyCounterexample.RegisterErasure
import OAI.Dynamics.EntropyCounterexample.RegisterInterval
import OAI.Dynamics.EntropyCounterexample.RegisterLinearity
import OAI.Dynamics.EntropyCounterexample.RegisterReset
import OAI.Dynamics.EntropyCounterexample.Saturation
import OAI.Dynamics.EntropyCounterexample.SaturationEntropy
import OAI.Dynamics.EntropyCounterexample.SkewProduct
import OAI.Dynamics.EntropyCounterexample.SmallCoverNaturality
import OAI.Dynamics.EntropyCounterexample.SparseLogBound
import OAI.Dynamics.EntropyCounterexample.SparseVisits
import OAI.Dynamics.EntropyCounterexample.SpectralRadius
import OAI.Dynamics.EntropyCounterexample.SphereAngularInput
import OAI.Dynamics.EntropyCounterexample.SphereAngularTransport
import OAI.Dynamics.EntropyCounterexample.SphereChartLimits
import OAI.Dynamics.EntropyCounterexample.SphereCharts
import OAI.Dynamics.EntropyCounterexample.SphereCompactSupport
import OAI.Dynamics.EntropyCounterexample.SphereCompactSupportParam
import OAI.Dynamics.EntropyCounterexample.SphereCoverGeometry
import OAI.Dynamics.EntropyCounterexample.SphereCutoffBounds
import OAI.Dynamics.EntropyCounterexample.SphereCutoffSupport
import OAI.Dynamics.EntropyCounterexample.SphereCutoffTransport
import OAI.Dynamics.EntropyCounterexample.SphereCutoffs
import OAI.Dynamics.EntropyCounterexample.SphereCutoffsAffine
import OAI.Dynamics.EntropyCounterexample.SphereDoubling
import OAI.Dynamics.EntropyCounterexample.SphereDoublingCharts
import OAI.Dynamics.EntropyCounterexample.SphereGeometry
import OAI.Dynamics.EntropyCounterexample.SphereInfinityChart
import OAI.Dynamics.EntropyCounterexample.SphereMainUpdate
import OAI.Dynamics.EntropyCounterexample.SphereMainUpdateTransport
import OAI.Dynamics.EntropyCounterexample.SphereOverlapDoubling
import OAI.Dynamics.EntropyCounterexample.SpherePerturbation
import OAI.Dynamics.EntropyCounterexample.SpherePolynomialPerturbation
import OAI.Dynamics.EntropyCounterexample.SphereSquareEquator
import OAI.Dynamics.EntropyCounterexample.SphereSquareFiber
import OAI.Dynamics.EntropyCounterexample.SphereTranslation
import OAI.Dynamics.EntropyCounterexample.StandardRegisterUpdate
import OAI.Dynamics.EntropyCounterexample.StandardSaturation
import OAI.Dynamics.EntropyCounterexample.TargetReduction
import OAI.Dynamics.EntropyCounterexample.TerminalEntropySupport
import OAI.Dynamics.EntropyCounterexample.TopologicalAttraction
import OAI.Dynamics.EntropyCounterexample.TopologyCoverSupport
import OAI.Dynamics.EntropyCounterexample.TranslationC1
import OAI.Dynamics.EntropyCounterexample.TranslationDerivative
import OAI.Geometry.SingularHomology.ActualSingularSubdivision
import OAI.Geometry.SingularHomology.ActualSingularSubdivisionMap
import OAI.Geometry.SingularHomology.AffineSimplexCone
import OAI.Geometry.SingularHomology.AffineSimplexGeometry
import OAI.Geometry.SingularHomology.AffineSingularRealization
import OAI.Geometry.SingularHomology.BarycentricSubdivision
import OAI.Geometry.SingularHomology.ChainComplexTransport
import OAI.Geometry.SingularHomology.ChainMapRangeLift
import OAI.Geometry.SingularHomology.CircleHomologySupport
import OAI.Geometry.SingularHomology.CoordinateHomology
import OAI.Geometry.SingularHomology.FiniteCoverHomology
import OAI.Geometry.SingularHomology.FiniteCoverHomologyRawBase
import OAI.Geometry.SingularHomology.FiniteGoodCoverHomology
import OAI.Geometry.SingularHomology.FiniteSimplicialHomology
import OAI.Geometry.SingularHomology.HomologyConjugacy
import OAI.Geometry.SingularHomology.HomologyConstant
import OAI.Geometry.SingularHomology.HomologyCycle
import OAI.Geometry.SingularHomology.HomologyEigenvalue
import OAI.Geometry.SingularHomology.HomologyEmpty
import OAI.Geometry.SingularHomology.HomologyEvaluation
import OAI.Geometry.SingularHomology.HomologyHomotopyEquiv
import OAI.Geometry.SingularHomology.HomologyNaturality
import OAI.Geometry.SingularHomology.HomologySpectrumFactor
import OAI.Geometry.SingularHomology.HomologySupport
import OAI.Geometry.SingularHomology.HomologyTransfer
import OAI.Geometry.SingularHomology.HomologyZero
import OAI.Geometry.SingularHomology.IteratedSubdivision
import OAI.Geometry.SingularHomology.IteratedSubdivisionMesh
import OAI.Geometry.SingularHomology.MapHomology
import OAI.Geometry.SingularHomology.MapRealizedHomology
import OAI.Geometry.SingularHomology.RecursiveSubdivisionMesh
import OAI.Geometry.SingularHomology.SimplexSingularCompatibility
import OAI.Geometry.SingularHomology.SimplexSingularRealization
import OAI.Geometry.SingularHomology.SimplexSubdivisionMesh
import OAI.Geometry.SingularHomology.SimplexSubtypeMesh
import OAI.Geometry.SingularHomology.SimplicialMayerVietoris
import OAI.Geometry.SingularHomology.SimplicialSphereHomology
import OAI.Geometry.SingularHomology.SingularAcyclicModels
import OAI.Geometry.SingularHomology.SingularAugmentation
import OAI.Geometry.SingularHomology.SingularChainFoundations
import OAI.Geometry.SingularHomology.SingularChainInclusion
import OAI.Geometry.SingularHomology.SingularChainsFinsupp
import OAI.Geometry.SingularHomology.SingularChainsFinsuppBoundary
import OAI.Geometry.SingularHomology.SingularCoverChains
import OAI.Geometry.SingularHomology.SingularCoverNaturality
import OAI.Geometry.SingularHomology.SingularCoverNaturalityExtended
import OAI.Geometry.SingularHomology.SingularCycleFilling
import OAI.Geometry.SingularHomology.SingularMayerVietorisSupport
import OAI.Geometry.SingularHomology.SingularRealizedSmallness
import OAI.Geometry.SingularHomology.SingularSimplexCircleLift
import OAI.Geometry.SingularHomology.SingularSimplexLebesgue
import OAI.Geometry.SingularHomology.SingularSmallChainSupport
import OAI.Geometry.SingularHomology.SingularSmallChains
import OAI.Geometry.SingularHomology.SingularSmallComparison
import OAI.Geometry.SingularHomology.SingularSmallNaturality
import OAI.Geometry.SingularHomology.SingularSubdivision
import OAI.Geometry.SingularHomology.SingularSubdivisionEventuallySmall
import OAI.Geometry.SingularHomology.SingularSubdivisionIterateRealization
import OAI.Geometry.SingularHomology.SingularSubdivisionSmallness
import OAI.Geometry.SingularHomology.SingularSubdivisionSupport
import OAI.Geometry.SingularHomology.SingularSupportNaturality
import OAI.Geometry.SingularHomology.SingularSupportedFilling
import OAI.Geometry.SingularHomology.SingularUniversalChainMap
import OAI.Geometry.SingularHomology.SingularUniversalFinsupp
import OAI.Geometry.SingularHomology.SingularUniversalOperator
import OAI.Geometry.SingularHomology.SkewProductHomology
import OAI.Geometry.SingularHomology.SmallCoverMayerVietoris
import OAI.Geometry.SingularHomology.SphereMayerVietorisEigen
import OAI.Geometry.SingularHomology.SphereSquareHomologyTransport
import OAI.Geometry.SingularHomology.SubdivisionQuasiIso
import OAI.Geometry.SingularHomology.SubdivisionSubtypeMesh
import OAI.Geometry.SingularHomology.SubdivisionSupport
import OAI.Geometry.SingularHomology.SubdivisionSupportMesh
import OAI.Geometry.SingularHomology.TetrahedronChainInjection
import OAI.Geometry.SingularHomology.TetrahedronGoodCover
import OAI.Geometry.SingularHomology.TetrahedronGoodCoverBundle
import OAI.Geometry.SingularHomology.TetrahedronHomologyEquiv
import OAI.Geometry.SingularHomology.TetrahedronHomologyRank
import OAI.Geometry.SingularHomology.TetrahedronRadialHomeomorph
import OAI.Geometry.SingularHomology.TetrahedronSingular