Guess(F, S, EXPRR, retract, coerce)ΒΆ

mantepse.spad line 1306

This package implements guessing of sequences. Packages for the most common cases are provided as GuessInteger, GuessPolynomial, etc.

algDepHP: (List List F, List GuessOption) -> Record(degreeStream: Stream NonNegativeInteger, guessStream: UnivariateFormalPowerSeries F -> Stream UnivariateFormalPowerSeries F, guessModGen: NonNegativeInteger -> (List U32Vector, Integer, Integer) -> Vector U32Vector, testGen: List PositiveInteger -> UnivariateFormalPowerSeries SparseMultivariatePolynomial(F, NonNegativeInteger) -> Vector UnivariateFormalPowerSeries SparseMultivariatePolynomial(F, NonNegativeInteger), exprStream: (EXPRR, Symbol) -> Stream EXPRR, kind: Symbol, qvar: Symbol, A: (NonNegativeInteger, NonNegativeInteger, SparseUnivariatePolynomial S) -> S, AF: (NonNegativeInteger, NonNegativeInteger, UnivariateFormalPowerSeries SparseMultivariatePolynomial(F, NonNegativeInteger)) -> SparseMultivariatePolynomial(F, NonNegativeInteger), AX: (NonNegativeInteger, Symbol, EXPRR) -> EXPRR, C: NonNegativeInteger -> List S)
algDepHP(list, options) returns a specification for Hermite-Pade approximation looking for algebraic dependencies
diffHP: List GuessOption -> Record(degreeStream: Stream NonNegativeInteger, guessStream: UnivariateFormalPowerSeries F -> Stream UnivariateFormalPowerSeries F, guessModGen: NonNegativeInteger -> (List U32Vector, Integer, Integer) -> Vector U32Vector, testGen: List PositiveInteger -> UnivariateFormalPowerSeries SparseMultivariatePolynomial(F, NonNegativeInteger) -> Vector UnivariateFormalPowerSeries SparseMultivariatePolynomial(F, NonNegativeInteger), exprStream: (EXPRR, Symbol) -> Stream EXPRR, kind: Symbol, qvar: Symbol, A: (NonNegativeInteger, NonNegativeInteger, SparseUnivariatePolynomial S) -> S, AF: (NonNegativeInteger, NonNegativeInteger, UnivariateFormalPowerSeries SparseMultivariatePolynomial(F, NonNegativeInteger)) -> SparseMultivariatePolynomial(F, NonNegativeInteger), AX: (NonNegativeInteger, Symbol, EXPRR) -> EXPRR, C: NonNegativeInteger -> List S)
diffHP options returns a specification for Hermite-Pade approximation with the differential operator
diffHP: Symbol -> List GuessOption -> Record(degreeStream: Stream NonNegativeInteger, guessStream: UnivariateFormalPowerSeries F -> Stream UnivariateFormalPowerSeries F, guessModGen: NonNegativeInteger -> (List U32Vector, Integer, Integer) -> Vector U32Vector, testGen: List PositiveInteger -> UnivariateFormalPowerSeries SparseMultivariatePolynomial(F, NonNegativeInteger) -> Vector UnivariateFormalPowerSeries SparseMultivariatePolynomial(F, NonNegativeInteger), exprStream: (EXPRR, Symbol) -> Stream EXPRR, kind: Symbol, qvar: Symbol, A: (NonNegativeInteger, NonNegativeInteger, SparseUnivariatePolynomial S) -> S, AF: (NonNegativeInteger, NonNegativeInteger, UnivariateFormalPowerSeries SparseMultivariatePolynomial(F, NonNegativeInteger)) -> SparseMultivariatePolynomial(F, NonNegativeInteger), AX: (NonNegativeInteger, Symbol, EXPRR) -> EXPRR, C: NonNegativeInteger -> List S) if S has RetractableTo Symbol and F has RetractableTo Symbol
diffHP options returns a specification for Hermite-Pade approximation with the $q$-dilation operator
guess: (List F, List (List F, List GuessOption) -> List EXPRR, List Symbol) -> List EXPRR
guess(l, guessers, ops) applies recursively the given guessers to the successive differences if ops contains the symbol guessSum and quotients if ops contains the symbol guessProduct to the list. Default options as described in GuessOptionFunctions0 are used.
guess: (List F, List (List F, List GuessOption) -> List EXPRR, List Symbol, List GuessOption) -> List EXPRR
guess(l, guessers, ops) applies recursively the given guessers to the successive differences if ops contains the symbol guessSum and quotients if ops contains the symbol guessProduct to the list. The given options are used.
guess: (List F, List GuessOption) -> List EXPRR
guess(l, options) applies recursively guessRat to the successive differences and quotients of the list. The given options are used.
guess: List F -> List EXPRR
guess l applies recursively guessRat to the successive differences and quotients of the list. Default options as described in GuessOptionFunctions0 are used.
guessADE: (List F, List GuessOption) -> List EXPRR
guessADE(l, options) tries to find an algebraic differential equation for a generating function whose first Taylor coefficients are given by l, using the given options.
guessADE: List F -> List EXPRR
guessADE l tries to find an algebraic differential equation for a generating function whose first Taylor coefficients are given by l, using the default options described in GuessOptionFunctions0.
guessADE: Symbol -> (List F, List GuessOption) -> List EXPRR if S has RetractableTo Symbol and F has RetractableTo Symbol
guessADE q returns a guesser that tries to find an algebraic differential equation for a generating function whose first Taylor coefficients are given by l, using the given options.
guessAlg: (List F, List GuessOption) -> List EXPRR
guessAlg(l, options) tries to find an algebraic equation for a generating function whose first Taylor coefficients are given by l, using the given options. It is equivalent to guessADE(l, options) with maxDerivative == 0.
guessAlg: List F -> List EXPRR
guessAlg l tries to find an algebraic equation for a generating function whose first Taylor coefficients are given by l, using the default options described in GuessOptionFunctions0. It is equivalent to guessADE(l, maxDerivative == 0).
guessAlgDep: (List List F, List GuessOption) -> List EXPRR
guessAlgDep ll tries to find an algebraic dependence between several power series whose first Taylor coefficients are given by members of ll, using the given options.
guessAlgDep: List List F -> List EXPRR
guessAlgDep ll tries to find an algebraic dependence between several power series whose first Taylor coefficients are given by members of ll, using the default options described in GuessOptionFunctions0.
guessBinRat: (List F, List GuessOption) -> List EXPRR
guessBinRat(l, options) tries to find a function of the form n+->binomial(a+b n, n) r(n), where r(n) is a rational function, that fits l.
guessBinRat: List F -> List EXPRR
guessBinRat(l, options) tries to find a function of the form n+->binomial(a+b n, n) r(n), where r(n) is a rational function, that fits l.
guessBinRat: Symbol -> (List F, List GuessOption) -> List EXPRR if S has RetractableTo Symbol and F has RetractableTo Symbol
guessBinRat q returns a guesser that tries to find a function of the form n+->qbinomial(a+b n, n) r(n), where r(q^n) is a q-rational function, that fits l.
guessExpRat: (List F, List GuessOption) -> List EXPRR
guessExpRat(l, options) tries to find a function of the form n+->(a+b n)^n r(n), where r(n) is a rational function, that fits l.
guessExpRat: List F -> List EXPRR
guessExpRat l tries to find a function of the form n+->(a+b n)^n r(n), where r(n) is a rational function, that fits l.
guessExpRat: Symbol -> (List F, List GuessOption) -> List EXPRR if S has RetractableTo Symbol and F has RetractableTo Symbol
guessExpRat q returns a guesser that tries to find a function of the form n+->(a+b q^n)^n r(q^n), where r(q^n) is a q-rational function, that fits l.
guessFE: (List F, List GuessOption) -> List EXPRR
guessFE(l, options) tries to find an algebraic substitution equation for a generating function whose first Taylor coefficients are given by l, using the given options.
guessFE: List F -> List EXPRR
guessFE l tries to find an algebraic substitution equation for a generating function whose first Taylor coefficients are given by l, using the default options described in GuessOptionFunctions0.
guessHolo: (List F, List GuessOption) -> List EXPRR
guessHolo(l, options) tries to find an ordinary linear differential equation for a generating function whose first Taylor coefficients are given by l, using the given options. It is equivalent to guessADE(l, options) with maxPower == 1.
guessHolo: List F -> List EXPRR
guessHolo l tries to find an ordinary linear differential equation for a generating function whose first Taylor coefficients are given by l, using the default options described in GuessOptionFunctions0. It is equivalent to guessADE(l, maxPower == 1).
guessHolo: Symbol -> (List F, List GuessOption) -> List EXPRR if S has RetractableTo Symbol and F has RetractableTo Symbol
guessHolo q returns a guesser that tries to find a linear differential equation for a generating function whose first Taylor coefficients are given by l, using the given options.
guessPade: (List F, List GuessOption) -> List EXPRR
guessPade(l, options) tries to find a rational function whose first Taylor coefficients are given by l, using the given options. It is equivalent to guessADE(l, maxDerivative == 0, maxPower == 1, allDegrees == true).
guessPade: List F -> List EXPRR
guessPade(l, options) tries to find a rational function whose first Taylor coefficients are given by l, using the default options described in GuessOptionFunctions0. It is equivalent to guessADE(l, options) with maxDerivative == 0, maxPower == 1, allDegrees == true.
guessPRec: (List F, List GuessOption) -> List EXPRR
guessPRec(l, options) tries to find a linear recurrence with polynomial coefficients whose first values are given by l, using the given options. It is equivalent to guessRec(l, options) with maxPower == 1.
guessPRec: List F -> List EXPRR
guessPRec l tries to find a linear recurrence with polynomial coefficients whose first values are given by l, using the default options described in GuessOptionFunctions0. It is equivalent to guessRec(l, maxPower == 1).
guessPRec: Symbol -> (List F, List GuessOption) -> List EXPRR if S has RetractableTo Symbol and F has RetractableTo Symbol
guessPRec q returns a guesser that tries to find a linear q-recurrence with polynomial coefficients whose first values are given by l, using the given options. It is equivalent to guessRec(q) with maxPower == 1.
guessRat: (List F, List GuessOption) -> List EXPRR
guessRat(l, options) tries to find a rational function whose first values are given by l, using the given options. It is equivalent to guessRec(l, maxShift == 0, maxPower == 1, allDegrees == true).
guessRat: List F -> List EXPRR
guessRat l tries to find a rational function whose first values are given by l, using the default options described in GuessOptionFunctions0. It is equivalent to guessRec(l, maxShift == 0, maxPower == 1, allDegrees == true).
guessRat: Symbol -> (List F, List GuessOption) -> List EXPRR if S has RetractableTo Symbol and F has RetractableTo Symbol
guessRat q returns a guesser that tries to find a q-rational function whose first values are given by l, using the given options. It is equivalent to guessRec with (l, maxShift == 0, maxPower == 1, allDegrees == true).
guessRec: (List F, List GuessOption) -> List EXPRR
guessRec(l, options) tries to find an ordinary difference equation whose first values are given by l, using the given options.
guessRec: List F -> List EXPRR
guessRec l tries to find an ordinary difference equation whose first values are given by l, using the default options described in GuessOptionFunctions0.
guessRec: Symbol -> (List F, List GuessOption) -> List EXPRR if S has RetractableTo Symbol and F has RetractableTo Symbol
guessRec q returns a guesser that finds an ordinary q-difference equation whose first values are given by l, using the given options.
shiftHP: List GuessOption -> Record(degreeStream: Stream NonNegativeInteger, guessStream: UnivariateFormalPowerSeries F -> Stream UnivariateFormalPowerSeries F, guessModGen: NonNegativeInteger -> (List U32Vector, Integer, Integer) -> Vector U32Vector, testGen: List PositiveInteger -> UnivariateFormalPowerSeries SparseMultivariatePolynomial(F, NonNegativeInteger) -> Vector UnivariateFormalPowerSeries SparseMultivariatePolynomial(F, NonNegativeInteger), exprStream: (EXPRR, Symbol) -> Stream EXPRR, kind: Symbol, qvar: Symbol, A: (NonNegativeInteger, NonNegativeInteger, SparseUnivariatePolynomial S) -> S, AF: (NonNegativeInteger, NonNegativeInteger, UnivariateFormalPowerSeries SparseMultivariatePolynomial(F, NonNegativeInteger)) -> SparseMultivariatePolynomial(F, NonNegativeInteger), AX: (NonNegativeInteger, Symbol, EXPRR) -> EXPRR, C: NonNegativeInteger -> List S)
shiftHP options returns a specification for Hermite-Pade approximation with the shift operator
shiftHP: Symbol -> List GuessOption -> Record(degreeStream: Stream NonNegativeInteger, guessStream: UnivariateFormalPowerSeries F -> Stream UnivariateFormalPowerSeries F, guessModGen: NonNegativeInteger -> (List U32Vector, Integer, Integer) -> Vector U32Vector, testGen: List PositiveInteger -> UnivariateFormalPowerSeries SparseMultivariatePolynomial(F, NonNegativeInteger) -> Vector UnivariateFormalPowerSeries SparseMultivariatePolynomial(F, NonNegativeInteger), exprStream: (EXPRR, Symbol) -> Stream EXPRR, kind: Symbol, qvar: Symbol, A: (NonNegativeInteger, NonNegativeInteger, SparseUnivariatePolynomial S) -> S, AF: (NonNegativeInteger, NonNegativeInteger, UnivariateFormalPowerSeries SparseMultivariatePolynomial(F, NonNegativeInteger)) -> SparseMultivariatePolynomial(F, NonNegativeInteger), AX: (NonNegativeInteger, Symbol, EXPRR) -> EXPRR, C: NonNegativeInteger -> List S) if S has RetractableTo Symbol and F has RetractableTo Symbol
shiftHP options returns a specification for Hermite-Pade approximation with the $q$-shift operator, or, if maxMixedDegree > 0 for mixed shifts
substHP: List GuessOption -> Record(degreeStream: Stream NonNegativeInteger, guessStream: UnivariateFormalPowerSeries F -> Stream UnivariateFormalPowerSeries F, guessModGen: NonNegativeInteger -> (List U32Vector, Integer, Integer) -> Vector U32Vector, testGen: List PositiveInteger -> UnivariateFormalPowerSeries SparseMultivariatePolynomial(F, NonNegativeInteger) -> Vector UnivariateFormalPowerSeries SparseMultivariatePolynomial(F, NonNegativeInteger), exprStream: (EXPRR, Symbol) -> Stream EXPRR, kind: Symbol, qvar: Symbol, A: (NonNegativeInteger, NonNegativeInteger, SparseUnivariatePolynomial S) -> S, AF: (NonNegativeInteger, NonNegativeInteger, UnivariateFormalPowerSeries SparseMultivariatePolynomial(F, NonNegativeInteger)) -> SparseMultivariatePolynomial(F, NonNegativeInteger), AX: (NonNegativeInteger, Symbol, EXPRR) -> EXPRR, C: NonNegativeInteger -> List S)
substHP options returns a specification for Hermite-Pade approximation with the substitution operator