RecurrenceOperator(R, F)

rec.spad line 24 [edit on github]

• R : Join(Comparable, IntegralDomain, ConvertibleTo(InputForm))
• F : Join(FunctionSpace(R), AbelianMonoid, RetractableTo(Integer), RetractableTo(Symbol), PartialDifferentialRing(Symbol), CombinatorialOpsCategory)

This package provides an operator for the n-th term of a recurrence and an operator for the coefficient of x^n in a function specified by a functional equation.

eltable? : F -> Boolean

eltable? r returns whether the operator determines (most likely) the sequence completely.

getEq : F -> F

getEq f returns the defining equation, if f represents the coefficient of an ADE or a recurrence.

makeFEq : (BasicOperator, Symbol, Symbol, F, List(F), Stream(F)) -> F

evalADE(f, x, n, eq, parameters, values) creates an expression that stands for the coefficient of x^n in the Taylor expansion of f(x), where f(x) is given by the functional equation eq. The argument values specifies the first few Taylor coefficients.

makeRec : (BasicOperator, Symbol, F, List(F), Stream(F)) -> F

makeRec(u, n, eq, parameters, values) creates an expression that stands for u(n), where u(n) is given by the equation eq. The argument parameters has to contain all variables (or kernels) that appear eventually in the stream of values. The argument values specifies the initial values of the recurrence u(0), u(1), ... For the moment we don't allow recursions that contain u inside of another operator.

values : () -> NonNegativeInteger

values() returns the number of initial values to display at most.

values : NonNegativeInteger -> NonNegativeInteger

values N sets the number of initial values to display at most.