ParametricRischDE(R, F)

R : Join(GcdDomain, Comparable, CharacteristicZero, RetractableTo(Integer), LinearlyExplicitOver(Integer))
F : Join(TranscendentalFunctionCategory, AlgebraicallyClosedField, FunctionSpace(R))

This package implements parametric RDE solver. Only simplest algebraic cases are implemented, the rest of algebraic case is unimplemented.The code throws errors on inimplmented cases.

exp_lower_bound : (SparseUnivariatePolynomial(F), LaurentPolynomial(F, SparseUnivariatePolynomial(F)), Integer, Integer, List(Kernel(F)), F, Mapping(Record(logands : List(F), basis : List(Vector(Fraction(Integer)))), List(Kernel(F)), List(F))) -> Integer: exp_lower_bound(a, b, ob, nc0, lk, eta, logi) computes lower degree bound for solution of a*D(y) + b*y = c in exponential case. ob is order of b, nc0 is lower bound on order of c, eta is derivative of the argument of exponential.

param_rde : (Integer, F, List(F), Symbol, List(Kernel(F)), Mapping(List(Record(ratpart : F, coeffs : Vector(F))), List(Kernel(F)), List(F)), Mapping(Record(logands : List(F), basis : List(Vector(Fraction(Integer)))), List(Kernel(F)), List(F))) -> List(Record(ratpart : F, coeffs : Vector(F))): param_rde(n, f, lg, x, lk, ext, logi) finds basis of solution to the equation dy/dx + n df/dx y + c1 g1 + ... cn gn = 0 where y is in field generated by lk and ci are constants.

param_rde : (Integer, F, F, List(F), Symbol, List(Kernel(F)), Mapping(List(Record(ratpart : F, coeffs : Vector(F))), List(Kernel(F)), List(F)), Mapping(Record(logands : List(F), basis : List(Vector(Fraction(Integer)))), List(Kernel(F)), List(F))) -> Record(particular : Union(Record(ratpart : F, coeffs : Vector(F)), "failed"), basis : List(Record(ratpart : F, coeffs : Vector(F)))): param_rde(n, f, h, lg, x, lk, ext, logi) finds a particular solution and basis of solutions to homogeneous equation for equation dy/dx + n df/dx y + c1 g1 + ... cn gn = h where y is in field generated by lk and ci are constants.

param_rde2 : (F, List(F), Symbol, List(Kernel(F)), Mapping(List(Record(ratpart : F, coeffs : Vector(F))), List(Kernel(F)), List(F)), Mapping(Record(logands : List(F), basis : List(Vector(Fraction(Integer)))), List(Kernel(F)), List(F))) -> List(Record(ratpart : F, coeffs : Vector(F))): param_rde2(fp, lg, x, lk, ext, logi) finds basis of solution to the equation dy/dx + fp y + c1 g1 + ... cn gn = 0 where y is in field generated by lk and ci are constants.