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, (List Kernel F, List F) -> Record(logands: List F, basis: List Vector Fraction Integer)) -> 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_rde2: (F, List F, Symbol, List Kernel F, (List Kernel F, List F) -> List Record(ratpart: F, coeffs: Vector F), (List Kernel F, List F) -> Record(logands: List F, basis: List Vector Fraction Integer)) -> 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.

param_rde: (Integer, F, F, List F, Symbol, List Kernel F, (List Kernel F, List F) -> List Record(ratpart: F, coeffs: Vector F), (List Kernel F, List F) -> Record(logands: List F, basis: List Vector Fraction Integer)) -> 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_rde: (Integer, F, List F, Symbol, List Kernel F, (List Kernel F, List F) -> List Record(ratpart: F, coeffs: Vector F), (List Kernel F, List F) -> Record(logands: List F, basis: List Vector Fraction Integer)) -> 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.