ParametricRischDE(R, F)ΒΆ

intpar.spad line 691

undocumented

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.