# ParametricRischDE(R, F)¶

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.