# PureAlgebraicIntegration(R, F, L)¶

This package provides functions for integration, limited integration, extended integration and the risch differential equation for pure algebraic integrands.

palgint: (F, Kernel F, Kernel F) -> IntegrationResult F

`palgint(f, x, y)` returns the integral of `f(x, y)dx` where `y` is an algebraic function of `x`.

palgLODE: (L, F, Kernel F, Kernel F, Symbol) -> Record(particular: Union(F, failed), basis: List F) if L has LinearOrdinaryDifferentialOperatorCategory F

`palgLODE(op, g, kx, y, x)` returns the solution of `op f = g`. `y` is an algebraic function of `x`.

palgRDE: (F, F, F, Kernel F, Kernel F, (F, F, Symbol) -> Union(F, failed)) -> Union(F, failed)

`palgRDE(nfp, f, g, x, y, foo)` returns a function `z(x, y)` such that `dz/dx + n * df/dx z(x, y) = g(x, y)` if such a `z` exists, “failed” otherwise; `y` is an algebraic function of `x`; `foo(a, b, x)` is a function that solves `du/dx + n * da/dx u(x) = u(x)` for an unknown `u(x)` not involving `y`. `nfp` is `n * df/dx`.

param_LODE: (List F, List F, Kernel F, Kernel F) -> Record(particular: List Record(ratpart: F, coeffs: Vector F), basis: List F)

`param_LODE(eq, lg, x, y)`

param_RDE: (F, List F, Kernel F, Kernel F) -> Record(particular: List Record(ratpart: F, coeffs: Vector F), basis: List F)

`param_RDE(fp, lg, x, y)`