PureAlgebraicIntegration(R, F, L)ΒΆ

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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)