PureAlgebraicIntegration(R, F, L)

intaf.spad line 321 [edit on github]

• R: Join(GcdDomain, RetractableTo Integer, Comparable, CharacteristicZero, LinearlyExplicitOver Integer)

• F: Join(FunctionSpace R, AlgebraicallyClosedField, TranscendentalFunctionCategory)

• L: SetCategory

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)