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.

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), Mapping(Union(F, "failed"), F, F, Symbol)) -> 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.

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.

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)