ParametricIntegration(R, F)ΒΆ

intpar.spad line 1529

undocumented

extendedint: (F, Symbol, List F) -> Record(particular: Union(Record(ratpart: F, coeffs: Vector F), failed), basis: List Record(ratpart: F, coeffs: Vector F))
extendedint(f, x, [g1, ..., gn]) returns solution of the system f = dh/dx + c1*g1 + ... + cn*gn and and a basis of the associated homogeneous system dh/dx + c1*g1 + ... + cn*gn = 0. Solutions are in the field generated by kernels of f and g1, ..., gn.
extendedint: (F, Symbol, List Kernel F, List F) -> Record(particular: Union(Record(ratpart: F, coeffs: Vector F), failed), basis: List Record(ratpart: F, coeffs: Vector F))
extendedint(f, x, [k1, ..., kn], [g1, ..., gn]) is like extendedint(f, [k1, ..., kn], [g1, ..., gn]) but looks for solutions in the field generated by k1, ..., kn.
extendedint: (Symbol, List Kernel F, List F) -> List Record(ratpart: F, coeffs: Vector F)
extendedint(x, [k1, ..., kn], [g1, ..., gn]) returns a basis of the homogeneous system dh/dx + c1*g1 + ... + cn*gn = 0. Solutions are in the field generated by k1, ..., kn.
logextint: (Symbol, List Kernel F, List F) -> Record(logands: List F, basis: List Vector Fraction Integer)
logextint(x, lk, lg) returns [[u1, ..., um], bas] giving basis of solution of the homogeneous systym c1*g1 + ... + cn*gn + c_{n+1}u1'/u1 + ... c_{n+m}um'/um = 0