ParametricIntegration(R, F)

intpar.spad line 1652 [edit on github]

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

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

This package implements general parametric integration. Most work is delegated to other packages.

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

polylog_int: (F, Symbol, Kernel F, NonNegativeInteger, List Kernel F, F) -> Union(Record(ratpart: F, coeff: F, prim: F), failed)

polylog_int(f, x, k0, [k1, ..., kn], g)