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 : (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.

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.

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+1u1'/u1 + ... c_n+mum'/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)