# ParametricIntegration(R, F)¶

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)`