Data.Taylor

newtype Taylor a

A Taylor series, with coefficients in the specified Semiring.

By varying the base Semiring, we can do various interesting things:

• Using Number, we can compute arbitrary higher order derivatives of functions.
• Using Complex, we can compute path derivatives of functions.
• Using the Free Semiring, we can implement symbolic differentiation.

Instances

• Lazy (Taylor a)
• Functor Taylor
• (Semiring a) => Semiring (Taylor a)
• (Ring a) => Ring (Taylor a)
• (CommutativeRing a) => CommutativeRing (Taylor a)
• (Eq a, Field a) => EuclideanRing (Taylor a)
• (Eq a, Field a) => Field (Taylor a)

coefficients :: forall a. Taylor a -> List a

Extract the coefficients as a lazy list.

constant :: forall a. Semiring a => a -> Taylor a

A Taylor series representing a constant function.

eval0 :: forall a. Taylor a -> a

Evaluate a Taylor series at zero.

d :: forall a. Semiring a => Taylor a -> Taylor a

The derivative of a Taylor series.

integrate :: forall a. Field a => Taylor a -> Taylor a

The integral of a Taylor series.

x :: forall a. Semiring a => Taylor a

A Taylor series which has a non-zero coefficient only for the x term.