numeric-prelude-0.4.2: An experimental alternative hierarchy of numeric type classes

MathObj.PowerSeries

Description

Power series, either finite or unbounded. (zipWith does exactly the right thing to make it work almost transparently.)

Synopsis

# Documentation

newtype T a Source

Constructors

 Cons Fieldscoeffs :: [a]

Instances

 Functor T C T C a b => C a (T b) (C a, C a b) => C a (T b) (Eq a, C a) => Eq (T a) (Ord a, C a) => Ord (T a) Show a => Show (T a) C a => C (T a) C a => C (T a) C a => C (T a) (C a, C a) => C (T a) C a => C (T a) C a => C (T a) C a => C (T a)

fromCoeffs :: [a] -> T a Source

lift0 :: [a] -> T a Source

lift1 :: ([a] -> [a]) -> T a -> T a Source

lift2 :: ([a] -> [a] -> [a]) -> T a -> T a -> T a Source

const :: a -> T a Source

truncate :: Int -> T a -> T a Source

evaluate :: C a => T a -> a -> a Source

Evaluate (truncated) power series.

evaluateCoeffVector :: C a v => T v -> a -> v Source

Evaluate (truncated) power series.

evaluateArgVector :: (C a v, C v) => T a -> v -> v Source

approximate :: C a => T a -> a -> [a] Source

Evaluate approximations that is evaluate all truncations of the series.

approximateCoeffVector :: C a v => T v -> a -> [v] Source

Evaluate approximations that is evaluate all truncations of the series.

approximateArgVector :: (C a v, C v) => T a -> v -> [v] Source

Evaluate approximations that is evaluate all truncations of the series.

compose :: (C a, C a) => T a -> T a -> T a Source

It fulfills ` evaluate x . evaluate y == evaluate (compose x y) `