Modulenumeric-prelude-0.4.4Haskell98

MathObj.PowerSeries

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

1 type
16 values

Packagenumeric-prelude-0.4.4
Exports17
LanguageHaskell98
LicenceBSD-3-Clause
SourcePowerSeries.hs

Example7 expressions

>>> import qualified MathObj.PowerSeries.Core as PS>>> import qualified MathObj.PowerSeries as PST>>> import qualified Test.QuickCheck as QC>>> import Test.NumericPrelude.Utility (equalTrunc, (/\))>>> import NumericPrelude.Numeric as NP>>> import NumericPrelude.Base as P>>> import Prelude ()

newtypenewtype T a

Constructors

Cons
- coeffs :: [a]

Instances14Functor, Eq, Ord, Show, C, …

Functor TDefined in numeric-prelude-0.4.4 · MathObj.PowerSeries
C TDefined in numeric-prelude-0.4.4 · MathObj.PowerSeries
(C a, C a b) => C a (T b)Defined in numeric-prelude-0.4.4 · MathObj.PowerSeries
C a b => C a (T b)Defined in numeric-prelude-0.4.4 · MathObj.PowerSeries
(Eq a, C a) => Eq (T a)Defined in numeric-prelude-0.4.4 · MathObj.PowerSeries
(C a, Ord a) => Ord (T a)Defined in numeric-prelude-0.4.4 · MathObj.PowerSeries
Show a => Show (T a)Defined in numeric-prelude-0.4.4 · MathObj.PowerSeries

C a => C (T a)Defined in numeric-prelude-0.4.4 · MathObj.PowerSeries

Property

prop> QC.choose (1,10) /\ \expon (QC.Positive x) xs -> let xt = x:xs in  equalTrunc 15 (PS.pow (const x) (1 % expon) (PST.coeffs (PST.fromCoeffs xt ^ expon)) ++ repeat zero) (xt ++ repeat zero)

C a => C (T a)Defined in numeric-prelude-0.4.4 · MathObj.PowerSeries
C a => C (T a)Defined in numeric-prelude-0.4.4 · MathObj.PowerSeries
C a => C (T a)Defined in numeric-prelude-0.4.4 · MathObj.PowerSeries
C a => C (T a)Defined in numeric-prelude-0.4.4 · MathObj.PowerSeries
(C a, C a) => C (T a)Defined in numeric-prelude-0.4.4 · MathObj.PowerSeries
C a => C (T a)Defined in numeric-prelude-0.4.4 · MathObj.PowerSeries

valuefromCoeffs :: [a] -> T a

valuelift0 :: [a] -> T a

valuelift1 :: ([a] -> [a]) -> T a -> T a

valuelift2 :: ([a] -> [a] -> [a]) -> T a -> T a -> T a

valueconst :: a -> T a

valueappPrec :: Int

valuetruncate :: Int -> T a -> T a

valueevaluate :: C a => T a -> a -> a

Evaluate (truncated) power series.

valueevaluateCoeffVector :: C a v => T v -> a -> v

Evaluate (truncated) power series.

valueevaluateArgVector :: (C a v, C v) => T a -> v -> v

valueapproximate :: C a => T a -> a -> [a]

Evaluate approximations that is evaluate all truncations of the series.

valueapproximateCoeffVector :: C a v => T v -> a -> [v]

Evaluate approximations that is evaluate all truncations of the series.

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

Evaluate approximations that is evaluate all truncations of the series.

valuecompose :: (C a, C a) => T a -> T a -> T a

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

valueshrink :: C a => a -> T a -> T a

valuedilate :: C a => a -> T a -> T a