MathObj.PowerSeries

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

Documentation

>>> 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 ()

newtype T a

Constructors

Cons

Fields

• coeffs :: [a]

Instances

Functor T

Defined in MathObj.PowerSeries

Methods

fmap :: (a -> b) -> T a -> T b

(<$) :: a -> T b -> T a

C T

Defined in MathObj.PowerSeries

Methods

zero :: C a => T a

(<+>) :: C a => T a -> T a -> T a

(*>) :: C a => a -> T a -> T a

C a b => C a (T b)

Defined in MathObj.PowerSeries

Methods

(*>) :: a -> T b -> T b

(C a, C a b) => C a (T b)

Defined in MathObj.PowerSeries

(Eq a, C a) => Eq (T a)

Defined in MathObj.PowerSeries

Methods

(==) :: T a -> T a -> Bool

(/=) :: T a -> T a -> Bool

(C a, Ord a) => Ord (T a)

Defined in MathObj.PowerSeries

Methods

compare :: T a -> T a -> Ordering

(<) :: T a -> T a -> Bool

(<=) :: T a -> T a -> Bool

(>) :: T a -> T a -> Bool

(>=) :: T a -> T a -> Bool

max :: T a -> T a -> T a

min :: T a -> T a -> T a

Show a => Show (T a)

Defined in MathObj.PowerSeries

Methods

showsPrec :: Int -> T a -> ShowS

show :: T a -> String

showList :: [T a] -> ShowS

C a => C (T a)

Defined in MathObj.PowerSeries

Methods

zero :: T a

(+) :: T a -> T a -> T a

(-) :: T a -> T a -> T a

negate :: T a -> T a

C a => C (T a)

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)

Defined in MathObj.PowerSeries

Methods

(*) :: T a -> T a -> T a

one :: T a

fromInteger :: Integer -> T a

(^) :: T a -> Integer -> T a

(C a, C a) => C (T a)

Defined in MathObj.PowerSeries

Methods

div :: T a -> T a -> T a

mod :: T a -> T a -> T a

divMod :: T a -> T a -> (T a, T a)

C a => C (T a)

Defined in MathObj.PowerSeries

Methods

differentiate :: T a -> T a

C a => C (T a)

Defined in MathObj.PowerSeries

Methods

(/) :: T a -> T a -> T a

recip :: T a -> T a

fromRational' :: Rational -> T a

(^-) :: T a -> Integer -> T a

C a => C (T a)

Defined in MathObj.PowerSeries

Methods

sqrt :: T a -> T a

root :: Integer -> T a -> T a

(^/) :: T a -> Rational -> T a

C a => C (T a)

Defined in MathObj.PowerSeries

Methods

pi :: T a

exp :: T a -> T a

log :: T a -> T a

logBase :: T a -> T a -> T a

(**) :: T a -> T a -> T a

sin :: T a -> T a

cos :: T a -> T a

tan :: T a -> T a

asin :: T a -> T a

acos :: T a -> T a

atan :: T a -> T a

sinh :: T a -> T a

cosh :: T a -> T a

tanh :: T a -> T a

asinh :: T a -> T a

acosh :: T a -> T a

atanh :: T a -> T a

fromCoeffs :: [a] -> T a

lift0 :: [a] -> T a

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

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

const :: a -> T a

appPrec :: Int

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

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

Evaluate (truncated) power series.

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

Evaluate (truncated) power series.

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

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

Evaluate approximations that is evaluate all truncations of the series.

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

Evaluate approximations that is evaluate all truncations of the series.

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

Evaluate approximations that is evaluate all truncations of the series.

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

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

shrink :: C a => a -> T a -> T a

dilate :: C a => a -> T a -> T a