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GHC 9.10.3 · lts/ghc-9.10.x · c74966e · 2026-09-27

Modulenumeric-prelude-0.4.4Haskell98

MathObj.PowerSeries.Example

  • 43 values
Example6 expressions
import qualified MathObj.PowerSeries.Core as PSimport qualified MathObj.PowerSeries.Example as PSEimport Test.NumericPrelude.Utility (equalTrunc)import NumericPrelude.Numeric as NPimport NumericPrelude.Base as Pimport Prelude ()

Default implementations.

14 declarations
valueexp :: C a => [a]
#
valuesin :: C a => [a]
#
valuecos :: C a => [a]
#
valuetan :: (C a, C a) => [a]
#
valuelog :: C a => [a]
#
valuepow :: C a => a -> [a]
#
Property
\m n -> equalTrunc 30 (PS.mul (PSE.pow m) (PSE.pow n)) (PSE.pow (m+n))

Generate Taylor series explicitly.

11 declarations
valueexpExpl :: C a => [a]
#
Property
equalTrunc 500 PSE.expExpl PSE.expODE
valuesinExpl :: C a => [a]
#
Property
equalTrunc 500 PSE.sinExpl PSE.sinODE
valuecosExpl :: C a => [a]
#
Property
equalTrunc 500 PSE.cosExpl PSE.cosODE
valuetanExpl :: (C a, C a) => [a]
#
Property
equalTrunc 50 PSE.tanExpl PSE.tanODE
valuetanExplSieve :: (C a, C a) => [a]
#
Property
equalTrunc 50 PSE.tanExpl PSE.tanExplSieve
valuelogExpl :: C a => [a]
#
Property
equalTrunc 500 PSE.logExpl PSE.logODE
valueatanExpl :: C a => [a]
#
Property
equalTrunc 500 PSE.atanExpl PSE.atanODE
valuesinhExpl :: C a => [a]
#
Property
equalTrunc 500 PSE.sinhExpl PSE.sinhODE
valuecoshExpl :: C a => [a]
#
Property
equalTrunc 500 PSE.coshExpl PSE.coshODE
valueatanhExpl :: C a => [a]
#
Property
equalTrunc 500 PSE.atanhExpl PSE.atanhODE

Power series of (1+x)^expon using the binomial series.

3 declarations
valuepowExpl :: C a => a -> [a]
#
Property
\expon -> equalTrunc 50 (PSE.powODE expon) (PSE.powExpl expon)
valuesqrtExpl :: C a => [a]
#
Property
equalTrunc 100 PSE.sqrtExpl PSE.sqrtODE
valueerf :: C a => [a]
#

Power series of error function (almost). More precisely erf = 2 / sqrt pi * integrate (x -> exp (-x^2)) , with erf 0 = 0.

Generate Taylor series from differential equations.

15 declarations
valuetanODESieve :: C a => [a]
#
Property
equalTrunc 50 PSE.tanODE PSE.tanODESieve
valueasinODE :: C a => [a]
#
Property
equalTrunc 50 PSE.asinODE (snd $ PS.inv PSE.sinODE)