| Safe Haskell | Safe |
|---|---|
| Language | Haskell2010 |
Math.Number.Interface
Synopsis
- nthroot :: Floating a => a -> a -> a
- logroot :: Floating a => a -> a -> a
- cuberoot :: (Floating a, Numerics a) => a -> a
- class Ord q => DedekindCut q r where
- class Approximations str a | a -> str where
- floatingApproximations :: a -> str Double
- rationalApproximations :: a -> str Rational
- class Infinitary a where
- infinite :: a
- class Infinitary a => PotentiallyInfinite a where
- is_infinite :: a -> Bool
- class Numerics a where
- newtonsMethod :: (a -> a) -> a -> a
- class RationalRoots a where
- rationalPower :: a -> Rational -> a
- class Num r => DifferentiallyClosed r where
- integralVector :: (VectorSpace b, Applicative f, Enum a, Num a) => (f a, f a) -> (a -> b) -> f a -> f b
- derivateVector :: (Applicative t, DifferentiallyClosed r) => t (r -> r) -> t r -> t r
- complexDerivate :: (RealFloat r, Closed r) => (Complex r -> Complex r) -> Complex r -> Complex r
- class DifferentialOperator t where
- partial :: DifferentiallyClosed a => (t a -> a) -> t a -> t a
- partial1_2 :: DifferentiallyClosed a => (a -> b -> a) -> a -> b -> a
- partial2_2 :: DifferentiallyClosed a => (b -> a -> a) -> b -> a -> a
- partial1_3 :: DifferentiallyClosed a => (a -> b -> c -> a) -> a -> b -> c -> a
- partial2_3 :: DifferentiallyClosed a => (b -> a -> c -> a) -> b -> a -> c -> a
- partial3_3 :: DifferentiallyClosed a => (b -> c -> a -> a) -> b -> c -> a -> a
- partial1_4 :: DifferentiallyClosed a => (a -> b -> c -> d -> a) -> a -> b -> c -> d -> a
- partial2_4 :: DifferentiallyClosed a => (b -> a -> c -> d -> a) -> b -> a -> c -> d -> a
- partial3_4 :: DifferentiallyClosed a => (b -> c -> a -> d -> a) -> b -> c -> a -> d -> a
- partial4_4 :: DifferentiallyClosed a => (b -> c -> d -> a -> a) -> b -> c -> d -> a -> a
- class Show r => ShowPrecision r where
- showAtPrecision :: r -> Integer -> String
- differential :: DifferentiallyClosed r => (r -> r) -> r -> Endo r
- derivateCommutator :: DifferentiallyClosed r => (r -> r) -> (r -> r) -> r -> r
- derivateAnticommutator :: DifferentiallyClosed r => (r -> r) -> (r -> r) -> r -> r
- derivates :: (StreamBuilder str, DifferentiallyClosed r) => (r -> r) -> str (r -> r)
- atan2Generic :: Floating a => a -> a -> a
- cot :: Floating a => a -> a
- sec :: Floating a => a -> a
- csc :: Floating a => a -> a
- arsinh :: Floating a => a -> a
- arcosh :: Floating a => a -> a
- artanh :: Floating a => a -> a
- arcoth :: Floating a => a -> a
- arsech :: Floating a => a -> a
- arcsch :: Floating a => a -> a
- coth :: Floating a => a -> a
- sech :: Floating a => a -> a
- csch :: Floating a => a -> a
- lineIntegral :: DifferentiallyClosed r => (r -> r) -> (r -> r) -> (r, r) -> r
- precisionCompare :: (Ord a, Num a) => a -> a -> a -> Bool
- liftInverse :: (Fractional a, Fractional b) => (a -> b) -> a -> b
Documentation
class Ord q => DedekindCut q r where Source #
Dedekind cut. Notice typically in constructive reals, it's possible to implement comparison between rational and real by utilizing denominator of the rational as describing desired accuracy but comparison between two reals is undecidable. Note, naming is chosen so the percentage mark is at side that can always be compared.
Methods
(%<) :: q -> r -> Bool Source #
(<%) :: r -> q -> Bool Source #
(%>) :: q -> r -> Bool Source #
Instances
class Approximations str a | a -> str where Source #
Methods
floatingApproximations :: a -> str Double Source #
rationalApproximations :: a -> str Rational Source #
Instances
| Approximations Stream R Source # | |
Defined in Math.Number.R | |
| Approximations Stream R Source # | |
Defined in Math.Number.Real | |
| Approximations Stream Double Source # | |
Defined in Math.Number.Stream | |
| Approximations Stream Float Source # | |
Defined in Math.Number.Stream | |
class Infinitary a where Source #
Instances
| Infinitary R Source # | |
Defined in Math.Number.R | |
| Infinitary R Source # | |
Defined in Math.Number.Real | |
| Infinitary Double Source # | |
Defined in Math.Number.Interface | |
| Infinitary Float Source # | |
Defined in Math.Number.Interface | |
| Infinitary (Closure Stream Rational) Source # | |
| Infinitary (Closure Stream R) Source # | |
| Infinitary (Closure Stream R) Source # | |
| Infinitary (Closure Stream Integer) Source # | |
class Infinitary a => PotentiallyInfinite a where Source #
Methods
is_infinite :: a -> Bool Source #
Instances
| PotentiallyInfinite Double Source # | |
Defined in Math.Number.Interface Methods is_infinite :: Double -> Bool Source # | |
| PotentiallyInfinite Float Source # | |
Defined in Math.Number.Interface Methods is_infinite :: Float -> Bool Source # | |
class RationalRoots a where Source #
Methods
rationalPower :: a -> Rational -> a Source #
Instances
| RationalRoots Double Source # | |
Defined in Math.Number.Interface | |
| RationalRoots Float Source # | |
Defined in Math.Number.Interface | |
| RationalRoots (Complex Double) Source # | |
Defined in Math.Number.Interface | |
| RationalRoots a => RationalRoots (Quantity a) Source # | |
Defined in Math.Number.DimensionalAnalysis | |
class Num r => DifferentiallyClosed r where Source #
Instances
integralVector :: (VectorSpace b, Applicative f, Enum a, Num a) => (f a, f a) -> (a -> b) -> f a -> f b Source #
derivateVector :: (Applicative t, DifferentiallyClosed r) => t (r -> r) -> t r -> t r Source #
complexDerivate :: (RealFloat r, Closed r) => (Complex r -> Complex r) -> Complex r -> Complex r Source #
class DifferentialOperator t where Source #
Methods
partial :: DifferentiallyClosed a => (t a -> a) -> t a -> t a Source #
Instances
| DifferentialOperator Vector2 Source # | |
Defined in Math.Matrix.Vector2 | |
| DifferentialOperator Vector3 Source # | |
Defined in Math.Matrix.Linear | |
| DifferentialOperator Vector4 Source # | |
Defined in Math.Matrix.LinearOperations | |
partial1_2 :: DifferentiallyClosed a => (a -> b -> a) -> a -> b -> a Source #
partial2_2 :: DifferentiallyClosed a => (b -> a -> a) -> b -> a -> a Source #
partial1_3 :: DifferentiallyClosed a => (a -> b -> c -> a) -> a -> b -> c -> a Source #
partial2_3 :: DifferentiallyClosed a => (b -> a -> c -> a) -> b -> a -> c -> a Source #
partial3_3 :: DifferentiallyClosed a => (b -> c -> a -> a) -> b -> c -> a -> a Source #
partial1_4 :: DifferentiallyClosed a => (a -> b -> c -> d -> a) -> a -> b -> c -> d -> a Source #
partial2_4 :: DifferentiallyClosed a => (b -> a -> c -> d -> a) -> b -> a -> c -> d -> a Source #
partial3_4 :: DifferentiallyClosed a => (b -> c -> a -> d -> a) -> b -> c -> a -> d -> a Source #
partial4_4 :: DifferentiallyClosed a => (b -> c -> d -> a -> a) -> b -> c -> d -> a -> a Source #
class Show r => ShowPrecision r where Source #
Minimal complete definition
Nothing
Methods
showAtPrecision :: r -> Integer -> String Source #
Instances
| ShowPrecision Dimension Source # | |
Defined in Math.Number.DimensionalAnalysis | |
| ShowPrecision R Source # | |
Defined in Math.Number.Real | |
| ShowPrecision String Source # | |
Defined in Math.Number.Interface | |
| ShowPrecision Integer Source # | |
Defined in Math.Number.Interface | |
| ShowPrecision () Source # | |
Defined in Math.Number.Interface Methods showAtPrecision :: () -> Integer -> String Source # | |
| ShowPrecision Double Source # | |
Defined in Math.Number.Interface | |
| ShowPrecision Float Source # | |
Defined in Math.Number.Interface | |
| ShowPrecision Int Source # | |
Defined in Math.Number.Interface | |
| ShowPrecision a => ShowPrecision (Complex a) Source # | |
Defined in Math.Number.Interface | |
| ShowPrecision s => ShowPrecision (Vector3 s) Source # | |
Defined in Math.Matrix.Vector3 | |
| ShowPrecision s => ShowPrecision (Vector4 s) Source # | |
Defined in Math.Matrix.Vector4 | |
differential :: DifferentiallyClosed r => (r -> r) -> r -> Endo r Source #
derivateCommutator :: DifferentiallyClosed r => (r -> r) -> (r -> r) -> r -> r Source #
computes \(f'(x)*g(x) - f(x)*g'(x)\)
derivateAnticommutator :: DifferentiallyClosed r => (r -> r) -> (r -> r) -> r -> r Source #
computes \(f'(x)*g(x) + f(x)*g'(x)\). Notice this is product rule.
derivates :: (StreamBuilder str, DifferentiallyClosed r) => (r -> r) -> str (r -> r) Source #
atan2Generic :: Floating a => a -> a -> a Source #
lineIntegral :: DifferentiallyClosed r => (r -> r) -> (r -> r) -> (r, r) -> r Source #
precisionCompare :: (Ord a, Num a) => a -> a -> a -> Bool Source #
compare to a certain precision, appropriate for floating point style numeric types. first argument is precision.
liftInverse :: (Fractional a, Fractional b) => (a -> b) -> a -> b Source #