Algebra.Algebraic

Documentation

class C a => C a where

Minimal implementation: root or '(^/)'.

Minimal complete definition

root | (^/)

Methods

sqrt :: a -> a

root :: Integer -> a -> a

(^/) :: a -> Rational -> a infixr 8

Instances

C Double

Methods

sqrt :: Double -> Double

root :: Integer -> Double -> Double

(^/) :: Double -> Rational -> Double

C Float

Methods

sqrt :: Float -> Float

root :: Integer -> Float -> Float

(^/) :: Float -> Rational -> Float

C T

Methods

sqrt :: T -> T

root :: Integer -> T -> T

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

C T

Methods

sqrt :: T -> T

root :: Integer -> T -> T

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

Floating a => C (T a)

Methods

sqrt :: T a -> T a

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

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

C a => C (T a)

Methods

sqrt :: T a -> T a

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

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

C a => C (T a)

Methods

sqrt :: T a -> T a

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

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

C a => C (T a)

Methods

sqrt :: T a -> T a

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

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

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

Methods

sqrt :: T a -> T a

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

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

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

Methods

sqrt :: T a -> T a

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

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

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

Methods

sqrt :: T a -> T a

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

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

C a => C (T a)

Methods

sqrt :: T a -> T a

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

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

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

Methods

sqrt :: T a v -> T a v

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

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

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

Methods

sqrt :: T i a -> T i a

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

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

C v => C (T a v)

Methods

sqrt :: T a v -> T a v

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

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

genericRoot :: (C a, C b) => b -> a -> a

power :: (C a, C b) => b -> a -> a

Properties

propSqrSqrt :: (Eq a, C a) => a -> Bool

propPowerCascade :: (Eq a, C a) => a -> Rational -> Rational -> Bool

propPowerProduct :: (Eq a, C a) => a -> Rational -> Rational -> Bool

propPowerDistributive :: (Eq a, C a) => Rational -> a -> a -> Bool