Safe Haskell	None
Language	Haskell98

Algebra.Algebraic

Contents

Properties

Synopsis

class C a => C a where
- sqrt :: a -> a
- root :: Integer -> a -> a
- (^/) :: a -> Rational -> a
genericRoot :: (C a, C b) => b -> a -> a
power :: (C a, C b) => b -> a -> a
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

Documentation

class C a => C a where Source #

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

Minimal complete definition

root | (^/)

Methods

sqrt :: a -> a Source #

root :: Integer -> a -> a Source #

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

Instances

C Double Source #
Instance details Defined in Algebra.Algebraic Methods sqrt :: Double -> Double Source # root :: Integer -> Double -> Double Source # (^/) :: Double -> Rational -> Double Source #
C Float Source #
Instance details Defined in Algebra.Algebraic Methods sqrt :: Float -> Float Source # root :: Integer -> Float -> Float Source # (^/) :: Float -> Rational -> Float Source #
C T Source #
Instance details Defined in Number.FixedPoint.Check Methods sqrt :: T -> T Source # root :: Integer -> T -> T Source # (^/) :: T -> Rational -> T Source #
C T Source #
Instance details Defined in Number.Positional.Check Methods sqrt :: T -> T Source # root :: Integer -> T -> T Source # (^/) :: T -> Rational -> T Source #
(Ord a, C a) => C (T a) Source #
Instance details Defined in Number.NonNegative Methods sqrt :: T a -> T a Source # root :: Integer -> T a -> T a Source # (^/) :: T a -> Rational -> T a Source #
Floating a => C (T a) Source #
Instance details Defined in MathObj.Wrapper.Haskell98 Methods sqrt :: T a -> T a Source # root :: Integer -> T a -> T a Source # (^/) :: T a -> Rational -> T a Source #
C a => C (T a) Source #
Instance details Defined in Number.PartiallyTranscendental Methods sqrt :: T a -> T a Source # root :: Integer -> T a -> T a Source # (^/) :: T a -> Rational -> T a Source #
C a => C (T a) Source #
Instance details Defined in MathObj.PowerSeries Methods sqrt :: T a -> T a Source # root :: Integer -> T a -> T a Source # (^/) :: T a -> Rational -> T a Source #
C a => C (T a) Source #
Instance details Defined in MathObj.PowerSeries2 Methods sqrt :: T a -> T a Source # root :: Integer -> T a -> T a Source # (^/) :: T a -> Rational -> T a Source #
(C a, C a) => C (T a) Source #
Instance details Defined in MathObj.PowerSum Methods sqrt :: T a -> T a Source # root :: Integer -> T a -> T a Source # (^/) :: T a -> Rational -> T a Source #
(C a, C a) => C (T a) Source #
Instance details Defined in MathObj.RootSet Methods sqrt :: T a -> T a Source # root :: Integer -> T a -> T a Source # (^/) :: T a -> Rational -> T a Source #
(C a, C a, Power a) => C (T a) Source #
Instance details Defined in Number.Complex Methods sqrt :: T a -> T a Source # root :: Integer -> T a -> T a Source # (^/) :: T a -> Rational -> T a Source #
C a => C (T a) Source #
Instance details Defined in MathObj.Wrapper.NumericPrelude Methods sqrt :: T a -> T a Source # root :: Integer -> T a -> T a Source # (^/) :: T a -> Rational -> T a Source #
(C a, C v, Show v, C a v) => C (T a v) Source #
Instance details Defined in Number.OccasionallyScalarExpression Methods sqrt :: T a v -> T a v Source # root :: Integer -> T a v -> T a v Source # (^/) :: T a v -> Rational -> T a v Source #
(Ord i, C a) => C (T i a) Source #
Instance details Defined in Number.Physical Methods sqrt :: T i a -> T i a Source # root :: Integer -> T i a -> T i a Source # (^/) :: T i a -> Rational -> T i a Source #
C v => C (T a v) Source #
Instance details Defined in Number.SI Methods sqrt :: T a v -> T a v Source # root :: Integer -> T a v -> T a v Source # (^/) :: T a v -> Rational -> T a v Source #

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

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

Properties

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

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

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

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