numeric-prelude-0.4.3.1: An experimental alternative hierarchy of numeric type classes

Algebra.Algebraic

Contents

Synopsis

# Documentation

class C a => C a where Source #

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

Minimal complete definition

Methods

sqrt :: a -> a Source #

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

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

Instances
 Source # Instance detailsDefined in Algebra.Algebraic Methods Source # Instance detailsDefined in Algebra.Algebraic Methods Source # Instance detailsDefined in Number.FixedPoint.Check Methodssqrt :: T -> T Source #root :: Integer -> T -> T Source #(^/) :: T -> Rational -> T Source # Source # Instance detailsDefined in Number.Positional.Check Methodssqrt :: T -> T Source #root :: Integer -> T -> T Source #(^/) :: T -> Rational -> T Source # (Ord a, C a) => C (T a) Source # Instance detailsDefined in Number.NonNegative Methodssqrt :: 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 detailsDefined in MathObj.Wrapper.Haskell98 Methodssqrt :: 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 detailsDefined in Number.PartiallyTranscendental Methodssqrt :: 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 detailsDefined in MathObj.PowerSeries Methodssqrt :: 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 detailsDefined in MathObj.PowerSeries2 Methodssqrt :: 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 detailsDefined in MathObj.PowerSum Methodssqrt :: 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 detailsDefined in MathObj.RootSet Methodssqrt :: 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 detailsDefined in Number.Complex Methodssqrt :: 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 detailsDefined in MathObj.Wrapper.NumericPrelude Methodssqrt :: 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 detailsDefined in Number.OccasionallyScalarExpression Methodssqrt :: 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 detailsDefined in Number.Physical Methodssqrt :: 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 detailsDefined in Number.SI Methodssqrt :: 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 #