Safe Haskell	None
Language	Haskell2010

Numeric.Algebra.Multiplicative.MGroup

Description

Provides typeclasses for division.

Since: 0.1

Synopsis

class MMonoid g => MGroup g where
- (.%.) :: g -> g -> g
mnegate :: MGroup g => g -> g

Documentation

class MMonoid g => MGroup g where Source #

Defines a multiplicative group.

Examples:

Expand

>>> :{
  -- Multiplication
  f1 :: (MGroup g) => g -> g
  f1 x = x .*. x
:}

>>> f1 5
25

>>> :{
  -- One
  f2 :: (MGroup g) => g -> g
  f2 x = x .*. one
:}

>>> f2 5
5

>>> :{
  -- Division
  f3 :: (MGroup g, Num g) => g -> g
  f3 x = x .%. 2
:}

>>> f3 6
3

Since: 0.1

Methods

(.%.) :: g -> g -> g infixl 7 Source #

Should satisfy:

-- inverse
a .%. a === one

Since: 0.1

Instances

Instances details

MGroup Int16 Source #	Since: 0.1
Instance details Defined in Numeric.Algebra.Multiplicative.MGroup Methods (.%.) :: Int16 -> Int16 -> Int16 Source #
MGroup Int32 Source #	Since: 0.1
Instance details Defined in Numeric.Algebra.Multiplicative.MGroup Methods (.%.) :: Int32 -> Int32 -> Int32 Source #
MGroup Int64 Source #	Since: 0.1
Instance details Defined in Numeric.Algebra.Multiplicative.MGroup Methods (.%.) :: Int64 -> Int64 -> Int64 Source #
MGroup Int8 Source #	Since: 0.1
Instance details Defined in Numeric.Algebra.Multiplicative.MGroup Methods (.%.) :: Int8 -> Int8 -> Int8 Source #
MGroup Word16 Source #	Since: 0.1
Instance details Defined in Numeric.Algebra.Multiplicative.MGroup Methods (.%.) :: Word16 -> Word16 -> Word16 Source #
MGroup Word32 Source #	Since: 0.1
Instance details Defined in Numeric.Algebra.Multiplicative.MGroup Methods (.%.) :: Word32 -> Word32 -> Word32 Source #
MGroup Word64 Source #	Since: 0.1
Instance details Defined in Numeric.Algebra.Multiplicative.MGroup Methods (.%.) :: Word64 -> Word64 -> Word64 Source #
MGroup Word8 Source #	Since: 0.1
Instance details Defined in Numeric.Algebra.Multiplicative.MGroup Methods (.%.) :: Word8 -> Word8 -> Word8 Source #
MGroup Integer Source #	Since: 0.1
Instance details Defined in Numeric.Algebra.Multiplicative.MGroup Methods (.%.) :: Integer -> Integer -> Integer Source #
MGroup Natural Source #	Since: 0.1
Instance details Defined in Numeric.Algebra.Multiplicative.MGroup Methods (.%.) :: Natural -> Natural -> Natural Source #
MGroup Double Source #	Since: 0.1
Instance details Defined in Numeric.Algebra.Multiplicative.MGroup Methods (.%.) :: Double -> Double -> Double Source #
MGroup Float Source #	Since: 0.1
Instance details Defined in Numeric.Algebra.Multiplicative.MGroup Methods (.%.) :: Float -> Float -> Float Source #
MGroup Int Source #	Since: 0.1
Instance details Defined in Numeric.Algebra.Multiplicative.MGroup Methods (.%.) :: Int -> Int -> Int Source #
MGroup Word Source #	Since: 0.1
Instance details Defined in Numeric.Algebra.Multiplicative.MGroup Methods (.%.) :: Word -> Word -> Word Source #
Fractional a => MGroup (AsFractional a) Source #	Since: 0.1
Instance details Defined in Numeric.Algebra.Multiplicative.MGroup Methods (.%.) :: AsFractional a -> AsFractional a -> AsFractional a Source #
Integral a => MGroup (AsIntegral a) Source #	Since: 0.1
Instance details Defined in Numeric.Algebra.Multiplicative.MGroup Methods (.%.) :: AsIntegral a -> AsIntegral a -> AsIntegral a Source #
RealFloat a => MGroup (Complex a) Source #	Since: 0.1
Instance details Defined in Numeric.Algebra.Multiplicative.MGroup Methods (.%.) :: Complex a -> Complex a -> Complex a Source #
MGroup (Ratio Integer) Source #	Since: 0.1
Instance details Defined in Numeric.Algebra.Multiplicative.MGroup Methods (.%.) :: Ratio Integer -> Ratio Integer -> Ratio Integer Source #
MGroup (Ratio Natural) Source #	Since: 0.1
Instance details Defined in Numeric.Algebra.Multiplicative.MGroup Methods (.%.) :: Ratio Natural -> Ratio Natural -> Ratio Natural Source #
HasResolution k => MGroup (Fixed k) Source #	Since: 0.1
Instance details Defined in Numeric.Algebra.Multiplicative.MGroup Methods (.%.) :: Fixed k -> Fixed k -> Fixed k Source #

mnegate :: MGroup g => g -> g Source #

Since: 0.1