Safe Haskell	None
Language	Haskell2010

Numeric.Algebra.Multiplicative.MMonoid

Description

Provides the MMonoid typeclass.

Since: 0.1

Synopsis

class MSemigroup m => MMonoid m where
- one :: m
pattern One :: (MMonoid m, Eq m) => m
pattern NonOne :: (MMonoid m, Eq m) => m -> m

Documentation

class MSemigroup m => MMonoid m where Source #

Defines a monoid over a multiplicative semigroup.

Examples:

Expand

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

>>> f1 5
25

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

>>> f2 5
5

Since: 0.1

Methods

one :: m Source #

Should satisfy:

-- identity
a .*. one === a === one .*. a

Since: 0.1

Instances

Instances details

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

pattern One :: (MMonoid m, Eq m) => m Source #

Pattern synonym for one.

Since: 0.1

pattern NonOne :: (MMonoid m, Eq m) => m -> m Source #

Pattern synonym for x /= one.

Since: 0.1