Safe Haskell	None
Language	Haskell2010

Numeric.Algebra.Additive.AGroup

Description

Provides the AGroup typeclass.

Since: 0.1

Synopsis

class AMonoid g => AGroup g where
- (.-.) :: g -> g -> g
anegate :: AGroup g => g -> g

Documentation

class AMonoid g => AGroup g where Source #

Defines an additive group.

Examples:

Expand

>>> :{
  -- Addition
  f1 :: (AGroup g) => g -> g
  f1 x = x .+. x
:}

>>> f1 5
10

>>> :{
  -- Zero
  f2 :: (AGroup g) => g -> g
  f2 x = x .+. zero
:}

>>> f2 5
5

>>> :{
  -- Subtraction
  f3 :: (AGroup g, Num g) => g -> g
  f3 x = x .-. 3
:}

>>> f3 5
2

Since: 0.1

Methods

(.-.) :: g -> g -> g infixl 6 Source #

Should satisfy:

-- inverse
a .-. a === zero

Since: 0.1

Instances

Instances details

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

anegate :: AGroup g => g -> g Source #

Since: 0.1