Safe Haskell	Safe
Language	Haskell98

Numeric.Additive.Group

Contents

Additive Groups

Synopsis

Additive Groups

class (LeftModule Integer r, RightModule Integer r, Monoidal r) => Group r where Source #

Methods

(-) :: r -> r -> r infixl 6 Source #

negate :: r -> r Source #

subtract :: r -> r -> r Source #

times :: Integral n => n -> r -> r infixl 7 Source #

Instances

Group Int Source #
Methods (-) :: Int -> Int -> Int Source # negate :: Int -> Int Source # subtract :: Int -> Int -> Int Source # times :: Integral n => n -> Int -> Int Source #
Group Int8 Source #
Methods (-) :: Int8 -> Int8 -> Int8 Source # negate :: Int8 -> Int8 Source # subtract :: Int8 -> Int8 -> Int8 Source # times :: Integral n => n -> Int8 -> Int8 Source #
Group Int16 Source #
Methods (-) :: Int16 -> Int16 -> Int16 Source # negate :: Int16 -> Int16 Source # subtract :: Int16 -> Int16 -> Int16 Source # times :: Integral n => n -> Int16 -> Int16 Source #
Group Int32 Source #
Methods (-) :: Int32 -> Int32 -> Int32 Source # negate :: Int32 -> Int32 Source # subtract :: Int32 -> Int32 -> Int32 Source # times :: Integral n => n -> Int32 -> Int32 Source #
Group Int64 Source #
Methods (-) :: Int64 -> Int64 -> Int64 Source # negate :: Int64 -> Int64 Source # subtract :: Int64 -> Int64 -> Int64 Source # times :: Integral n => n -> Int64 -> Int64 Source #
Group Integer Source #
Methods (-) :: Integer -> Integer -> Integer Source # negate :: Integer -> Integer Source # subtract :: Integer -> Integer -> Integer Source # times :: Integral n => n -> Integer -> Integer Source #
Group Word Source #
Methods (-) :: Word -> Word -> Word Source # negate :: Word -> Word Source # subtract :: Word -> Word -> Word Source # times :: Integral n => n -> Word -> Word Source #
Group Word8 Source #
Methods (-) :: Word8 -> Word8 -> Word8 Source # negate :: Word8 -> Word8 Source # subtract :: Word8 -> Word8 -> Word8 Source # times :: Integral n => n -> Word8 -> Word8 Source #
Group Word16 Source #
Methods (-) :: Word16 -> Word16 -> Word16 Source # negate :: Word16 -> Word16 Source # subtract :: Word16 -> Word16 -> Word16 Source # times :: Integral n => n -> Word16 -> Word16 Source #
Group Word32 Source #
Methods (-) :: Word32 -> Word32 -> Word32 Source # negate :: Word32 -> Word32 Source # subtract :: Word32 -> Word32 -> Word32 Source # times :: Integral n => n -> Word32 -> Word32 Source #
Group Word64 Source #
Methods (-) :: Word64 -> Word64 -> Word64 Source # negate :: Word64 -> Word64 Source # subtract :: Word64 -> Word64 -> Word64 Source # times :: Integral n => n -> Word64 -> Word64 Source #
Group () Source #
Methods (-) :: () -> () -> () Source # negate :: () -> () Source # subtract :: () -> () -> () Source # times :: Integral n => n -> () -> () Source #
Group Euclidean Source #
Methods (-) :: Euclidean -> Euclidean -> Euclidean Source # negate :: Euclidean -> Euclidean Source # subtract :: Euclidean -> Euclidean -> Euclidean Source # times :: Integral n => n -> Euclidean -> Euclidean Source #
Group r => Group (ZeroRng r) Source #
Methods (-) :: ZeroRng r -> ZeroRng r -> ZeroRng r Source # negate :: ZeroRng r -> ZeroRng r Source # subtract :: ZeroRng r -> ZeroRng r -> ZeroRng r Source # times :: Integral n => n -> ZeroRng r -> ZeroRng r Source #
(Abelian r, Group r) => Group (RngRing r) Source #
Methods (-) :: RngRing r -> RngRing r -> RngRing r Source # negate :: RngRing r -> RngRing r Source # subtract :: RngRing r -> RngRing r -> RngRing r Source # times :: Integral n => n -> RngRing r -> RngRing r Source #
Group r => Group (Opposite r) Source #
Methods (-) :: Opposite r -> Opposite r -> Opposite r Source # negate :: Opposite r -> Opposite r Source # subtract :: Opposite r -> Opposite r -> Opposite r Source # times :: Integral n => n -> Opposite r -> Opposite r Source #
Group r => Group (End r) Source #
Methods (-) :: End r -> End r -> End r Source # negate :: End r -> End r Source # subtract :: End r -> End r -> End r Source # times :: Integral n => n -> End r -> End r Source #
Division r => Group (Log r) Source #
Methods (-) :: Log r -> Log r -> Log r Source # negate :: Log r -> Log r Source # subtract :: Log r -> Log r -> Log r Source # times :: Integral n => n -> Log r -> Log r Source #
Group r => Group (Trig r) Source #
Methods (-) :: Trig r -> Trig r -> Trig r Source # negate :: Trig r -> Trig r Source # subtract :: Trig r -> Trig r -> Trig r Source # times :: Integral n => n -> Trig r -> Trig r Source #
Group r => Group (Quaternion' r) Source #
Methods (-) :: Quaternion' r -> Quaternion' r -> Quaternion' r Source # negate :: Quaternion' r -> Quaternion' r Source # subtract :: Quaternion' r -> Quaternion' r -> Quaternion' r Source # times :: Integral n => n -> Quaternion' r -> Quaternion' r Source #
Group r => Group (Hyper r) Source #
Methods (-) :: Hyper r -> Hyper r -> Hyper r Source # negate :: Hyper r -> Hyper r Source # subtract :: Hyper r -> Hyper r -> Hyper r Source # times :: Integral n => n -> Hyper r -> Hyper r Source #
Group r => Group (Dual' r) Source #
Methods (-) :: Dual' r -> Dual' r -> Dual' r Source # negate :: Dual' r -> Dual' r Source # subtract :: Dual' r -> Dual' r -> Dual' r Source # times :: Integral n => n -> Dual' r -> Dual' r Source #
Group r => Group (Quaternion r) Source #
Methods (-) :: Quaternion r -> Quaternion r -> Quaternion r Source # negate :: Quaternion r -> Quaternion r Source # subtract :: Quaternion r -> Quaternion r -> Quaternion r Source # times :: Integral n => n -> Quaternion r -> Quaternion r Source #
Group r => Group (Hyper' r) Source #
Methods (-) :: Hyper' r -> Hyper' r -> Hyper' r Source # negate :: Hyper' r -> Hyper' r Source # subtract :: Hyper' r -> Hyper' r -> Hyper' r Source # times :: Integral n => n -> Hyper' r -> Hyper' r Source #
Group r => Group (Dual r) Source #
Methods (-) :: Dual r -> Dual r -> Dual r Source # negate :: Dual r -> Dual r Source # subtract :: Dual r -> Dual r -> Dual r Source # times :: Integral n => n -> Dual r -> Dual r Source #
Group r => Group (Complex r) Source #
Methods (-) :: Complex r -> Complex r -> Complex r Source # negate :: Complex r -> Complex r Source # subtract :: Complex r -> Complex r -> Complex r Source # times :: Integral n => n -> Complex r -> Complex r Source #
GCDDomain d => Group (Fraction d) Source #
Methods (-) :: Fraction d -> Fraction d -> Fraction d Source # negate :: Fraction d -> Fraction d Source # subtract :: Fraction d -> Fraction d -> Fraction d Source # times :: Integral n => n -> Fraction d -> Fraction d Source #
Group r => Group (e -> r) Source #
Methods (-) :: (e -> r) -> (e -> r) -> e -> r Source # negate :: (e -> r) -> e -> r Source # subtract :: (e -> r) -> (e -> r) -> e -> r Source # times :: Integral n => n -> (e -> r) -> e -> r Source #
(Group a, Group b) => Group (a, b) Source #
Methods (-) :: (a, b) -> (a, b) -> (a, b) Source # negate :: (a, b) -> (a, b) Source # subtract :: (a, b) -> (a, b) -> (a, b) Source # times :: Integral n => n -> (a, b) -> (a, b) Source #
Group s => Group (Covector s a) Source #
Methods (-) :: Covector s a -> Covector s a -> Covector s a Source # negate :: Covector s a -> Covector s a Source # subtract :: Covector s a -> Covector s a -> Covector s a Source # times :: Integral n => n -> Covector s a -> Covector s a Source #
(Group a, Group b, Group c) => Group (a, b, c) Source #
Methods (-) :: (a, b, c) -> (a, b, c) -> (a, b, c) Source # negate :: (a, b, c) -> (a, b, c) Source # subtract :: (a, b, c) -> (a, b, c) -> (a, b, c) Source # times :: Integral n => n -> (a, b, c) -> (a, b, c) Source #
Group s => Group (Map s b a) Source #
Methods (-) :: Map s b a -> Map s b a -> Map s b a Source # negate :: Map s b a -> Map s b a Source # subtract :: Map s b a -> Map s b a -> Map s b a Source # times :: Integral n => n -> Map s b a -> Map s b a Source #
(Group a, Group b, Group c, Group d) => Group (a, b, c, d) Source #
Methods (-) :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) Source # negate :: (a, b, c, d) -> (a, b, c, d) Source # subtract :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) Source # times :: Integral n => n -> (a, b, c, d) -> (a, b, c, d) Source #
(Group a, Group b, Group c, Group d, Group e) => Group (a, b, c, d, e) Source #
Methods (-) :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) Source # negate :: (a, b, c, d, e) -> (a, b, c, d, e) Source # subtract :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) Source # times :: Integral n => n -> (a, b, c, d, e) -> (a, b, c, d, e) Source #