algebra-3.1: Constructive abstract algebra

Contents

Synopsis

class (LeftModule Integer r, RightModule Integer r, Monoidal r) => Group r whereSource

Methods

(-) :: r -> r -> rSource

negate :: r -> rSource

subtract :: r -> r -> rSource

times :: Integral n => n -> r -> rSource

Instances

 Group Int Group Int8 Group Int16 Group Int32 Group Int64 Group Integer Group Word Group Word8 Group Word16 Group Word32 Group Word64 Group () Group Euclidean (LeftModule Integer (Complex r), RightModule Integer (Complex r), Monoidal (Complex r), Group r) => Group (Complex r) (LeftModule Integer (Quaternion r), RightModule Integer (Quaternion r), Monoidal (Quaternion r), Group r) => Group (Quaternion r) (LeftModule Integer (Dual r), RightModule Integer (Dual r), Monoidal (Dual r), Group r) => Group (Dual r) (LeftModule Integer (Hyper' r), RightModule Integer (Hyper' r), Monoidal (Hyper' r), Group r) => Group (Hyper' r) (LeftModule Integer (Hyper r), RightModule Integer (Hyper r), Monoidal (Hyper r), Group r) => Group (Hyper r) (LeftModule Integer (Dual' r), RightModule Integer (Dual' r), Monoidal (Dual' r), Group r) => Group (Dual' r) (LeftModule Integer (Quaternion' r), RightModule Integer (Quaternion' r), Monoidal (Quaternion' r), Group r) => Group (Quaternion' r) (LeftModule Integer (Trig r), RightModule Integer (Trig r), Monoidal (Trig r), Group r) => Group (Trig r) (LeftModule Integer (Log r), RightModule Integer (Log r), Monoidal (Log r), Division r) => Group (Log r) (LeftModule Integer (End r), RightModule Integer (End r), Monoidal (End r), Group r) => Group (End r) (LeftModule Integer (Opposite r), RightModule Integer (Opposite r), Monoidal (Opposite r), Group r) => Group (Opposite r) (LeftModule Integer (RngRing r), RightModule Integer (RngRing r), Monoidal (RngRing r), Abelian r, Group r) => Group (RngRing r) (LeftModule Integer (ZeroRng r), RightModule Integer (ZeroRng r), Monoidal (ZeroRng r), Group r) => Group (ZeroRng r) (LeftModule Integer (e -> r), RightModule Integer (e -> r), Monoidal (e -> r), Group r) => Group (e -> r) (LeftModule Integer (a, b), RightModule Integer (a, b), Monoidal (a, b), Group a, Group b) => Group (a, b) (LeftModule Integer (:->: e r), RightModule Integer (:->: e r), Monoidal (:->: e r), HasTrie e, Group r) => Group (:->: e r) (LeftModule Integer (Covector s a), RightModule Integer (Covector s a), Monoidal (Covector s a), Group s) => Group (Covector s a) (LeftModule Integer (a, b, c), RightModule Integer (a, b, c), Monoidal (a, b, c), Group a, Group b, Group c) => Group (a, b, c) (LeftModule Integer (Map s b a), RightModule Integer (Map s b a), Monoidal (Map s b a), Group s) => Group (Map s b a) (LeftModule Integer (a, b, c, d), RightModule Integer (a, b, c, d), Monoidal (a, b, c, d), Group a, Group b, Group c, Group d) => Group (a, b, c, d) (LeftModule Integer (a, b, c, d, e), RightModule Integer (a, b, c, d, e), Monoidal (a, b, c, d, e), Group a, Group b, Group c, Group d, Group e) => Group (a, b, c, d, e)