Numeric.Additive.Class

Additive Semigroups

class Additive r where

 (a + b) + c = a + (b + c)
 sinnum 1 a = a
 sinnum (2 * n) a = sinnum n a + sinnum n a
 sinnum (2 * n + 1) a = sinnum n a + sinnum n a + a

Methods

(+) :: r -> r -> r

sinnum1p :: Whole n => n -> r -> r

sinnum1p n r = sinnum (1 + n) r

sumWith1 :: Foldable1 f => (a -> r) -> f a -> r

Instances

Additive Bool

Additive Int

Additive Int8

Additive Int16

Additive Int32

Additive Int64

Additive Integer

Additive Word

Additive Word8

Additive Word16

Additive Word32

Additive Word64

Additive ()

Additive Natural

Additive Euclidean

Additive r => Additive (Complex r)

Additive r => Additive (Quaternion r)

Additive r => Additive (Dual r)

Additive r => Additive (Hyper' r)

Additive r => Additive (Hyper r)

Additive r => Additive (Dual' r)

Additive (BasisCoblade m)

Additive r => Additive (Quaternion' r)

Additive r => Additive (Trig r)

Multiplicative r => Additive (Log r)

Additive r => Additive (End r)

Additive r => Additive (Opposite r)

Abelian r => Additive (RngRing r)

Additive r => Additive (ZeroRng r)

Additive r => Additive (b -> r)

(Additive a, Additive b) => Additive (a, b)

(HasTrie b, Additive r) => Additive (:->: b r)

Additive r => Additive (Covector r a)

(Additive a, Additive b, Additive c) => Additive (a, b, c)

Additive r => Additive (Map r b a)

(Additive a, Additive b, Additive c, Additive d) => Additive (a, b, c, d)

(Additive a, Additive b, Additive c, Additive d, Additive e) => Additive (a, b, c, d, e)

sum1 :: (Foldable1 f, Additive r) => f r -> r

Additive Abelian semigroups

class Additive r => Abelian r

an additive abelian semigroup

a + b = b + a

Instances

Abelian Bool

Abelian Int

Abelian Int8

Abelian Int16

Abelian Int32

Abelian Int64

Abelian Integer

Abelian Word

Abelian Word8

Abelian Word16

Abelian Word32

Abelian Word64

Abelian ()

Abelian Natural

Abelian Euclidean

(Additive (Complex r), Abelian r) => Abelian (Complex r)

(Additive (Quaternion r), Abelian r) => Abelian (Quaternion r)

(Additive (Dual r), Abelian r) => Abelian (Dual r)

(Additive (Hyper' r), Abelian r) => Abelian (Hyper' r)

(Additive (Hyper r), Abelian r) => Abelian (Hyper r)

(Additive (Dual' r), Abelian r) => Abelian (Dual' r)

Additive (BasisCoblade m) => Abelian (BasisCoblade m)

(Additive (Quaternion' r), Abelian r) => Abelian (Quaternion' r)

(Additive (Trig r), Abelian r) => Abelian (Trig r)

(Additive (Log r), Commutative r) => Abelian (Log r)

(Additive (End r), Abelian r) => Abelian (End r)

(Additive (Opposite r), Abelian r) => Abelian (Opposite r)

(Additive (RngRing r), Abelian r) => Abelian (RngRing r)

(Additive (ZeroRng r), Abelian r) => Abelian (ZeroRng r)

(Additive (e -> r), Abelian r) => Abelian (e -> r)

(Additive (a, b), Abelian a, Abelian b) => Abelian (a, b)

(Additive (:->: e r), HasTrie e, Abelian r) => Abelian (:->: e r)

(Additive (Covector s a), Abelian s) => Abelian (Covector s a)

(Additive (a, b, c), Abelian a, Abelian b, Abelian c) => Abelian (a, b, c)

(Additive (Map s b a), Abelian s) => Abelian (Map s b a)

(Additive (a, b, c, d), Abelian a, Abelian b, Abelian c, Abelian d) => Abelian (a, b, c, d)

(Additive (a, b, c, d, e), Abelian a, Abelian b, Abelian c, Abelian d, Abelian e) => Abelian (a, b, c, d, e)

Additive Monoids

class Additive r => Idempotent r

An additive semigroup with idempotent addition.

 a + a = a

Instances

Idempotent Bool

Idempotent ()

(Additive (Complex r), Idempotent r) => Idempotent (Complex r)

(Additive (Quaternion r), Idempotent r) => Idempotent (Quaternion r)

(Additive (Dual r), Idempotent r) => Idempotent (Dual r)

(Additive (Hyper' r), Idempotent r) => Idempotent (Hyper' r)

(Additive (Hyper r), Idempotent r) => Idempotent (Hyper r)

(Additive (Dual' r), Idempotent r) => Idempotent (Dual' r)

(Additive (Quaternion' r), Idempotent r) => Idempotent (Quaternion' r)

(Additive (Trig r), Idempotent r) => Idempotent (Trig r)

(Additive (Log r), Band r) => Idempotent (Log r)

(Additive (Opposite r), Idempotent r) => Idempotent (Opposite r)

(Additive (ZeroRng r), Idempotent r) => Idempotent (ZeroRng r)

(Additive (e -> r), Idempotent r) => Idempotent (e -> r)

(Additive (a, b), Idempotent a, Idempotent b) => Idempotent (a, b)

(Additive (:->: e r), HasTrie e, Idempotent r) => Idempotent (:->: e r)

(Additive (Covector r a), Idempotent r) => Idempotent (Covector r a)

(Additive (a, b, c), Idempotent a, Idempotent b, Idempotent c) => Idempotent (a, b, c)

(Additive (a, b, c, d), Idempotent a, Idempotent b, Idempotent c, Idempotent d) => Idempotent (a, b, c, d)

(Additive (a, b, c, d, e), Idempotent a, Idempotent b, Idempotent c, Idempotent d, Idempotent e) => Idempotent (a, b, c, d, e)

sinnum1pIdempotent :: Natural -> r -> r

Partitionable semigroups

class Additive m => Partitionable m where

Methods

partitionWith :: (m -> m -> r) -> m -> NonEmpty r

partitionWith f c returns a list containing f a b for each a b such that a + b = c,

Instances

Partitionable Bool

Partitionable ()

Partitionable Natural

(Additive (Complex r), Partitionable r) => Partitionable (Complex r)

(Additive (Quaternion r), Partitionable r) => Partitionable (Quaternion r)

(Additive (Dual r), Partitionable r) => Partitionable (Dual r)

(Additive (Hyper' r), Partitionable r) => Partitionable (Hyper' r)

(Additive (Hyper r), Partitionable r) => Partitionable (Hyper r)

(Additive (Dual' r), Partitionable r) => Partitionable (Dual' r)

(Additive (Quaternion' r), Partitionable r) => Partitionable (Quaternion' r)

(Additive (Trig r), Partitionable r) => Partitionable (Trig r)

(Additive (Log r), Factorable r) => Partitionable (Log r)

(Additive (a, b), Partitionable a, Partitionable b) => Partitionable (a, b)

(Additive (a, b, c), Partitionable a, Partitionable b, Partitionable c) => Partitionable (a, b, c)

(Additive (a, b, c, d), Partitionable a, Partitionable b, Partitionable c, Partitionable d) => Partitionable (a, b, c, d)

(Additive (a, b, c, d, e), Partitionable a, Partitionable b, Partitionable c, Partitionable d, Partitionable e) => Partitionable (a, b, c, d, e)