algebra-4.3.1: Constructive abstract algebra

Safe HaskellSafe
LanguageHaskell98

Numeric.Rig.Class

Synopsis

Documentation

class (Semiring r, Unital r, Monoidal r) => Rig r where #

A Ring without (n)egation

Methods

fromNatural :: Natural -> r #

Instances

Rig Bool # 

Methods

fromNatural :: Natural -> Bool #

Rig Int # 

Methods

fromNatural :: Natural -> Int #

Rig Int8 # 

Methods

fromNatural :: Natural -> Int8 #

Rig Int16 # 

Methods

fromNatural :: Natural -> Int16 #

Rig Int32 # 

Methods

fromNatural :: Natural -> Int32 #

Rig Int64 # 

Methods

fromNatural :: Natural -> Int64 #

Rig Integer # 
Rig Natural # 
Rig Word # 

Methods

fromNatural :: Natural -> Word #

Rig Word8 # 

Methods

fromNatural :: Natural -> Word8 #

Rig Word16 # 
Rig Word32 # 
Rig Word64 # 
Rig () # 

Methods

fromNatural :: Natural -> () #

Rig Euclidean # 
Rng r => Rig (RngRing r) # 

Methods

fromNatural :: Natural -> RngRing r #

Rig r => Rig (Opposite r) # 

Methods

fromNatural :: Natural -> Opposite r #

(Abelian r, Monoidal r) => Rig (End r) # 

Methods

fromNatural :: Natural -> End r #

(Commutative r, Ring r) => Rig (Trig r) # 

Methods

fromNatural :: Natural -> Trig r #

(TriviallyInvolutive r, Ring r) => Rig (Quaternion' r) # 
(Commutative r, Rig r) => Rig (Hyper r) # 

Methods

fromNatural :: Natural -> Hyper r #

Rig (BasisCoblade m) # 
(Commutative r, Ring r) => Rig (Dual' r) # 

Methods

fromNatural :: Natural -> Dual' r #

(TriviallyInvolutive r, Ring r) => Rig (Quaternion r) # 
(Commutative r, Rig r) => Rig (Hyper' r) # 

Methods

fromNatural :: Natural -> Hyper' r #

(Commutative r, Ring r) => Rig (Dual r) # 

Methods

fromNatural :: Natural -> Dual r #

(Commutative r, Ring r) => Rig (Complex r) # 

Methods

fromNatural :: Natural -> Complex r #

GCDDomain d => Rig (Fraction d) # 

Methods

fromNatural :: Natural -> Fraction d #

(Rig a, Rig b) => Rig (a, b) # 

Methods

fromNatural :: Natural -> (a, b) #

(Rig r, CounitalCoalgebra r m) => Rig (Covector r m) # 

Methods

fromNatural :: Natural -> Covector r m #

(Rig a, Rig b, Rig c) => Rig (a, b, c) # 

Methods

fromNatural :: Natural -> (a, b, c) #

(Rig r, CounitalCoalgebra r m) => Rig (Map r b m) # 

Methods

fromNatural :: Natural -> Map r b m #

(Rig a, Rig b, Rig c, Rig d) => Rig (a, b, c, d) # 

Methods

fromNatural :: Natural -> (a, b, c, d) #

(Rig a, Rig b, Rig c, Rig d, Rig e) => Rig (a, b, c, d, e) # 

Methods

fromNatural :: Natural -> (a, b, c, d, e) #