Algebra.Structures.Ring

The representation of the ring structure.

Documentation

class Ring a where

Definition of rings.

Methods

(<+>) :: a -> a -> a

Addition

(<*>) :: a -> a -> a

Multiplication

neg :: a -> a

Compute additive inverse

zero :: a

The additive identity

one :: a

The multiplicative identity

Instances

Ring Z

Ring ZSqrt5

Ring EllipticCurve

(GCDDomain a, Eq a) => Ring (FieldOfFractions a)

Nat n => Ring (Zn n)

(CommutativeRing r, Eq r) => Ring (UPoly r x)

propRing :: (Ring a, Eq a) => a -> a -> a -> Property

Specification of rings. Test that the arguments satisfy the ring axioms.

(<->) :: Ring a => a -> a -> a

Subtraction

(<^>) :: Ring a => a -> Integer -> a

Exponentiation

(*>) :: Ring a => Integer -> a -> a

Multiply from left with an integer; n *> x means x + x + ... + x, n times.

(<*) :: Ring a => a -> Integer -> a

sumRing :: Ring a => [a] -> a

Summation

productRing :: Ring a => [a] -> a

Product