Algebra.Structures.Ring
Description
The representation of the ring structure.
- class Ring a where
- propAddAssoc :: (Ring a, Eq a) => a -> a -> a -> (Bool, String)
- propAddIdentity :: (Ring a, Eq a) => a -> (Bool, String)
- propAddInv :: (Ring a, Eq a) => a -> (Bool, String)
- propAddComm :: (Ring a, Eq a) => a -> a -> (Bool, String)
- propMulAssoc :: (Ring a, Eq a) => a -> a -> a -> (Bool, String)
- propMulIdentity :: (Ring a, Eq a) => a -> (Bool, String)
- propRightDist :: (Ring a, Eq a) => a -> a -> a -> (Bool, String)
- propLeftDist :: (Ring a, Eq a) => a -> a -> a -> (Bool, String)
- propRing :: (Ring a, Eq a) => a -> a -> a -> Property
- (<->) :: Ring a => a -> a -> a
- (<^>) :: Ring a => a -> Integer -> a
- sumRing :: Ring a => [a] -> a
- productRing :: Ring a => [a] -> a
Documentation
Definition of rings.
Methods
Addition
Multiplication
Compute additive inverse
The additive identity
The multiplicative identity
propRightDist :: (Ring a, Eq a) => a -> a -> a -> (Bool, String)Source
Multiplication is right-distributive over addition.
propLeftDist :: (Ring a, Eq a) => a -> a -> a -> (Bool, String)Source
Multiplication is left-ditributive over addition.
propRing :: (Ring a, Eq a) => a -> a -> a -> PropertySource
Specification of rings. Test that the arguments satisfy the ring axioms.
productRing :: Ring a => [a] -> aSource
Product