Algebra.Ring.Ideal

Documentation

data Ideal r

Constructors

Ideal (Sized n r)

Instances

Eq r => Eq (Ideal r)

Methods

(==) :: Ideal r -> Ideal r -> Bool

(/=) :: Ideal r -> Ideal r -> Bool

Ord r => Ord (Ideal r)

Methods

compare :: Ideal r -> Ideal r -> Ordering

(<) :: Ideal r -> Ideal r -> Bool

(<=) :: Ideal r -> Ideal r -> Bool

(>) :: Ideal r -> Ideal r -> Bool

(>=) :: Ideal r -> Ideal r -> Bool

max :: Ideal r -> Ideal r -> Ideal r

min :: Ideal r -> Ideal r -> Ideal r

Show r => Show (Ideal r)

Methods

showsPrec :: Int -> Ideal r -> ShowS

show :: Ideal r -> String

showList :: [Ideal r] -> ShowS

NFData r => NFData (Ideal r)

Methods

rnf :: Ideal r -> ()

addToIdeal :: (Monoidal r, Eq r) => r -> Ideal r -> Ideal r infixr 9

toIdeal :: (Eq r, Monoidal r) => [r] -> Ideal r

appendIdeal :: Ideal r -> Ideal r -> Ideal r

generators :: Ideal r -> [r]

filterIdeal :: (Eq r, Monoidal r) => (r -> Bool) -> Ideal r -> Ideal r

mapIdeal :: (r -> r') -> Ideal r -> Ideal r'

principalIdeal :: r -> Ideal r

isEmptyIdeal :: Ideal t -> Bool