Safe Haskell	None
Language	Haskell2010

Algebra.Ring.Ideal

Documentation

newtype Ideal r Source #

Constructors

Ideal (Seq r)

Instances

Instances details

Functor Ideal Source #
Instance details Defined in Algebra.Ring.Ideal Methods fmap :: (a -> b) -> Ideal a -> Ideal b # (<$) :: a -> Ideal b -> Ideal a #
Foldable Ideal Source #
Instance details Defined in Algebra.Ring.Ideal Methods fold :: Monoid m => Ideal m -> m # foldMap :: Monoid m => (a -> m) -> Ideal a -> m # foldMap' :: Monoid m => (a -> m) -> Ideal a -> m # foldr :: (a -> b -> b) -> b -> Ideal a -> b # foldr' :: (a -> b -> b) -> b -> Ideal a -> b # foldl :: (b -> a -> b) -> b -> Ideal a -> b # foldl' :: (b -> a -> b) -> b -> Ideal a -> b # foldr1 :: (a -> a -> a) -> Ideal a -> a # foldl1 :: (a -> a -> a) -> Ideal a -> a # toList :: Ideal a -> [a] # null :: Ideal a -> Bool # length :: Ideal a -> Int # elem :: Eq a => a -> Ideal a -> Bool # maximum :: Ord a => Ideal a -> a # minimum :: Ord a => Ideal a -> a # sum :: Num a => Ideal a -> a # product :: Num a => Ideal a -> a #
Traversable Ideal Source #
Instance details Defined in Algebra.Ring.Ideal Methods traverse :: Applicative f => (a -> f b) -> Ideal a -> f (Ideal b) # sequenceA :: Applicative f => Ideal (f a) -> f (Ideal a) # mapM :: Monad m => (a -> m b) -> Ideal a -> m (Ideal b) # sequence :: Monad m => Ideal (m a) -> m (Ideal a) #
Show r => Show (Ideal r) Source #
Instance details Defined in Algebra.Ring.Ideal Methods showsPrec :: Int -> Ideal r -> ShowS # show :: Ideal r -> String # showList :: [Ideal r] -> ShowS #
NFData r => NFData (Ideal r) Source #
Instance details Defined in Algebra.Ring.Ideal Methods rnf :: Ideal r -> () #

addToIdeal :: (Monoidal r, DecidableZero r) => r -> Ideal r -> Ideal r infixr 9 Source #

toIdeal :: (DecidableZero r, Monoidal r) => [r] -> Ideal r Source #

appendIdeal :: Ideal r -> Ideal r -> Ideal r Source #

generators :: Ideal r -> [r] Source #

filterIdeal :: (r -> Bool) -> Ideal r -> Ideal r Source #

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

principalIdeal :: r -> Ideal r Source #

isEmptyIdeal :: Ideal t -> Bool Source #

someSizedIdeal :: Ideal r -> SomeSized Vector r Source #