halg-core-0.6.0.0: Core types and functions of halg computational algebra suite.

Algebra.Ring.Ideal

# Documentation

newtype Ideal r Source #

Constructors

 Ideal (Seq r)

#### Instances

Instances details
 Source # Instance detailsDefined in Algebra.Ring.Ideal Methodsfmap :: (a -> b) -> Ideal a -> Ideal b #(<\$) :: a -> Ideal b -> Ideal a # Source # Instance detailsDefined in Algebra.Ring.Ideal Methodsfold :: 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 # Source # Instance detailsDefined in Algebra.Ring.Ideal Methodstraverse :: 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 detailsDefined in Algebra.Ring.Ideal MethodsshowsPrec :: Int -> Ideal r -> ShowS #show :: Ideal r -> String #showList :: [Ideal r] -> ShowS # NFData r => NFData (Ideal r) Source # Instance detailsDefined in Algebra.Ring.Ideal Methodsrnf :: Ideal r -> () #

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

toIdeal :: (DecidableZero r, Monoidal r) => [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 #

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