Data.Permutation

Data type for representing a Permutation

Documentation

type Orbit a = Vector a

Orbits (Cycles) are represented by vectors

data Permutation a

Cyclic representation of a permutation.

Constructors

Permutation

Fields

• _orbits :: Vector (Orbit a)
• _indexes :: Vector (Int, Int)

  idxes (fromEnum a) = (i,j) implies that a is the j^th item in the i^th orbit

Instances

Functor Permutation

Defined in Data.Permutation

Methods

fmap :: (a -> b) -> Permutation a -> Permutation b

(<$) :: a -> Permutation b -> Permutation a

Foldable Permutation

Defined in Data.Permutation

Methods

fold :: Monoid m => Permutation m -> m

foldMap :: Monoid m => (a -> m) -> Permutation a -> m

foldr :: (a -> b -> b) -> b -> Permutation a -> b

foldr' :: (a -> b -> b) -> b -> Permutation a -> b

foldl :: (b -> a -> b) -> b -> Permutation a -> b

foldl' :: (b -> a -> b) -> b -> Permutation a -> b

foldr1 :: (a -> a -> a) -> Permutation a -> a

foldl1 :: (a -> a -> a) -> Permutation a -> a

toList :: Permutation a -> [a]

null :: Permutation a -> Bool

length :: Permutation a -> Int

elem :: Eq a => a -> Permutation a -> Bool

maximum :: Ord a => Permutation a -> a

minimum :: Ord a => Permutation a -> a

sum :: Num a => Permutation a -> a

product :: Num a => Permutation a -> a

Traversable Permutation

Defined in Data.Permutation

Methods

traverse :: Applicative f => (a -> f b) -> Permutation a -> f (Permutation b)

sequenceA :: Applicative f => Permutation (f a) -> f (Permutation a)

mapM :: Monad m => (a -> m b) -> Permutation a -> m (Permutation b)

sequence :: Monad m => Permutation (m a) -> m (Permutation a)

Eq a => Eq (Permutation a)

Defined in Data.Permutation

Methods

(==) :: Permutation a -> Permutation a -> Bool

(/=) :: Permutation a -> Permutation a -> Bool

Show a => Show (Permutation a)

Defined in Data.Permutation

Methods

showsPrec :: Int -> Permutation a -> ShowS

show :: Permutation a -> String

showList :: [Permutation a] -> ShowS

Generic (Permutation a)

Defined in Data.Permutation

Associated Types

type Rep (Permutation a) :: Type -> Type

Methods

from :: Permutation a -> Rep (Permutation a) x

to :: Rep (Permutation a) x -> Permutation a

NFData a => NFData (Permutation a)

Defined in Data.Permutation

Methods

rnf :: Permutation a -> ()

type Rep (Permutation a)

Defined in Data.Permutation

type Rep (Permutation a) = D1 (MetaData "Permutation" "Data.Permutation" "hgeometry-combinatorial-0.9.0.0-6qy5VaQ7muxJuEfibyCL9S" False) (C1 (MetaCons "Permutation" PrefixI True) (S1 (MetaSel (Just "_orbits") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (Vector (Orbit a))) :*: S1 (MetaSel (Just "_indexes") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (Vector (Int, Int)))))

orbits :: forall a a. Lens (Permutation a) (Permutation a) (Vector (Orbit a)) (Vector (Orbit a))

indexes :: forall a. Lens' (Permutation a) (Vector (Int, Int))

elems :: Permutation a -> Vector a

size :: Permutation a -> Int

cycleOf :: Enum a => Permutation a -> a -> Orbit a

The cycle containing a given item

next :: Vector v a => v a -> Int -> a

Next item in a cyclic permutation

previous :: Vector v a => v a -> Int -> a

Previous item in a cyclic permutation

lookupIdx :: Enum a => Permutation a -> a -> (Int, Int)

Lookup the indices of an element, i.e. in which orbit the item is, and the index within the orbit.

runnign time: \(O(1)\)

apply :: Enum a => Permutation a -> a -> a

Apply the permutation, i.e. consider the permutation as a function.

orbitFrom :: Eq a => a -> (a -> a) -> [a]

Find the cycle in the permutation starting at element s

cycleRep :: (Vector v a, Enum a, Eq a) => v a -> (a -> a) -> Permutation a

Given a vector with items in the permutation, and a permutation (by its functional representation) construct the cyclic representation of the permutation.

toCycleRep :: Enum a => Int -> [[a]] -> Permutation a

Given the size n, and a list of Cycles, turns the cycles into a cyclic representation of the Permutation.

genIndexes :: Enum a => Int -> [[a]] -> Vector (Int, Int)