Copyright	(C) Frank Staals
License	see the LICENSE file
Maintainer	Frank Staals
Safe Haskell	None
Language	Haskell2010

Data.Permutation

Description

Data type for representing a Permutation

Synopsis

type Orbit a = Vector a
data Permutation a = Permutation {
- _orbits :: Vector (Orbit a)
- _indexes :: 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
next :: Vector v a => v a -> Int -> a
previous :: Vector v a => v a -> Int -> a
lookupIdx :: Enum a => Permutation a -> a -> (Int, Int)
apply :: Enum a => Permutation a -> a -> a
orbitFrom :: Eq a => a -> (a -> a) -> [a]
cycleRep :: (Vector v a, Enum a, Eq a) => v a -> (a -> a) -> Permutation a
toCycleRep :: Enum a => Int -> [[a]] -> Permutation a
genIndexes :: Enum a => Int -> [[a]] -> Vector (Int, Int)

Documentation

type Orbit a = Vector a Source #

Orbits (Cycles) are represented by vectors

data Permutation a Source #

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 Source #
Instance details Defined in Data.Permutation Methods fmap :: (a -> b) -> Permutation a -> Permutation b # (<$) :: a -> Permutation b -> Permutation a #
Foldable Permutation Source #
Instance details 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 Source #
Instance details 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) Source #
Instance details Defined in Data.Permutation Methods (==) :: Permutation a -> Permutation a -> Bool # (/=) :: Permutation a -> Permutation a -> Bool #
Show a => Show (Permutation a) Source #
Instance details Defined in Data.Permutation Methods showsPrec :: Int -> Permutation a -> ShowS # show :: Permutation a -> String # showList :: [Permutation a] -> ShowS #
Generic (Permutation a) Source #
Instance details 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) Source #
Instance details Defined in Data.Permutation Methods rnf :: Permutation a -> () #
type Rep (Permutation a) Source #
Instance details Defined in Data.Permutation type Rep (Permutation a) = D1 (MetaData "Permutation" "Data.Permutation" "hgeometry-combinatorial-0.11.0.0-Cktt0ZWYuCrAhHfx7XTJDd" 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)) Source #

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

elems :: Permutation a -> Vector a Source #

size :: Permutation a -> Int Source #

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

The cycle containing a given item

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

Next item in a cyclic permutation

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

Previous item in a cyclic permutation

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

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 Source #

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

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

Find the cycle in the permutation starting at element s

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

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 Source #

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) Source #