hgeometry-combinatorial-0.12.0.2: Data structures, and Data types.
Copyright(C) Frank Staals
Licensesee the LICENSE file
MaintainerFrank Staals
Safe HaskellNone
LanguageHaskell2010

Data.Permutation

Description

Data type for representing a Permutation

Synopsis

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

Instances

Instances details
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 #

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

Show a => Show (Permutation a) Source # 
Instance details

Defined in Data.Permutation

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-0.12.0.2-BPOszceZMWb3Na6sqXbM08" '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 #

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 #