Data.Fin.Permutation

See Permutation

Documentation

data Permutation n

Permutation of n elements

Any permutation can be expressed as a product of transpositions. Ergo, construct with Semigroup operations and swap.

Instances

Eq (Permutation n)

Defined in Data.Fin.Permutation

Methods

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

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

Show (Permutation n)

Defined in Data.Fin.Permutation

Methods

showsPrec :: Int -> Permutation n -> ShowS

show :: Permutation n -> String

showList :: [Permutation n] -> ShowS

Natural n => Semigroup (Permutation n)

Defined in Data.Fin.Permutation

Methods

(<>) :: Permutation n -> Permutation n -> Permutation n

sconcat :: NonEmpty (Permutation n) -> Permutation n

stimes :: Integral b => b -> Permutation n -> Permutation n

Natural n => Monoid (Permutation n)

Defined in Data.Fin.Permutation

Methods

mempty :: Permutation n

mappend :: Permutation n -> Permutation n -> Permutation n

mconcat :: [Permutation n] -> Permutation n

Natural n => Group (Permutation n)

Defined in Data.Fin.Permutation

Methods

invert :: Permutation n -> Permutation n

Natural n => Universe (Permutation n)

Defined in Data.Fin.Permutation

Methods

universe :: [Permutation n]

Natural n => Finite (Permutation n)

Defined in Data.Fin.Permutation

Methods

universeF :: [Permutation n]

apply :: Permutation n -> List n a -> List n a

unapply :: Permutation n -> List n a -> List n a

swap :: Natural n => Fin n -> Fin n -> Permutation n

Transposition of the giventh elements

orbit :: Natural n => Permutation n -> Fin n -> NonEmpty (Fin n)

Orbit of the given index under the given permutation

cycles :: forall n. Natural n => Permutation (Succ n) -> NonEmpty (NonEmpty (Fin (Succ n)))

All the cycles of the given permutation, which are necessarily disjoint