Math.Algebra.Group.PermutationGroup

Synopsis

# Documentation

newtype Permutation a Source

Type for permutations, considered as group elements.

Constructors

 P (Map a a)

Instances

 Eq a => Eq (Permutation a) (Ord a, Show a) => Fractional (Permutation a) (Ord a, Show a) => Num (Permutation a) Ord a => Ord (Permutation a) (Ord a, Show a) => Show (Permutation a)

(.^) :: Ord k => k -> Permutation k -> kSource

x .^ g returns the image of a vertex or point x under the action of the permutation g

p :: Ord a => [[a]] -> Permutation aSource

Construct a permutation from a list of cycles

(^-) :: (Ord k, Show k) => Permutation k -> Int -> Permutation kSource

A trick: g^-1 returns the inverse of g

(-^) :: Ord t => [t] -> Permutation t -> [t]Source

b -^ g returns the image of an edge or block b under the action of g

elts :: (Num a, Ord a) => [a] -> [a]Source

Generators for Cn, the cyclic group of order n

Generators for Sn, the symmetric group on [1..n]

Generators for An, the alternating group on [1..n]

Given generators for a group, return a (sorted) list of all elements of the group