Math.Algebra.Group.SchreierSims

Documentation

cosetRepsGx :: (Ord k, Show k) => [Permutation k] -> k -> Map k (Permutation k)

schreierGeneratorsGx :: (Ord k, Show k) => (k, Map k (Permutation k)) -> [Permutation k] -> [Permutation k]

sift :: (Ord k, Show k) => [(k, Map k (Permutation k))] -> Permutation k -> Maybe (Permutation k)

findBase :: Ord a => [Permutation a] -> a

sgs :: (Ord a, Show a) => [Permutation a] -> [Permutation a]

Given generators for a permutation group, return a strong generating set. The result is calculated using Schreier-Sims algorithm, and is relative to the base implied by the Ord instance

bsgs :: (Ord k, Show k) => [Permutation k] -> [(k, Map k (Permutation k))]

bsgs' :: (Ord k, Show k) => [k] -> [Permutation k] -> [(k, Map k (Permutation k))]

newLevel :: (Ord a, Show a) => [a] -> [Permutation a] -> ([a], ((a, Map a (Permutation a)), [Permutation a]))

newLevel' :: (Ord t, Show t) => t -> [Permutation t] -> ((t, Map t (Permutation t)), [Permutation t])

ss :: (Ord k, Show k) => [k] -> [Permutation k] -> [((k, Map k (Permutation k)), [Permutation k])]

ss' :: (Ord k, Show k) => [k] -> [((k, Map k (Permutation k)), [Permutation k])] -> [((k, Map k (Permutation k)), [Permutation k])] -> [((k, Map k (Permutation k)), [Permutation k])]

isMemberBSGS :: (Ord k, Show k) => [(k, Map k (Permutation k))] -> Permutation k -> Bool

eltsBSGS :: Num b => [(a, Map k b)] -> [b]

cartProd :: [[a]] -> [[a]]

orderBSGS :: [(a1, Map k a)] -> Integer

isMember :: (Ord t, Show t) => [Permutation t] -> Permutation t -> Bool

Given generators for a group, determine whether a permutation is a member of the group, using Schreier-Sims algorithm

elts :: (Ord t, Show t) => [Permutation t] -> [Permutation t]

Given generators for a group, return a (sorted) list of all elements of the group, using Schreier-Sims algorithm

order :: (Ord t, Show t) => [Permutation t] -> Integer

Given generators for a group, return the order of the group (the number of elements), using Schreier-Sims algorithm

isSubgp :: (Ord k, Show k) => [Permutation k] -> [Permutation k] -> Bool

isNormal :: (Ord k, Show k) => [Permutation k] -> [Permutation k] -> Bool

index :: (Ord t1, Ord t, Show t1, Show t) => [Permutation t] -> [Permutation t1] -> Integer

reduceGens :: (Ord k, Show k) => [Permutation k] -> [Permutation k]

reduceGensBSGS :: (Ord k, Show k) => [Permutation k] -> ([Permutation k], [(k, Map k (Permutation k))])

normalClosure :: (Ord k, Show k) => [Permutation k] -> [Permutation k] -> [Permutation k]

commutatorGp :: (Ord k, Show k) => [Permutation k] -> [Permutation k] -> [Permutation k]

derivedSubgp :: (Ord k, Show k) => [Permutation k] -> [Permutation k]