Math.Algebra.Group.RandomSchreierSims

Documentation

testProdRepl :: IO ()

initProdRepl :: (Ord a, Show a) => [Permutation a] -> IO (Int, IOArray Int (Permutation a))

nextProdRepl :: (Ord a, Show a) => (Int, IOArray Int (Permutation a)) -> IO (Maybe (Permutation a))

updateArray :: (Integral t, Num i, Ix i, MArray a1 a m, HasInverses a) => a1 i a -> i -> i -> t -> m (Maybe 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 random Schreier-Sims algorithm, so has a small (<10^-6) chance of being incomplete. The sgs is relative to the base implied by the Ord instance.

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

rss' :: (Eq a, Num a, Ord k, Show k) => (Int, IOArray Int (Permutation k)) -> [((k, Map k (Permutation k)), [Permutation k])] -> a -> IO [((k, Map k (Permutation k)), [Permutation k])]

initLevels :: (Num a, Ord k) => [Permutation k] -> [((k, Map k a), [a1])]

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

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

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

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

Given a strong generating set gs, isMemberSGS gs is a membership test for the group