HaskellForMaths-0.4.5: Combinatorics, group theory, commutative algebra, non-commutative algebra

Safe HaskellNone
LanguageHaskell98

Math.Algebra.Group.SchreierSims

Synopsis

Documentation

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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] Source

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 Source

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

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

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

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

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