HaskellForMaths-0.4.8: Combinatorics, group theory, commutative algebra, non-commutative algebra

Safe HaskellNone
LanguageHaskell98

Math.Algebra.Group.SchreierSims

Synopsis

Documentation

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

sift :: 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 :: Ord t => [Permutation t] -> [(t, Map t (Permutation t))] Source

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

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

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

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

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

isMemberBSGS :: 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 :: (Ord k, Foldable t) => t (Permutation k) -> [Permutation k] -> Bool Source

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

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