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

Safe HaskellNone

Math.Algebra.Group.SchreierSims

Synopsis

Documentation

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

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

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

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, Show t) => [Permutation t] -> [(t, Map t (Permutation t))]Source

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

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

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

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

ss' :: (Ord t, Show 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, Show k) => [(k, Map k (Permutation k))] -> Permutation k -> BoolSource

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

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

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

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

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] -> IntegerSource

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] -> BoolSource

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

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

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