Safe Haskell | None |
---|---|

Language | Haskell98 |

- cosetRepsGx :: Ord k => [Permutation k] -> k -> Map k (Permutation k)
- schreierGeneratorsGx :: Ord k => (k, Map k (Permutation k)) -> [Permutation k] -> [Permutation k]
- sift :: Ord 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]
- bsgs :: Ord k => [Permutation k] -> [(k, Map k (Permutation k))]
- bsgs' :: Ord k => [k] -> [Permutation k] -> [(k, Map k (Permutation k))]
- newLevel :: Ord a => [a] -> [Permutation a] -> ([a], ((a, Map a (Permutation a)), [Permutation a]))
- newLevel' :: Ord t => t -> [Permutation t] -> ((t, Map t (Permutation t)), [Permutation t])
- ss :: Ord k => [k] -> [Permutation k] -> [((k, Map k (Permutation k)), [Permutation k])]
- ss' :: Ord 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 => [(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
- elts :: (Ord t, Show t) => [Permutation t] -> [Permutation t]
- order :: (Ord t, Show t) => [Permutation t] -> Integer
- isSubgp :: Ord k => [Permutation k] -> [Permutation k] -> Bool
- isNormal :: Ord k => [Permutation k] -> [Permutation k] -> Bool
- index :: (Show t1, Show t, Ord t1, Ord t) => [Permutation t] -> [Permutation t1] -> Integer
- reduceGens :: Ord k => [Permutation k] -> [Permutation k]
- reduceGensBSGS :: Ord k => [Permutation k] -> ([Permutation k], [(k, Map k (Permutation k))])
- normalClosure :: Ord k => [Permutation k] -> [Permutation k] -> [Permutation k]
- commutatorGp :: Ord k => [Permutation k] -> [Permutation k] -> [Permutation k]
- derivedSubgp :: Ord k => [Permutation k] -> [Permutation k]

# Documentation

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

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

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

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

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

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

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

isNormal :: Ord k => [Permutation k] -> [Permutation k] -> Bool Source

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

reduceGens :: Ord k => [Permutation k] -> [Permutation k] Source

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

normalClosure :: Ord k => [Permutation k] -> [Permutation k] -> [Permutation k] Source

commutatorGp :: Ord k => [Permutation k] -> [Permutation k] -> [Permutation k] Source

derivedSubgp :: Ord k => [Permutation k] -> [Permutation k] Source