Safe Haskell | None |
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Math.Algebra.Group.SchreierSims
- cosetRepsGx :: (Ord k, Show k) => [Permutation k] -> k -> Map k (Permutation k)
- schreierGeneratorsGx :: (Ord k, Show k) => (k, Map k (Permutation k)) -> [Permutation k] -> [Permutation k]
- sift :: (Ord k, Show 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 t, Show t) => [Permutation t] -> [(t, Map t (Permutation t))]
- bsgs' :: (Ord t, Show t) => [t] -> [Permutation t] -> [(t, Map t (Permutation t))]
- newLevel :: (Ord t, Show t) => [t] -> [Permutation t] -> ([t], ((t, Map t (Permutation t)), [Permutation t]))
- newLevel' :: (Ord t, Show t) => t -> [Permutation t] -> ((t, Map t (Permutation t)), [Permutation t])
- ss :: (Ord t, Show t) => [t] -> [Permutation t] -> [((t, Map t (Permutation t)), [Permutation t])]
- 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])]
- isMemberBSGS :: (Ord k, Show 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, Show k) => [Permutation k] -> [Permutation k] -> Bool
- isNormal :: (Ord k, Show k) => [Permutation k] -> [Permutation k] -> Bool
- index :: (Ord t, Ord t1, Show t, Show t1) => [Permutation t] -> [Permutation t1] -> Integer
- reduceGens :: (Ord t, Show t) => [Permutation t] -> [Permutation t]
- reduceGensBSGS :: (Ord t, Show t) => [Permutation t] -> ([Permutation t], [(t, Map t (Permutation t))])
- normalClosure :: (Ord t, Show t) => [Permutation t] -> [Permutation t] -> [Permutation t]
- commutatorGp :: (Ord t, Show t) => [Permutation t] -> [Permutation t] -> [Permutation t]
- derivedSubgp :: (Ord t, Show t) => [Permutation t] -> [Permutation t]
Documentation
cosetRepsGx :: (Ord k, Show k) => [Permutation k] -> k -> Map k (Permutation k)Source
schreierGeneratorsGx :: (Ord k, Show k) => (k, Map k (Permutation k)) -> [Permutation 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
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
reduceGens :: (Ord t, Show t) => [Permutation t] -> [Permutation t]Source
reduceGensBSGS :: (Ord t, Show t) => [Permutation t] -> ([Permutation t], [(t, Map t (Permutation t))])Source
normalClosure :: (Ord t, Show t) => [Permutation t] -> [Permutation t] -> [Permutation t]Source
commutatorGp :: (Ord t, Show t) => [Permutation t] -> [Permutation t] -> [Permutation t]Source
derivedSubgp :: (Ord t, Show t) => [Permutation t] -> [Permutation t]Source