Safe Haskell | None |
---|---|
Language | Haskell98 |
Math.Algebra.Group.SchreierSims
- cosetRepsGx :: Ord k => [Permutation k] -> k -> Map k (Permutation k)
- schreierGeneratorsGx :: Ord t => (t, Map t (Permutation t)) -> [Permutation t] -> [Permutation t]
- 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 t => [Permutation t] -> [(t, Map t (Permutation t))]
- bsgs' :: Ord t => [t] -> [Permutation t] -> [(t, Map t (Permutation t))]
- newLevel :: Ord t => [t] -> [Permutation t] -> ([t], ((t, Map t (Permutation t)), [Permutation t]))
- newLevel' :: Ord t => t -> [Permutation t] -> ((t, Map t (Permutation t)), [Permutation t])
- ss :: Ord t => [t] -> [Permutation t] -> [((t, Map t (Permutation t)), [Permutation t])]
- 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])]
- 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 :: (Foldable t, Ord k) => t (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 t => [Permutation t] -> [Permutation t]
- reduceGensBSGS :: Ord t => [Permutation t] -> ([Permutation t], [(t, Map t (Permutation t))])
- normalClosure :: Ord t => [Permutation t] -> [Permutation t] -> [Permutation t]
- commutatorGp :: Ord t => [Permutation t] -> [Permutation t] -> [Permutation t]
- derivedSubgp :: Ord t => [Permutation t] -> [Permutation t]
Documentation
cosetRepsGx :: Ord k => [Permutation k] -> k -> Map k (Permutation k) Source #
schreierGeneratorsGx :: Ord t => (t, Map t (Permutation t)) -> [Permutation t] -> [Permutation t] 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 t => [t] -> [Permutation t] -> ([t], ((t, Map t (Permutation t)), [Permutation t])) Source #
newLevel' :: Ord t => t -> [Permutation t] -> ((t, Map t (Permutation t)), [Permutation t]) 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 #
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 :: (Foldable t, Ord k) => t (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 t => [Permutation t] -> [Permutation t] Source #
reduceGensBSGS :: Ord t => [Permutation t] -> ([Permutation t], [(t, Map t (Permutation t))]) Source #
normalClosure :: Ord t => [Permutation t] -> [Permutation t] -> [Permutation t] Source #
commutatorGp :: Ord t => [Permutation t] -> [Permutation t] -> [Permutation t] Source #
derivedSubgp :: Ord t => [Permutation t] -> [Permutation t] Source #