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

Safe Haskell | None

Math.Algebra.Group.SchreierSims

Synopsis

- 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 -> 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, Show k) => [Permutation k] -> [Permutation k] -> Bool Source

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

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

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