HaskellForMaths-0.4.8: Combinatorics, group theory, commutative algebra, non-commutative algebra

Safe Haskell | None
Language | Haskell98

Math.Algebra.Group.CayleyGraph

Synopsis

- data Digraph a = DG [a] [(a, a)]
- cayleyDigraphP :: (Num a, Ord a) => [a] -> Digraph a
- cayleyGraphP :: (Ord a, Show a) => [Permutation a] -> Graph (Permutation a)
- cayleyDigraphS :: Ord a => ([a], [([a], [a])]) -> Digraph [a]
- cayleyGraphS :: Ord a => ([a], [([a], [a])]) -> Graph [a]
- fromTranspositions :: [SGen] -> Permutation Int
- fromTrans :: [SGen] -> [Int]
- bubblesort :: Ord t => [t] -> [t]
- toTrans :: Ord a => [a] -> [SGen]
- toTranspositions :: (Enum a, Ord a, Num a) => Permutation a -> [SGen]
- inversions :: (Ord t, Enum t, Num t) => Permutation t -> [(t, t)]

# Documentation

data Digraph a Source #

Constructors

DG [a] [(a, a)] |

Instances

Eq a => Eq (Digraph a) Source # |
Methods (==) :: Digraph a -> Digraph a -> Bool # (/=) :: Digraph a -> Digraph a -> Bool #
Ord a => Ord (Digraph a) Source # |
Methods compare :: Digraph a -> Digraph a -> Ordering # (<) :: Digraph a -> Digraph a -> Bool # (<=) :: Digraph a -> Digraph a -> Bool # (>) :: Digraph a -> Digraph a -> Bool # (>=) :: Digraph a -> Digraph a -> Bool # max :: Digraph a -> Digraph a -> Digraph a # min :: Digraph a -> Digraph a -> Digraph a #
Show a => Show (Digraph a) Source # |
Methods showsPrec :: Int -> Digraph a -> ShowS # show :: Digraph a -> String # showList :: [Digraph a] -> ShowS #

cayleyDigraphP :: (Num a, Ord a) => [a] -> Digraph a Source #

cayleyGraphP :: (Ord a, Show a) => [Permutation a] -> Graph (Permutation a) Source #

The Cayley graph (undirected) on the generators (and their inverses), for a group given as permutations

cayleyDigraphS :: Ord a => ([a], [([a], [a])]) -> Digraph [a] Source #

cayleyGraphS :: Ord a => ([a], [([a], [a])]) -> Graph [a] Source #

The Cayley graph (undirected) on the generators (and their inverses), for a group given as generators and relations

fromTranspositions :: [SGen] -> Permutation Int Source #

fromTrans :: [SGen] -> [Int] Source #

bubblesort :: Ord t => [t] -> [t] Source #

toTrans :: Ord a => [a] -> [SGen] Source #

toTranspositions :: (Enum a, Ord a, Num a) => Permutation a -> [SGen] Source #

inversions :: (Ord t, Enum t, Num t) => Permutation t -> [(t, t)] Source #