HaskellForMaths-0.4.9: 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 a => [a] -> [a]
- toTrans :: Ord a => [a] -> [SGen]
- toTranspositions :: (Num a, Enum a, Ord a) => Permutation a -> [SGen]
- inversions :: (Num b, Enum b, Ord b) => Permutation b -> [(b, b)]

# Documentation

data Digraph a Source #

Constructors

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

#### Instances

Instances details

Eq a => Eq (Digraph a) Source # |
Instance details Defined in Math.Algebra.Group.CayleyGraph Methods (==) :: Digraph a -> Digraph a -> Bool (/=) :: Digraph a -> Digraph a -> Bool
Ord a => Ord (Digraph a) Source # |
Instance details Defined in Math.Algebra.Group.CayleyGraph 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 # |
Instance details Defined in Math.Algebra.Group.CayleyGraph 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 a => [a] -> [a] Source #

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

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

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