HaskellForMaths-0.4.9: Combinatorics, group theory, commutative algebra, non-commutative algebra
Safe HaskellNone
LanguageHaskell98

Math.Algebra.Group.CayleyGraph

Synopsis

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

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 #