MathObj.Permutation.CycleList

Portability	requires multi-parameter type classes
Stability	provisional
Maintainer	mik@math.uni-jena.de

Description

Permutation of Integers represented by cycles.

Synopsis

type Cycle i = [i]

type T i = [Cycle i]

fromFunction :: Ix i => (i, i) -> (i -> i) -> T i

cycleRightAction :: Eq i => i -> Cycle i -> i

cycleLeftAction :: Eq i => Cycle i -> i -> i

cycleAction :: Eq i => [i] -> i -> i

cycleOrbit :: Ord i => Cycle i -> i -> [i]

(*>) :: Eq i => T i -> i -> i

cyclesOrbit :: Ord i => T i -> i -> [i]

orbit :: Ord i => (i -> i) -> i -> [i]

takeUntilRepetition :: Ord a => [a] -> [a]

takeUntilRepetitionSlow :: Eq a => [a] -> [a]

choose :: Set a -> Maybe a

keepEssentials :: T i -> T i

isEssential :: Cycle i -> Bool

inverse :: T i -> T i

Documentation

type Cycle i = [i]

Source

type T i = [Cycle i]

Source

fromFunction :: Ix i => (i, i) -> (i -> i) -> T i

Source

cycleRightAction :: Eq i => i -> Cycle i -> i

Source

cycleLeftAction :: Eq i => Cycle i -> i -> i

Source

cycleAction :: Eq i => [i] -> i -> i

Source

cycleOrbit :: Ord i => Cycle i -> i -> [i]

Source

(*>) :: Eq i => T i -> i -> i

Source

Right (left?) group action on the Integers. Close to, but not the same as the module action in Algebra.Module.

cyclesOrbit :: Ord i => T i -> i -> [i]

Source

orbit :: Ord i => (i -> i) -> i -> [i]

Source

takeUntilRepetition :: Ord a => [a] -> [a]

Source

candidates for Utility ?

takeUntilRepetitionSlow :: Eq a => [a] -> [a]

Source

choose :: Set a -> Maybe a

Source

keepEssentials :: T i -> T i

Source

isEssential :: Cycle i -> Bool

Source

inverse :: T i -> T i

Source

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