MathObj.Permutation.Table

Portability	Permutation represented by an array of the images.
Stability	provisional
Maintainer	numericprelude@henning-thielemann.de

Description

Synopsis

type T i = Array i i

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

toFunction :: Ix i => T i -> i -> i

fromPermutation :: (Ix i, C p) => p i -> T i

fromCycles :: Ix i => (i, i) -> [[i]] -> T i

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

cycle :: Ix i => [i] -> T i -> T i

inverse :: Ix i => T i -> T i

compose :: Ix i => T i -> T i -> T i

swap :: (a, b) -> (b, a)

choose :: Set a -> Maybe (a, Set a)

closure :: Ix i => [T i] -> [T i]

closureSlow :: Ix i => [T i] -> [T i]

Documentation

type T i = Array i i

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

toFunction :: Ix i => T i -> i -> i

fromPermutation :: (Ix i, C p) => p i -> T i

fromCycles :: Ix i => (i, i) -> [[i]] -> T i

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

cycle :: Ix i => [i] -> T i -> T i

inverse :: Ix i => T i -> T i

compose :: Ix i => T i -> T i -> T i

swap :: (a, b) -> (b, a)

candidate for Utility

choose :: Set a -> Maybe (a, Set a)

Extremely naïve algorithm to generate a list of all elements in a group. Should be replaced by a Schreier-Sims system if this code is ever used for anything bigger than .. say .. groups of order 512 or so.

closure :: Ix i => [T i] -> [T i]

closureSlow :: Ix i => [T i] -> [T i]

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