Copyright	(c) Henning Thielemann 2006
Maintainer	numericprelude@henning-thielemann.de
Stability	provisional
Portability
Safe Haskell	Safe-Inferred
Language	Haskell98

MathObj.Permutation.Table

Description

Permutation represented by an array of the images.

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
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 Source #

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

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

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

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

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

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

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

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

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

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] Source #

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