HaskellForMaths-0.4.5: Combinatorics, group theory, commutative algebra, non-commutative algebra

Safe Haskell | None

Math.Algebra.Group.Subquotients

Synopsis

- isLeft :: Either t t1 -> Bool
- isRight :: Either t t1 -> Bool
- unRight :: Ord a => Permutation (Either t a) -> Permutation a
- restrictLeft :: Ord a => Permutation (Either a t) -> Permutation a
- ptStab :: (Ord a, Show a) => [Permutation a] -> [a] -> [Permutation a]
- isTransitive :: Ord t => [Permutation t] -> Bool
- transitiveConstituentHomomorphism :: (Ord a, Show a) => [Permutation a] -> [a] -> ([Permutation a], [Permutation a])
- transitiveConstituentHomomorphism' :: (Ord b, Show b) => [Permutation b] -> [b] -> ([Permutation b], [Permutation b])
- minimalBlock :: Ord t => [Permutation t] -> [t] -> [[t]]
- blockSystems :: Ord t => [Permutation t] -> [[[t]]]
- blockSystemsSGS :: Ord a => [Permutation a] -> [[[a]]]
- isPrimitive :: Ord t => [Permutation t] -> Bool
- isPrimitiveSGS :: Ord a => [Permutation a] -> Bool
- blockHomomorphism :: (Ord t, Show t) => [Permutation t] -> [[t]] -> ([Permutation t], [Permutation [t]])
- blockHomomorphism' :: (Ord b, Show b) => [Permutation b] -> [[b]] -> ([Permutation b], [Permutation [b]])
- normalClosure :: (Ord a, Show a) => [Permutation a] -> [Permutation a] -> [Permutation a]
- intersectionNormalClosure :: (Ord a, Show a) => [Permutation a] -> [Permutation a] -> [Permutation a]
- centralizerSymTrans :: (Ord a, Show a) => [Permutation a] -> [Permutation a]

# Documentation

isLeft :: Either t t1 -> Bool Source

isRight :: Either t t1 -> Bool Source

unRight :: Ord a => Permutation (Either t a) -> Permutation aSource

restrictLeft :: Ord a => Permutation (Either a t) -> Permutation aSource

ptStab :: (Ord a, Show a) => [Permutation a] -> [a] -> [Permutation a]Source

isTransitive :: Ord t => [Permutation t] -> Bool Source

transitiveConstituentHomomorphism :: (Ord a, Show a) => [Permutation a] -> [a] -> ([Permutation a], [Permutation a])Source

Given a group gs and a transitive constituent ys, return the kernel and image of the transitive constituent homomorphism. That is, suppose that gs acts on a set xs, and ys is a subset of xs on which gs acts transitively. Then the transitive constituent homomorphism is the restriction of the action of gs to an action on the ys.

transitiveConstituentHomomorphism' :: (Ord b, Show b) => [Permutation b] -> [b] -> ([Permutation b], [Permutation b])Source

minimalBlock :: Ord t => [Permutation t] -> [t] -> [[t]]Source

blockSystems :: Ord t => [Permutation t] -> [[[t]]]Source

Given a transitive group gs, find all non-trivial block systems. That is, if gs act on xs, find all the ways that the xs can be divided into blocks, such that the gs also have a permutation action on the blocks

blockSystemsSGS :: Ord a => [Permutation a] -> [[[a]]]Source

A more efficient version of blockSystems, if we have an sgs

isPrimitive :: Ord t => [Permutation t] -> Bool Source

A permutation group is primitive if it has no non-trivial block systems

isPrimitiveSGS :: Ord a => [Permutation a] -> Bool Source

blockHomomorphism :: (Ord t, Show t) => [Permutation t] -> [[t]] -> ([Permutation t], [Permutation [t]])Source

Given a transitive group gs, and a block system for gs, return the kernel and image of the block homomorphism (the homomorphism onto the action of gs on the blocks)

blockHomomorphism' :: (Ord b, Show b) => [Permutation b] -> [[b]] -> ([Permutation b], [Permutation [b]])Source

normalClosure :: (Ord a, Show a) => [Permutation a] -> [Permutation a] -> [Permutation a]Source

intersectionNormalClosure :: (Ord a, Show a) => [Permutation a] -> [Permutation a] -> [Permutation a]Source

centralizerSymTrans :: (Ord a, Show a) => [Permutation a] -> [Permutation a]Source