HaskellForMaths-0.4.8: Combinatorics, group theory, commutative algebra, non-commutative algebra

Safe Haskell | None
Language | Haskell98

Math.Algebra.Group.Subquotients

Synopsis

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

# Documentation

isLeft :: Either t1 t -> Bool Source #

isRight :: Either t1 t -> Bool Source #

unRight :: Ord b => Permutation (Either t b) -> Permutation b Source #

restrictLeft :: Ord b => Permutation (Either b t) -> Permutation b Source #

ptStab :: (Foldable t, Show b, Ord b) => [Permutation b] -> t b -> [Permutation b] 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' :: (Show b, Ord b, Foldable t) => [Permutation b] -> t b -> ([Permutation b], [Permutation b]) Source #

minimalBlock :: Ord a => [Permutation a] -> [a] -> [[a]] 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' :: (Show b, Ord b) => [Permutation b] -> [[b]] -> ([Permutation b], [Permutation [b]]) Source #

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

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

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