Math.Projects.RootSystem

Documentation

data Type

Constructors

A

B

C

D

E

F

G

basisElt :: Int -> Int -> [Q]

simpleSystem :: Type -> Int -> [[Q]]

w :: Fractional a => [a] -> [a] -> [a]

closure :: (Ord a, Fractional a) => [[a]] -> [[a]]

weylPerms :: Type -> Int -> [Permutation [Q]]

weylMatrices :: Type -> Int -> [[[Q]]]

wMx :: [Q] -> [[Q]]

cartanMatrix :: Type -> Int -> [[Q]]

setDiag :: a -> [[a]] -> [[a]]

dynkinFromCartan :: Num a => [[a]] -> [[a]]

dynkinDiagram :: Type -> Int -> [[Q]]

coxeterFromDynkin :: (Eq a1, Num a2, Num a1) => [[a1]] -> [[a2]]

coxeterMatrix :: Num a => Type -> Int -> [[a]]

fromCoxeterMatrix :: [[Int]] -> ([SGen], [([SGen], [a])])

fromCoxeterMatrix2 :: [[Int]] -> ([SGen], [([SGen], [SGen])])

coxeterPresentation :: Type -> Int -> ([SGen], [([SGen], [a])])

eltsCoxeter :: Type -> Int -> [[SGen]]

poincarePoly :: Type -> Int -> [Int]

elemMx :: Int -> Int -> Int -> [[Q]]

lieMult :: Num a => a -> a -> a

(+|+) :: [[a]] -> [[a]] -> [[a]]

(+-+) :: [a] -> [a] -> [a]

form :: Num a => Type -> Int -> [[a]]

rootSystem :: Type -> Int -> [[Q]]

numRoots :: (Num a, Eq a) => Type -> a -> a

orderWeyl :: Integral a => Type -> a -> Integer

factorial :: Integral a => a -> Integer