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

Safe Haskell | None
Language | Haskell98

Math.Projects.RootSystem

# Documentation

data Type Source #

Constructors

A |
B |
C |
D |
E |
F |
G |

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

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

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

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

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

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

wMx :: [Q] -> [[Q]] Source #

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

setDiag :: a -> [[a]] -> [[a]] Source #

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

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

coxeterFromDynkin :: (Eq a1, Num a1, Num a) => [[a1]] -> [[a]] Source #

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

fromCoxeterMatrix :: [[Int]] -> ([SGen], [([SGen], [t])]) Source #

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

coxeterPresentation :: Type -> Int -> ([SGen], [([SGen], [t])]) Source #

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

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

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

lieMult :: Num a => a -> a -> a Source #

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

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

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

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

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

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

factorial :: Integral a => a -> Integer Source #