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HaskellForMaths-0.4.9: Combinatorics, group theory, commutative algebra, non-commutative algebra

Safe HaskellNone
LanguageHaskell98

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 :: (Ord a, Fractional 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 a2, Num a1) => [[a1]] -> [[a2]] Source #

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

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

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

coxeterPresentation :: Type -> Int -> ([SGen], [([SGen], [a])]) 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 :: (Num a, Eq a) => Type -> a -> a Source #

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

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