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

Safe Haskell | None

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 a, Num a1) => [[a1]] -> [[a]]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 -> aSource

(+|+) :: [[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 -> aSource

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

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