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authorJeshiba <baconp@gmail.com>2017-07-17 10:21:26 -0400
committerJeshiba <baconp@gmail.com>2017-07-17 10:21:26 -0400
commite36c52e338b82695da51030927ec5f6efdb3bbc4 (patch)
tree64a751a12dbfc50df97ac11c61fe6129c9992f03 /Math/Combinatorics/RootSystem.hs
parent73f5c3f45e5971f9b5c78d0a0fcac23b4561b869 (diff)
cleaned up the code.
- removed useless comments - added documentation, mainly in PitmanTransform.hs
Diffstat (limited to 'Math/Combinatorics/RootSystem.hs')
-rw-r--r--Math/Combinatorics/RootSystem.hs15
1 files changed, 2 insertions, 13 deletions
diff --git a/Math/Combinatorics/RootSystem.hs b/Math/Combinatorics/RootSystem.hs
index a1674b7..9ed7c89 100644
--- a/Math/Combinatorics/RootSystem.hs
+++ b/Math/Combinatorics/RootSystem.hs
@@ -9,15 +9,9 @@ import Prelude hiding ( (*>) )
import Data.Ratio
import Data.List
import Data.Maybe
---import qualified Data.List as L
import qualified Data.Set as S
import Math.Algebra.LinearAlgebra
---import Math.Algebra.Group.PermutationGroup hiding (elts, order, closure)
---import Math.Algebra.Group.SchreierSims as SS
---import Math.Algebra.Group.StringRewriting as SG
-
---import Math.Algebra.Field.Base (Q)-- for Q
type Q = Rational
data Type = A | B | C | D | E | F | G deriving Show
@@ -64,11 +58,9 @@ simpleSystem t n = error $ "Invalid root system of type " ++ (show t) ++ " and r
dimensionOfHostSpace :: Type -> Int -> Int
dimensionOfHostSpace t n = length $ head $ simpleSystem t n
--- ROOT SYSTEMS
--- Calculating the full root system from the fundamental roots
-- Humphreys p3
--- Weyl group element corresponding to a root
+-- Reflection corresponding to a root
-- s alpha beta = s_\alpha \beta
s :: [Q] -> [Q] -> [Q]
s alpha beta = beta <-> (dynkinIndex alpha beta) *> alpha
@@ -90,9 +82,6 @@ longestElement ss = longestElement' [] posRoots
else let alpha = (head (S.toList ys)) in
longestElement' (alpha:xs) (s alpha <$> rs)
---negateM :: Num a => [[a]] -> [[a]]
---negateM = fmap (fmap negate)
-
-- |all positive roots
positiveRoots :: SimpleSystem -> [[Q]]
@@ -207,7 +196,7 @@ allRoots ss = S.toList $ closure S.empty (S.fromList ss) where
boundary' = S.fromList [s alpha beta | alpha <- ss, beta <- S.toList boundary] S.\\ interior'
in closure interior' boundary'
-
+-- Old code in HaskellForMaths
{--
-- WEYL GROUP
-- The finite reflection group generated by the root system