From e36c52e338b82695da51030927ec5f6efdb3bbc4 Mon Sep 17 00:00:00 2001
From: Jeshiba <baconp@gmail.com>
Date: Mon, 17 Jul 2017 10:21:26 -0400
Subject: cleaned up the code.

- removed useless comments
- added documentation, mainly in PitmanTransform.hs
---
 Math/Combinatorics/RootSystem.hs | 15 ++-------------
 1 file changed, 2 insertions(+), 13 deletions(-)

(limited to 'Math/Combinatorics/RootSystem.hs')

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
-- 
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