On Sat, Jun 16, 2012 at 11:17 PM, Daniel Hlynskyi
Hello. Simplification rules are quite simple:
normalize (Sum [a]) = normalize a normalize (Sum xs) | (I 0) `elem` xs = map nomalize . Sum $ filter (/= I 0) xs | otherwise = map normalize xs normalize (Prod xs) | (I 0) `elem` xs = I 0 normalize (Prod xs) | (I 1) `elem` xs = map nomalize . Prod $ filter (/= I 1) xs | otherwise = map normalize xs normalize (Pow a (I 0)) = I 1 normalize (Pow a (I 1)) = normalize a
and so on. But rules like theese cannot simplify some expressions, for example, `Prod [Pow V (I 0), Pow V (I 1)] `.
It's because you're doing it in the wrong direction : in a tree always normalize leaves before you try to normalize branches. normalize (Sum xs) = case sort . filter (/= I 0) . map normalize $ xs of [] -> I 0 [a] -> a ys -> sumPrefix ys where sumPrefix (I n : I m : ys) = sumPrefix $ I (n+m) : ys sumPrefix ys = ys See how I normalize the elements of xs before anything else. Note that this isn't quite the right way to represent a poly if you want to get to a canonical representation. -- Jedaï