quotientsByGCD

scripts/script6.hs

@@ -1,11 +1,13 @@
 import Math.Algebra.Hspray
-import Data.Ratio
-x = lone 1 :: Spray Rational
-y = lone 2 :: Spray Rational
-z = lone 3 :: Spray Rational
-poly = ((2%3) *^ (x^**^3 ^*^ y ^*^ z) ^+^ x^**^2) ^*^ ((7%4) *^ (x ^*^ y ^*^ z))
-p1 = x^**^2 ^*^ y^**^2
-p2 = x ^+^ (y ^*^ z^**^2)
-r = bbDivision poly [p1, p2]
--- prettySpray show "x" poly
--- "(7 % 4) * x^(3, 1, 1) + (7 % 6) * x^(4, 2, 2)"
+x = qlone 1
+y = qlone 2
+
+sprayA = (x^**^3 ^-^ 4 *^ x^**^2 ^+^ 5 *^ x) ^*^ y^**^2
+sprayB = (x^**^2 ^-^ 6 *^ x) ^*^ y
+
+(qA, qB) = quotientsByGCD sprayA sprayB
+
+g = gcdSpray sprayA sprayB
+((qA', _), (qB', _)) = (sprayDivision sprayA g, sprayDivision sprayB g)
+
+

src/Math/Algebra/Hspray.hs

@@ -217,6 +217,7 @@ module Math.Algebra.Hspray
   , isPolynomialOf
   , bombieriSpray
   , collinearSprays
+  , quotientsByGCD
   ) where
 import qualified Algebra.Additive              as AlgAdd
 import qualified Algebra.Differential          as AlgDiff
@@ -1746,6 +1747,20 @@ collinearSprays spray1 spray2 = r *^ spray2 == spray1
 
 -- division stuff -------------------------------------------------------------
 
+-- | quotients of two univariate sprays by their gcd
+quotientsByGCD :: 
+  (Eq a, AlgField.C a) => Spray a -> Spray a -> (Spray a, Spray a)
+quotientsByGCD sprayA sprayB = 
+  go (sprayA, sprayB) (unitSpray, zeroSpray) (zeroSpray, unitSpray)
+  where 
+    go (oldr, r) (olds, s) (oldt, t) 
+      | isZeroSpray r = (t, s)
+      | otherwise     = 
+          go (r, remainder) (s, olds ^-^ quo ^*^ s) (t, oldt ^-^ quo ^*^ t)
+        where
+          (quo, remainder) = sprayDivision oldr r
+
+
 -- | index of the maximum of a list
 -- maxWithIndex :: Ord a => [a] -> (Int, a)
 -- maxWithIndex = maximumBy (comparing snd) . zip [0 .. ]