polynomialSubresultants unit test

CHANGELOG.md

@@ -279,4 +279,11 @@ check whether a variable is involved in a function-like object (a spray or a
 ratio of sprays), and `dropVariables`, to drop a given number of leading 
 variables in a function-like object. The `dropVariables` functions is very 
 unsafe: if a variable is dropped while it is involved, the result can be an 
-invalid function-like object.
+invalid function-like object.
+
+
+## 0.5.2.0 - 2024-05-XX
+
+* Function `polynomialSubresultants`, to compute the polynomial subresultants 
+of two sprays (while the `subresultants` function computes the principal 
+subresultants).

hspray.cabal

@@ -1,5 +1,5 @@
 name:                hspray
-version:             0.5.1.0
+version:             0.5.2.0
 synopsis:            Multivariate polynomials and fractions of multivariate polynomials.
 description:         Manipulation of multivariate polynomials over a commutative ring and fractions of multivariate polynomials over a commutative field, Gröbner bases, resultant and subresultants, and greatest common divisor. It is possible to deal with multivariate polynomials whose coefficients are fractions of multivariate polynomials, and they can be interpreted as parametric polynomials with symbolic parameters.
 homepage:            https://github.com/stla/hspray#readme

src/Math/Algebra/Hspray.hs

@@ -2446,7 +2446,8 @@ resultant var p q =
     det = detLaplace $ 
           sylvesterMatrix (sprayCoefficients p') (sprayCoefficients q')
 
--- | Subresultants of two sprays
+-- | Subresultants of two sprays (the /principal/ subresultants, while the 
+-- `polynomialSubresultants` function returns the polynomial subresultants)
 subresultants :: (Eq a, AlgRing.C a) 
   => Int     -- ^ indicator of the variable with respect to which the subresultants are desired (e.g. 1 for x)
   -> Spray a 
@@ -2533,32 +2534,14 @@ resultant' var sprayA sprayB
           h'  = exactDivisionBy (h^**^delta) (h ^*^ g'^**^delta)
           h'' = exactDivisionBy (h'^**^degp') (h' ^*^ ellq'^**^degp')
 
-{- sresMatrix :: (Eq a, AlgRing.C a) => Spray a -> Spray a -> Int -> Spray a
-sresMatrix p q i = if n == m && i == n 
-  then q
-  else detLaplace matrix
-  where
-    d = max (numberOfVariables p) (numberOfVariables q)
-    x = lone d
-    pcoeffs = reverse $ sprayCoefficients' d p
-    qcoeffs = reverse $ sprayCoefficients' d q
-    pcoeff k = if k < 0 then zeroSpray else pcoeffs !! k
-    qcoeff k = if k < 0 then zeroSpray else qcoeffs !! k
-    n = length pcoeffs - 1
-    m = length qcoeffs - 1
-    prow k = replicate k zeroSpray ++ 
-              [pcoeff j | j <- [n, n-1 .. 2*i - m + k + 2]] ++ 
-                [x^**^(m-i-1-k) ^*^ p]
-    prows = [prow k | k <- [0 .. m - i - 1]]
-    qrow k = replicate k zeroSpray ++ 
-              [qcoeff j | j <- [m, m-1 .. 2*i - n + k + 2]] ++
-                [x^**^(n-i-1-k) ^*^ q]
-    qrows = [qrow k | k <- [0 .. n - i - 1]]
-    matrix = fromLists (prows ++ qrows) 
- -}
-
+-- | Polynomial subresultants of two sprays (the `subresultants` function 
+-- computes the /principal/ subresultants)
 polynomialSubresultants :: 
-  (Eq a, AlgRing.C a) => Int -> Spray a -> Spray a -> [Spray a]
+    (Eq a, AlgRing.C a) 
+  => Int     -- ^ index of the variable with respect to which the subresultants will be computed (e.g. 2 for @y@)
+  -> Spray a 
+  -> Spray a 
+  -> [Spray a]
 polynomialSubresultants var p q 
   | var < 1 || var > d               
     = error "polynomialSubresultants: invalid variable index." 

tests/Main.hs

@@ -43,6 +43,7 @@ import           Math.Algebra.Hspray            ( Spray,
                                                   subresultants,
                                                   resultant1,
                                                   subresultants1,
+                                                  polynomialSubresultants,
                                                   sprayDivision,
                                                   gcdSpray,
                                                   QSpray',
@@ -804,9 +805,36 @@ main = defaultMain $ testGroup
         test1 = rx == rx'
         test2 = ry == ry'
         test3 = rz == rz'
-      assertBool "" (test1 && test2 && test3),
+      assertBool "" (test1 && test2 && test3)
 
-    testCase "gcdSpray - univariate example" $ do
+    , testCase "polynomialSubresultants" $ do
+      let
+        x = qlone 1
+        y = qlone 2
+        p = x^**^3^*^y^**^3 ^+^ x^**^2 ^+^ 3*^x ^+^ unitSpray
+        q = x^**^4 ^+^ 2*^x^**^3 ^-^ x^*^y^**^4
+        srs1 = map prettyQSpray (polynomialSubresultants 1 p q)
+        srs2 = map prettyQSpray (polynomialSubresultants 2 p q)
+      assertEqual "" 
+        (srs1, srs2)
+        (
+          [
+            "y^21 + 15*y^14 - 11*y^11 + y^8 + 37*y^7 + 4*y^4 - 8*y^3 - 1"
+          , "x.y^17 + 14*x.y^10 - 11*x.y^7 + x.y^4 + 39*x.y^3 + 5*x + 2*y^10 - y^7 + 14*y^3 + 2"
+          , "-5*x^2.y^3 + x^2 - x.y^10 - 7*x.y^3 + 3*x - 2*y^3 + 1"
+          , "x^3.y^3 + x^2 + 3*x + 1"
+          ],
+          [
+            "x^24 + 6*x^23 + 12*x^22 + 8*x^21 - x^11 - 12*x^10 - 58*x^9 - 144*x^8 - 195*x^7 - 144*x^6 - 58*x^5 - 12*x^4 - x^3"
+          , "x^13 + 5*x^12 + 7*x^11 + 2*x^10 + x^9.y + 6*x^8.y + 11*x^7.y + 6*x^6.y + x^5.y"
+          , "x^10 + 2*x^9 + x^6.y + 3*x^5.y + x^4.y"
+          , "x^3.y^3 + x^2 + 3*x + 1"
+          ]
+
+        )
+
+
+    , testCase "gcdSpray - univariate example" $ do
       let
         x = lone 1 :: Spray Rational
         sprayD = x^**^2 ^+^ unitSpray