fix: polynomial factorization over rational function field

- when making factors primitive, the unit needs to be adjusted using the correct power.
thofma · May 3, 2024 · 6cac7c7 · 6cac7c7
1 parent b259604
commit 6cac7c7
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diff --git a/src/EllCrv/MinimalModels.jl b/src/EllCrv/MinimalModels.jl
@@ -727,7 +727,7 @@ function _factor_rational_function_field(p)
   for (p, e) in facpn
     uu, pp = _make_primitive(p)
     D[Kt(pp)] = e
-    u = u/uu
+    u = u/uu^e
   end
   new_unit = new_unit * u
   @assert is_unit(u)
@@ -736,7 +736,7 @@ function _factor_rational_function_field(p)
   for (p, e) in facpd
     uu, pp = _make_primitive(p)
     p = Kt(pp)
-    u = u/uu
+    u = u/uu^e
     if !haskey(D, p)
       D[p] = -e
     else

diff --git a/test/EllCrv/MinimalModels.jl b/test/EllCrv/MinimalModels.jl
@@ -67,5 +67,14 @@
   E = elliptic_curve(Kt.([0, t^21, (z + 1)//216, -7//1296, (z + 3)//t]))
   EE, = integral_model(E)
   EE = Hecke.reduce_model(E)
+
+  let 
+    Qx, x = QQ["x"]
+    K, a = number_field(x^16 + 36*x^12 - 120*x^10 + 392*x^8 - 432*x^6 + 216*x^4 - 48*x^2 + 4, "x")
+    Kt, t = rational_function_field(K, "t")
+    p = ((101//168*x^15 - 1//84*x^13 + 905//42*x^11 - 6101//84*x^9 + 19627//84*x^7 - 5356//21*x^5 + 4379//42*x^3 - 67//6*x)*t^7 + (17//56*x^15 - 1//42*x^13 + 919//84*x^11 - 149//4*x^9 + 3425//28*x^7 - 5905//42*x^5 + 1627//21*x^3 - 185//14*x)*t^3)//(t^8 + (11//42*x^14 - 5//42*x^12 + 65//7*x^10 - 752//21*x^8 + 2347//21*x^6 - 3067//21*x^4 + 428//7*x^2 - 164//21)*t^4 + 29//42*x^14 + 13//42*x^12 + 524//21*x^10 - 502//7*x^8 + 4975//21*x^6 - 565//3*x^4 + 1082//21*x^2 - 5)
+    fun = Hecke._factor_rational_function_field(p)
+    @test unit(fun) * prod(q^e for (q, e) in fun) == p
+  end
 end