Fix is_squarefree for non-fields (#1511)

src/HeckeMiscPoly.jl

@@ -515,23 +515,28 @@ end
 #
 ################################################################################
 
-function is_squarefree(f::PolyElem)
-    R = coefficient_ring(f)
+function is_squarefree(f::PolyElem{<:FieldElement})
+  R = coefficient_ring(f)
 
-    if iszero(f) || degree(f) == 0
-        return true
-    end
+  if iszero(f) || degree(f) == 0
+    return true
+  end
 
-    if !is_monic(f)
-        g = divexact(f, leading_coefficient(f))
-    else
-        g = f
-    end
+  if !is_monic(f)
+    g = divexact(f, leading_coefficient(f))
+  else
+    g = f
+  end
 
-    if characteristic(R) == 0 || R isa FinField
-        return is_constant(gcd(g, derivative(g)))
-    else
-        fac = factor_squarefree(g)
-        return all(e <= 1 for (_, e) in fac)
-    end
+  if characteristic(R) == 0 || R isa FinField
+    return is_constant(gcd(g, derivative(g)))
+  else
+    fac = factor_squarefree(g)
+    return all(e <= 1 for (_, e) in fac)
+  end
+end
+
+function is_squarefree(f::PolyElem{<:RingElement})
+  fac = factor_squarefree(f)
+  return all(e <= 1 for (_, e) in fac)
 end

test/flint/fmpz_poly-test.jl

@@ -416,6 +416,11 @@ end
   g = x^30 + 73*x^28 + 2504*x^27 - 1359*x^26 - 4680*x^25 - 148311*x^24 - 159120*x^23 - 2615547*x^22 - 9732528*x^21 - 2087859*x^20 - 28418280*x^19 - 19101979*x^18 - 80724312*x^17 - 252445155*x^16 - 549998688*x^15 - 1003657917*x^14 - 2740409376*x^13 - 3199593893*x^12 - 2678402184*x^11 - 5168185293*x^10 - 2855108728*x^9 - 984488613*x^8 - 364079376*x^7 + 2870497527*x^6 + 5561735376*x^5 + 6329635407*x^4 + 3459410600*x^3 + 601207031*x^2 + 822759704*x + 294114975
   @test length(factor(g)) == 6
   @test length(factor(4 * g)) == 7
+
+  @test is_squarefree(7*x^2 + 2)
+  @test is_squarefree(2*x)
+  @test !is_squarefree(4*x)
+  @test !is_squarefree(2*x^2)
 end
 
 @testset "ZZPolyRingElem.square_root" begin