Fixes small_generating_set, mininimal_primes over a number field

src/Rings/mpoly-ideals.jl

@@ -1203,17 +1203,27 @@ function minimal_primes(
 
   # This will in many cases lead to an easy simplification of the problem
   if factor_generators
-    J = typeof(I)[ideal(R, elem_type(R)[])]
+    J = [ideal(R, gens(I))] # A copy of I as initialization
     for g in gens(I)
       K = typeof(I)[]
       is_zero(g) && continue
       for (b, k) in factor(g)
+        # Split the already collected components with b
         for j in J
           push!(K, j + ideal(R, b))
         end
       end
       J = K
     end
+
+    unique_comp = typeof(I)[]
+    for q in J
+      is_one(q) && continue
+      q in unique_comp && continue
+      push!(unique_comp, q)
+    end
+    J = unique_comp
+
     # unique! seems to fail here. We have to do it manually.
     pre_result = filter!(!is_one, vcat([minimal_primes(j; algorithm, factor_generators=false) for j in J]...))
     result = typeof(I)[]
@@ -2110,7 +2120,8 @@ function small_generating_set(
   computed_gb = IdealGens(ring, sing_gb, true)
   if !haskey(I.gb,computed_gb.ord)
   # if not yet present, store gb for later use
-    I.gb[computed_gb.ord] = computed_gb
+    I.gb[computed_gb.ord]      = computed_gb
+    I.gb[computed_gb.ord].isGB = true
   end
 
   # we do not have a notion of minimal generating set in this context!
@@ -2328,4 +2339,3 @@ end
 function hash(I::Ideal, c::UInt)
   return hash(base_ring(I), c)
 end
-

test/Rings/mpoly.jl

@@ -159,7 +159,6 @@ end
   l = minimal_primes(i, algorithm=:charSets)
   @test length(l) == 2
   @test l[1] == i1 && l[2] == i2 || l[1] == i2 && l[2] == i1
-
   R, (a, b, c, d) = polynomial_ring(ZZ, [:a, :b, :c, :d])
   i = ideal(R, [R(9), (a+3)*(b+3)])
   i1 = ideal(R, [R(3), a])
@@ -232,6 +231,19 @@ end
   R, (x, y) = polynomial_ring(QQ, [:x, :y])
   I = ideal(R, [one(R)])
   @test is_prime(I) == false
+
+  J = ideal(R, [x*(x-1), y*(y-1), x*y])
+  l = minimal_primes(J)
+  @test length(l) == 3
+
+  QQt, t = QQ[:t]
+  kk, a = extension_field(t^2 + 1)
+
+  R, (x, y) = kk[:x, :y]
+  J = ideal(R, [x^2 + 1, y^2 + 1, (x - a)*(y - a)])
+  l = minimal_primes(J)
+  @test length(l) == 3
+
 end
 
 @testset "Groebner" begin
@@ -601,4 +613,3 @@ end
   I = ideal(P, elem_type(P)[])
   @test !radical_membership(x, I)
 end
-