[ToricVarieites] Combine test_files toric_blowups and toric_blowdowns

test/AlgebraicGeometry/ToricVarieties/toric_blowdowns.jl

@@ -1,8 +1,43 @@
 @testset "Toric blowdowns" begin
 
   P2 = projective_space(NormalToricVariety, 2)
-  bl = blow_up(P2, [1, 1])
+  BP2 = domain(blow_up(P2, 1; coordinate_name = "e"))
+
+  @testset "Basic properties of BP2" begin
+    @test is_normal(BP2) == true
+    @test is_affine(BP2) == false
+    @test is_projective(BP2) == true
+    @test is_projective_space(BP2) == false
+    @test is_smooth(BP2) == true
+    @test is_complete(BP2) == true
+    @test is_orbifold(BP2) == true
+    @test is_simplicial(BP2) == true
+    @test has_torusfactor(BP2) == false
+  end
+
+  @testset "Basic attributes of BP2" begin
+    @test betti_number(BP2, 0) == 1
+    @test betti_number(BP2, 1) == 0
+    @test betti_number(BP2, 2) == 2
+    @test betti_number(BP2, 3) == 0
+    @test betti_number(BP2, 4) == 1
+    @test euler_characteristic(BP2) == 4
+    @test torsion_free_rank(picard_group(BP2)) == 2
+  end
 
+  amb = load(joinpath(Oscar.oscardir, "test/AlgebraicGeometry/ToricVarieties", "pr3006.ntv"))
+  (x1, x2, x3, x4, x, y, z) = gens(cox_ring(amb));
+  bd1 = blow_up(amb, ideal([x, y, x1]); coordinate_name = "e1")
+  amb1 = domain(bd1)
+
+  @testset "Trigger issue of PR3006" begin
+    @test is_complete(amb1)
+    @test is_simplicial(amb1)
+  end
+
+  P2 = projective_space(NormalToricVariety, 2)
+  bl = blow_up(P2, [1, 1])
+
   @testset "Basic tests for simple toric blowdown" begin
     @test torsion_free_rank(domain(grid_morphism(bl))) == 2
     @test torsion_free_rank(codomain(grid_morphism(bl))) == 2