Comparing ideal sheaves

[lkastner]

Followup on #4348 , @benlorenz remarked that there sometimes was a failure in /home/runner/work/Oscar.jl/Oscar.jl/test/AlgebraicGeometry/ToricVarieties/toric_blowups.jl:76, see #4353 (comment)

The issue can be reproduced by manually defining P2:

julia> RS = [1 0; -1 -1; 0 1]
3×2 Matrix{Int64}:
  1   0
 -1  -1
  0   1

julia> IM = incidence_matrix([[1,2],[2,3],[1,3]])
3×3 IncidenceMatrix
[1, 2]
[2, 3]
[1, 3]


julia> F = polyhedral_fan(IM, RS; non_redundant=true)
Polyhedral fan in ambient dimension 2

julia> P2 = normal_toric_variety(F)
Normal toric variety

julia> S = cox_ring(P2)
Multivariate polynomial ring in 3 variables over QQ graded by
  x1 -> [1]
  x2 -> [1]
  x3 -> [1]

julia> I = ideal(S, [S[1], S[2]])
Ideal generated by
  x1
  x2

julia> bl2 = blow_up(P2, I)
Toric blowup morphism

julia> II = IdealSheaf(P2, I)
Sheaf of ideals
  on normal, smooth toric variety
with restrictions
  1: Ideal (x_1_1, x_2_1)
  2: Ideal (1, x_1_2)
  3: Ideal (x_1_3, 1)

julia> bl = blow_up(P2, [1, 1])
Toric blowup morphism

julia> II == center_unnormalized(bl) # should be true according to test file
false

So there seems to be something else going on.

Manually executing the code for == gives:

julia> I = II
Sheaf of ideals
  on normal, smooth toric variety
with restrictions
  1: Ideal (x_1_1, 1)
  2: Ideal (1, x_1_2)
  3: Ideal (x_1_3, x_2_3)

julia> J = center_unnormalized(bl)
Sheaf of ideals
  on normal, smooth toric variety
with restrictions
  1: Ideal (x_2_1, x_1_1)
  2: Ideal (1)
  3: Ideal (1)

julia> X = space(I)
Normal, smooth toric variety

julia> X === space(J)
true

julia> Oscar.basic_patches(default_covering(X))
3-element Vector{AffineNormalToricVariety}:
 Normal toric variety
 Normal toric variety
 Normal toric variety

julia> for U in Oscar.basic_patches(default_covering(X))
       println(I(U))
       end
Ideal (x_1_1, 1)
Ideal (1, x_1_2)
Ideal (x_1_3, x_2_3)

julia> for U in Oscar.basic_patches(default_covering(X))
       println(J(U))
       end
Ideal (x_2_1, x_1_1)
Ideal (1)
Ideal (1)

julia> 

@HereAround

[lkastner]

Nvm, figured out how to fix this in #4356