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bug: git_equivalent gives false positive #21

@giannipetrella

Description

@giannipetrella

As title says:

julia>  Q = Quiver("1---------2,1-3,2---3"); d = [1, 2, 3];


julia> nu = [5, -1, -1]; theta = canonical_stability(Q, d)
3-element StaticArraysCore.SVector{3, Int64} with indices SOneTo(3):
 21
  0
 -7


julia> git_equivalent(Q, d, nu, theta)
true

But this cannot be true, as theta lies on a wall and nu does not:

julia> W = vgit_walls(Q, d; top_dimension=false); map(QuiverTools.Oscar.dim, W)
5-element Vector{Int64}:
 1
 1
 0
 1
 1

julia> map(w -> theta in w, W)
5-element Vector{Bool}:
 0
 1
 0
 0
 0

julia> map(w -> nu in w, W)
5-element Vector{Bool}:
 0
 0
 0
 0
 0

This is caused by a malfunction of Oscar.dim when applied to Oscar.intersect(line, w):

julia> map(QuiverTools.Oscar.rays, W)
5-element Vector{Oscar.SubObjectIterator{Oscar.RayVector{Nemo.QQFieldElem}}}:
 [[0, 1, -2//3]]
 [[1, 0, -1//3]]
 0-element Oscar.SubObjectIterator{Oscar.RayVector{Nemo.QQFieldElem}}
 [[1, -1//2, 0]]
 [[1, 1, -1]]

julia> # clearly W[2] is the half-line through the origin and (3, 0, -1)


julia> L = QuiverTools.Oscar.convex_hull(nu, theta); QuiverTools.Oscar.dim(L)
1


julia> map(w -> QuiverTools.Oscar.dim(intersect(L, w)), W)
5-element Vector{Int64}:
 -1
 -1
 -1
 -1
 -1

julia> # but the second intersection is not empty!

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