[FTheoryTools] Absorb convenience functions for blowups into FTheoryT…

…ools

experimental/FTheoryTools/src/auxiliary.jl

@@ -453,3 +453,112 @@ eval_poly(n::Number, R) = R(n)
 #
 # julia> eval_poly("-x1 - 3//5*x2^3 + 5 - 3", Qx)
 # -x1 - 3//5*x2^3 + 2
+
+
+
+###########################################################################
+# 10: Convenience functions for blowups
+# 10: FOR INTERNAL USE ONLY (as of Feb 1, 2025 and PR 4523)
+# 10: They are not in use (as of Feb 1, 2025 and PR 4523)
+# 10: Gauge in the future if they are truly needed!
+###########################################################################
+
+@doc raw"""
+    _martins_desired_blowup(m::NormalToricVariety, I::ToricIdealSheafFromCoxRingIdeal; coordinate_name::String = "e")
+
+Blow up the toric variety along a toric ideal sheaf.
+
+!!! warning
+    This function is type unstable. The type of the domain of the output `f` is always a subtype of `AbsCoveredScheme` (meaning that `domain(f) isa AbsCoveredScheme` is always true). 
+    Sometimes, the type of the domain will be a toric variety (meaning that `domain(f) isa NormalToricVariety` is true) if the algorithm can successfully detect this.
+    In the future, the detection algorithm may be improved so that this is successful more often.
+
+!!! warning
+    This is an internal method. It is NOT exported.
+
+# Examples
+```jldoctest
+julia> P3 = projective_space(NormalToricVariety, 3)
+Normal toric variety
+
+julia> x1, x2, x3, x4 = gens(cox_ring(P3))
+4-element Vector{MPolyDecRingElem{QQFieldElem, QQMPolyRingElem}}:
+ x1
+ x2
+ x3
+ x4
+
+julia> II = ideal_sheaf(P3, ideal([x1*x2]))
+Sheaf of ideals
+  on normal toric variety
+with restrictions
+  1: Ideal (x_1_1*x_2_1)
+  2: Ideal (x_2_2)
+  3: Ideal (x_1_3)
+  4: Ideal (x_1_4*x_2_4)
+
+julia> f = Oscar._martins_desired_blowup(P3, II);
+```
+"""
+function _martins_desired_blowup(v::NormalToricVarietyType, I::ToricIdealSheafFromCoxRingIdeal; coordinate_name::Union{String, Nothing} = nothing)
+  coords = _ideal_sheaf_to_minimal_supercone_coordinates(v, I)
+  if !isnothing(coords)
+    return blow_up_along_minimal_supercone_coordinates(v, coords; coordinate_name=coordinate_name) # Apply toric method
+  else
+    return blow_up(I) # Reroute to scheme theory
+  end
+end
+
+
+@doc raw"""
+    _martins_desired_blowup(v::NormalToricVariety, I::MPolyIdeal; coordinate_name::String = "e")
+
+Blow up the toric variety by subdividing the cone in the list
+of *all* cones of the fan of `v` which corresponds to the
+provided ideal `I`. Note that this cone need not be maximal.
+
+By default, we pick "e" as the name of the homogeneous coordinate for
+the exceptional prime divisor. As third optional argument one can supply
+a custom variable name.
+
+# Examples
+```jldoctest
+julia> P3 = projective_space(NormalToricVariety, 3)
+Normal toric variety
+
+julia> (x1,x2,x3,x4) = gens(cox_ring(P3))
+4-element Vector{MPolyDecRingElem{QQFieldElem, QQMPolyRingElem}}:
+ x1
+ x2
+ x3
+ x4
+
+julia> I = ideal([x2,x3])
+Ideal generated by
+  x2
+  x3
+
+julia> bP3 = domain(Oscar._martins_desired_blowup(P3, I))
+Normal toric variety
+
+julia> cox_ring(bP3)
+Multivariate polynomial ring in 5 variables over QQ graded by
+  x1 -> [1 0]
+  x2 -> [0 1]
+  x3 -> [0 1]
+  x4 -> [1 0]
+  e -> [1 -1]
+
+julia> I2 = ideal([x2 * x3])
+Ideal generated by
+  x2*x3
+
+julia> b2P3 = Oscar._martins_desired_blowup(P3, I2);
+
+julia> codomain(b2P3) == P3
+true
+```
+"""
+function _martins_desired_blowup(v::NormalToricVarietyType, I::MPolyIdeal; coordinate_name::Union{String, Nothing} = nothing)
+  return _martins_desired_blowup(v, ideal_sheaf(v, I))
+end