[FTheoryTools] Unify blowup of singularities among toric varieties and schemes

experimental/Schemes/CoveredProjectiveSchemes.jl

@@ -238,7 +238,7 @@ gluing_morphisms(PG::ProjectiveGluing) = (PG.f, PG.g)
     )
     C in coverings(Y) || error("covering not listed")
     for P in values(projective_patches)
-      base_scheme(P) in patches(C) || error("base scheme not found in covering")
+      any(x->x===base_scheme(P), patches(C)) || error("base scheme not found in covering")
     end
     for (U, V) in keys(gluings(C))
       (U, V) in keys(projective_gluings) || error("not all projective gluings were provided")

experimental/Schemes/Types.jl

@@ -422,12 +422,12 @@ end
   end
 end
 
-mutable struct ToricIdealSheafFromCoxRingIdeal{SpaceType, OpenType, OutputType,
-                                               RestrictionType
-                                              } <: AbsIdealSheaf{
-                                                                 SpaceType, OpenType,
-                                                                 OutputType, RestrictionType
-                                                                }
+@attributes mutable struct ToricIdealSheafFromCoxRingIdeal{SpaceType, OpenType, OutputType,
+                                                           RestrictionType
+                                                          } <: AbsIdealSheaf{
+                                                                             SpaceType, OpenType,
+                                                                             OutputType, RestrictionType
+                                                                            }
 
   X::NormalToricVariety
   I::MPolyIdeal

src/AlgebraicGeometry/Schemes/AffineSchemes/Objects/Properties.jl

@@ -88,9 +88,9 @@ end
 # (2.1) MPolyRing in first argument
 
 function is_subscheme(
-    X::AbsAffineScheme{BRT, RT},
-    Y::AbsAffineScheme{BRT, RT}
-  ) where {BRT, RT<:MPolyRing}
+    X::AbsAffineScheme{BRT, <:MPolyRing},
+    Y::AbsAffineScheme{BRT, <:MPolyRing}
+  ) where {BRT}
   return OO(X) === OO(Y)
 end
 
@@ -138,9 +138,9 @@ end
 
 
 function is_subscheme(
-    X::AbsAffineScheme{BRT, RT},
-    Y::AbsAffineScheme{BRT, RT}
-  ) where {BRT, RT<:MPolyQuoRing}
+    X::AbsAffineScheme{BRT, <:MPolyQuoRing},
+    Y::AbsAffineScheme{BRT, <:MPolyQuoRing}
+  ) where {BRT}
   R = ambient_coordinate_ring(X)
   R === ambient_coordinate_ring(Y) || return false
   return issubset(saturated_ideal(defining_ideal(Y)), saturated_ideal(defining_ideal(X)))
@@ -192,9 +192,9 @@ end
 
 
 function is_subscheme(
-    X::AbsAffineScheme{BRT, RT},
-    Y::AbsAffineScheme{BRT, RT}
-  ) where {BRT, RT<:MPolyLocRing}
+    X::AbsAffineScheme{BRT, <:MPolyLocRing},
+    Y::AbsAffineScheme{BRT, <:MPolyLocRing}
+  ) where {BRT}
   R = ambient_coordinate_ring(X)
   R === ambient_coordinate_ring(Y) || return false
   UX = inverted_set(OO(X))
@@ -257,9 +257,9 @@ end
 
 
 function is_subscheme(
-    X::AbsAffineScheme{BRT, RT},
-    Y::AbsAffineScheme{BRT, RT}
-  ) where {BRT, RT<:MPolyQuoLocRing{<:Any, <:Any, <:Any, <:Any, <:MPolyPowersOfElement}}
+    X::AbsAffineScheme{BRT, <:MPolyQuoLocRing{<:Any, <:Any, <:Any, <:Any, <:MPolyPowersOfElement}},
+    Y::AbsAffineScheme{BRT, <:MPolyQuoLocRing{<:Any, <:Any, <:Any, <:Any, <:MPolyPowersOfElement}}
+  ) where {BRT}
   R = ambient_coordinate_ring(X)
   R === ambient_coordinate_ring(Y) || return false
   UX = inverted_set(OO(X))

src/AlgebraicGeometry/ToricVarieties/NormalToricVarieties/attributes.jl

@@ -448,9 +448,17 @@ Ideal generated by
 ```
 """
 function toric_ideal(R::MPolyRing, antv::AffineNormalToricVariety)
-    C = cone(pm_object(antv).WEIGHT_CONE)
+  C = cone(pm_object(antv).WEIGHT_CONE)
+  HB = matrix(ZZ, hilbert_basis(C))
+  # If the cone is smooth, the Hilbert basis is itself a basis and the toric
+  # ideal is zero. We catch this here as 4ti2 is unhappy about some of the
+  # smooth cones.
+  if rank(HB) == nrows(HB)
+    return ideal(R, [R(0)])
+  else
     gens = pm_object(C).CONE_TORIC_IDEAL.BINOMIAL_GENERATORS
     return binomial_exponents_to_ideal(R, gens)
+  end
 end
 
 

src/AlgebraicGeometry/ToricVarieties/ToricLineBundles/attributes.jl

@@ -228,9 +228,9 @@ julia> parent(s) == cox_ring(toric_variety(l))
 true
 ```
 """
-@attr MPolyDecRingElem{QQFieldElem, QQMPolyRingElem} function generic_section(l::ToricLineBundle)
+function generic_section(l::ToricLineBundle)
   if length(basis_of_global_sections(l)) == 0
     return zero(cox_ring(toric_variety(l)))
   end
-  return sum([rand(Int) * b for b in basis_of_global_sections(l)]);
+  return sum([rand(Int) * b for b in basis_of_global_sections(l)])
 end

src/Rings/MPolyMap/MPolyQuo.jl

@@ -110,6 +110,15 @@ function _evaluate_plain(F::MPolyAnyMap{<: MPolyQuoRing}, u)
   return evaluate(lift(u), _images(F))
 end
 
+function _evaluate_plain(F::MPolyAnyMap{<:MPolyQuoRing, <:MPolyQuoRing}, u)
+  # This workaround deals with the fact that arithmetic in quotient rings is TERRIBLY slow.
+  # All the simplify calls make it unusable in this case, probably due to the fact that
+  # setting `is_reduced` flags does not pay off in such iterative procedures.
+  A = codomain(F)
+  v = evaluate(lift(u), lift.(_images(F)))
+  return simplify(A(v))
+end
+
 function _evaluate_general(F::MPolyAnyMap{<: MPolyQuoRing}, u)
   if domain(F) === codomain(F) && coefficient_map(F) === nothing
     return evaluate(map_coefficients(coefficient_map(F), lift(u),

src/Rings/MPolyMap/MPolyRing.jl

@@ -136,6 +136,13 @@ function _evaluate_plain(F::MPolyAnyMap{<: MPolyRing}, u)
   return evaluate(u, F.img_gens)
 end
 
+# See the comment in MPolyQuo.jl
+function _evaluate_plain(F::MPolyAnyMap{<:MPolyRing, <:MPolyQuoRing}, u)
+  A = codomain(F)
+  v = evaluate(lift(u), lift.(_images(F)))
+  return simplify(A(v))
+end
+
 function _evaluate_general(F::MPolyAnyMap{<: MPolyRing}, u)
   if domain(F) === codomain(F) && coefficient_map(F) === nothing
     return evaluate(map_coefficients(coefficient_map(F), u,