Experiment to harvest yet more speed

experimental/FTheoryTools/src/AbstractFTheoryModels/attributes.jl

@@ -1135,7 +1135,7 @@ function chern_class_c1(m::AbstractFTheoryModel; check::Bool = true)
   end
 
   # Trigger potential short-cut computation of cohomology ring
-  cohomology_ring(ambient_space(m); check)
+  cohomology_ring(ambient_space(m); check = check)
 
   # Compute the cohomology class corresponding to the hypersurface equation
   cy = cohomology_class(toric_divisor_class(ambient_space(m), degree(hypersurface_equation(m))))
@@ -1183,8 +1183,11 @@ function chern_class_c2(m::AbstractFTheoryModel; check::Bool = true)
     return get_attribute(m, :chern_class_c2)
   end
 
-  # Trigger potential short-cut computation of cohomology ring
-  cohomology_ring(ambient_space(m); check)
+  # Compute elements of the cohomology ring corresponding to the torus invariant prime divisors
+  c_ds = [g.f for g in gens(cohomology_ring(ambient_space(m); check = false))]
+  R = parent(c_ds[1])
+  projection_map = hom(R, cohomology_ring(ambient_space(m); check = false), gens(R))
+  len_c_ds = length(c_ds)
 
   # Compute the cohomology class corresponding to the hypersurface equation
   cy = cohomology_class(toric_divisor_class(ambient_space(m), degree(hypersurface_equation(m))))
@@ -1193,17 +1196,15 @@ function chern_class_c2(m::AbstractFTheoryModel; check::Bool = true)
   mnf = Oscar._minimal_nonfaces(ambient_space(m))
   indices = [findall(x -> x == 1, Vector{Int}(mnf[i, :])) for i in 1:Polymake.nrows(mnf)]
 
-  # Compute c4 of the toric ambient space
-  c_ds = [polynomial(cohomology_class(d)) for d in torusinvariant_prime_divisors(ambient_space(m))]
-  len_c_ds = length(c_ds)
-  c2_t_ambient = zero(cohomology_ring(ambient_space(m)))
+  # Compute c2 of the toric ambient space
+  c2_t_ambient = zero(R)
   for i in 1:len_c_ds - 1
     for j in i+1:len_c_ds
       [i,j] in indices && continue
       c2_t_ambient = c2_t_ambient + c_ds[i] * c_ds[j]
     end
   end
-  c2_t_ambient = cohomology_class(ambient_space(m), c2_t_ambient)
+  c2_t_ambient = cohomology_class(ambient_space(m), projection_map(c2_t_ambient))
 
   # Compute and set h
   h = c2_t_ambient - cy * chern_class_c1(m; check = check)
@@ -1249,8 +1250,11 @@ function chern_class_c3(m::AbstractFTheoryModel; check::Bool = true)
     return get_attribute(m, :chern_class_c3)
   end
 
-  # Trigger potential short-cut computation of cohomology ring
-  cohomology_ring(ambient_space(m); check)
+  # Compute elements of the cohomology ring corresponding to the torus invariant prime divisors
+  c_ds = [g.f for g in gens(cohomology_ring(ambient_space(m); check = false))]
+  R = parent(c_ds[1])
+  projection_map = hom(R, cohomology_ring(ambient_space(m); check = false), gens(R))
+  len_c_ds = length(c_ds)
 
   # Compute the cohomology class corresponding to the hypersurface equation
   cy = cohomology_class(toric_divisor_class(ambient_space(m), degree(hypersurface_equation(m))))
@@ -1259,10 +1263,8 @@ function chern_class_c3(m::AbstractFTheoryModel; check::Bool = true)
   mnf = Oscar._minimal_nonfaces(ambient_space(m))
   indices = [findall(x -> x == 1, Vector{Int}(mnf[i, :])) for i in 1:Polymake.nrows(mnf)]
 
-  # Compute c4 of the toric ambient space
-  c_ds = [polynomial(cohomology_class(d)) for d in torusinvariant_prime_divisors(ambient_space(m))]
-  len_c_ds = length(c_ds)
-  c3_t_ambient = zero(cohomology_ring(ambient_space(m)))
+  # Compute c3 of the toric ambient space
+  c3_t_ambient = zero(R)
   for i in 1:len_c_ds - 2
     for j in i+1:len_c_ds - 1
       [i,j] in indices && continue
@@ -1273,7 +1275,7 @@ function chern_class_c3(m::AbstractFTheoryModel; check::Bool = true)
       end
     end
   end
-  c3_t_ambient = cohomology_class(ambient_space(m), c3_t_ambient)
+  c3_t_ambient = cohomology_class(ambient_space(m), projection_map(c3_t_ambient))
 
   # Compute and set h
   h = c3_t_ambient - cy * chern_class_c2(m; check = check)
@@ -1319,8 +1321,12 @@ function chern_class_c4(m::AbstractFTheoryModel; check::Bool = true)
     return get_attribute(m, :chern_class_c4)
   end
 
-  # Trigger potential short-cut computation of cohomology ring
-  cohomology_ring(ambient_space(m); check)
+  # Compute elements of the cohomology ring corresponding to the torus invariant prime divisors
+  q = Oscar._cohomology_ring_with_quotient_map(ambient_space(m); check = false)
+  c_ds = [g.f for g in gens(q[1])]
+  R = parent(c_ds[1])
+  projection_map = q[2]
+  len_c_ds = length(c_ds)
 
   # Compute the cohomology class corresponding to the hypersurface equation
   cy = cohomology_class(toric_divisor_class(ambient_space(m), degree(hypersurface_equation(m))))
@@ -1330,9 +1336,7 @@ function chern_class_c4(m::AbstractFTheoryModel; check::Bool = true)
   indices = [findall(x -> x == 1, Vector{Int}(mnf[i, :])) for i in 1:Polymake.nrows(mnf)]
 
   # Compute c4 of the toric ambient space
-  c_ds = [polynomial(cohomology_class(d)) for d in torusinvariant_prime_divisors(ambient_space(m))]
-  len_c_ds = length(c_ds)
-  c4_t_ambient = zero(cohomology_ring(ambient_space(m)))
+  c4_t_ambient = zero(R)
   for i in 1:len_c_ds - 3
     for j in i+1:len_c_ds - 2
       [i,j] in indices && continue
@@ -1347,7 +1351,7 @@ function chern_class_c4(m::AbstractFTheoryModel; check::Bool = true)
       end
     end
   end
-  c4_t_ambient = cohomology_class(ambient_space(m), c4_t_ambient)
+  c4_t_ambient = cohomology_class(ambient_space(m), projection_map(c4_t_ambient))
 
   # Compute and set h
   h = c4_t_ambient - cy * chern_class_c3(m; check = check)

src/AlgebraicGeometry/ToricVarieties/CohomologyClasses/special_attributes.jl

@@ -30,6 +30,19 @@ function cohomology_ring(v::NormalToricVarietyType; check::Bool = true)
 end
 
 
+function _cohomology_ring_with_quotient_map(v::NormalToricVarietyType; check::Bool = true)
+  if check
+    @req is_simplicial(v) && is_complete(v) "The cohomology ring is only supported for simplicial and complete toric varieties"
+  end
+  R, _ = graded_polynomial_ring(coefficient_ring(v), coordinate_names(v), cached = false)
+  linear_relations = ideal_of_linear_relations(R, v)
+  stanley_reisner = stanley_reisner_ideal(R, v)
+  q = quo(R, linear_relations + stanley_reisner)
+  set_attribute!(v, :cohomology_ring, q[1])
+  return q
+end
+
+
 @doc raw"""
     volume_form(v::NormalToricVariety)