[FTheoryTools] Code improvements as suggested by lgoettgens

experimental/FTheoryTools/src/G4Fluxes/properties.jl

@@ -122,7 +122,7 @@ G4-flux candidate
   # Compute the cohomology class corresponding to the hypersurface equation
   cy = polynomial(cohomology_class(toric_divisor_class(ambient_space(m), degree(hypersurface_equation(m)))))
 
-  n = length(gens(cox_ring(base_space(m))))
+  n = ngens(cox_ring(base_space(m)))
   c_ds = [polynomial(cohomology_class(d)) for d in torusinvariant_prime_divisors(ambient_space(m))[1:n]]
   zero_sec = zero_section_class(m)
 
@@ -243,13 +243,13 @@ G4-flux candidate
   cy = polynomial(cohomology_class(toric_divisor_class(ambient_space(m), degree(hypersurface_equation(m)))))
 
   # Identify the cohomology classes of all base divisors
-  n = length(gens(cox_ring(base_space(m))))
+  n = ngens(cox_ring(base_space(m)))
   c_ds = [polynomial(cohomology_class(d)) for d in torusinvariant_prime_divisors(ambient_space(m))[1:n]]
 
   # Identify the cohomology classes of all exceptional divisors
   gS = gens(cox_ring(ambient_space(m)))
-  exceptional_divisor_positions = findall(x -> occursin(r"^e\d+$", x), string.(gS))
-  exceptional_divisors = [torusinvariant_prime_divisors(ambient_space(m))[k] for k in exceptional_divisor_positions];
+  exceptional_divisor_positions = findall(x -> occursin(r"^e\d+$", x), string.(symbols(cox_ring(ambient_space(m)))))
+  exceptional_divisors = torusinvariant_prime_divisors(ambient_space(m))[exceptional_divisor_positions]
   c_ei = [polynomial(cohomology_class(d)) for d in exceptional_divisors]
 
   # now execute the checks if any non-Abelian gauge group factor is broken

experimental/FTheoryTools/src/G4Fluxes/special_attributes.jl

@@ -38,12 +38,12 @@ julia> length(g4_amb_list) == 172
 true
 ```
 """
-function ambient_space_models_of_g4_fluxes(m::AbstractFTheoryModel; check::Bool = true)::Vector{CohomologyClass}
+function ambient_space_models_of_g4_fluxes(m::AbstractFTheoryModel; check::Bool = true)
 
   # Entry check
   @req base_space(m) isa NormalToricVariety "Base space must be a toric variety for computation of ambient space G4 candidates"
   if has_attribute(m, :ambient_space_models_of_g4_fluxes)
-    return get_attribute(m, :ambient_space_models_of_g4_fluxes)
+    return get_attribute(m, :ambient_space_models_of_g4_fluxes)::Vector{CohomologyClass}
   end
 
   # Execute entry tests in computation of basis_of_h22. If any of these fail, no need to proceed. Hence, do this first.
@@ -104,7 +104,7 @@ function ambient_space_models_of_g4_fluxes(m::AbstractFTheoryModel; check::Bool
 
   set_attribute!(m, :ambient_space_models_of_g4_fluxes, filtered_h22_basis)
   set_attribute!(m, :ambient_space_models_of_g4_fluxes_indices, filtered_h22_basis_indices)
-  return filtered_h22_basis
+  return filtered_h22_basis::Vector{CohomologyClass}
 
 end
 
@@ -195,7 +195,7 @@ julia> passes_elementary_quantization_checks(g4)
 true
 ```
 """
-function well_quantized_ambient_space_models_of_g4_fluxes(m::AbstractFTheoryModel; check::Bool = true)::Tuple{QQMatrix, QQMatrix}
+function well_quantized_ambient_space_models_of_g4_fluxes(m::AbstractFTheoryModel; check::Bool = true)
 
   # (1) Entry checks
   @req base_space(m) isa NormalToricVariety "Computation of well-quantized G4-fluxes only supported for toric base and ambient spaces"
@@ -205,7 +205,7 @@ function well_quantized_ambient_space_models_of_g4_fluxes(m::AbstractFTheoryMode
     @req is_simplicial(ambient_space(m)) "Computation of well-quantized G4-fluxes only supported for simplicial toric ambient space"
   end
   if has_attribute(m, :well_quantized_ambient_space_models_of_g4_fluxes)
-    return get_attribute(m, :well_quantized_ambient_space_models_of_g4_fluxes)
+    return get_attribute(m, :well_quantized_ambient_space_models_of_g4_fluxes)::Tuple{QQMatrix, QQMatrix}
   end
 
 
@@ -226,19 +226,21 @@ function well_quantized_ambient_space_models_of_g4_fluxes(m::AbstractFTheoryMode
 
 
   # (3) Are intersection numbers known?
-  inter_dict = Dict{NTuple{4, Int64}, ZZRingElem}()
-  s_inter_dict = Dict{String, ZZRingElem}()
-  if has_attribute(m, :inter_dict)
-    inter_dict = get_attribute(m, :inter_dict)
-  end
-  if has_attribute(m, :s_inter_dict)
-    s_inter_dict = get_attribute(m, :s_inter_dict)
-  end
+  inter_dict = if has_attribute(m, :inter_dict)
+    get_attribute(m, :inter_dict)
+  else
+    Dict{NTuple{4, Int64}, ZZRingElem}()
+  end::Dict{NTuple{4, Int64}, ZZRingElem}
+  s_inter_dict = if has_attribute(m, :s_inter_dict)
+    get_attribute(m, :s_inter_dict)
+  else
+    Dict{String, ZZRingElem}()
+  end::Dict{String, ZZRingElem}
 
 
   # (4) Obtain critical information - this may take significant time!
   ambient_space_flux_candidates_basis = ambient_space_models_of_g4_fluxes(m, check = check)
-  ambient_space_flux_candidates_basis_indices = get_attribute(m, :ambient_space_models_of_g4_fluxes_indices)
+  ambient_space_flux_candidates_basis_indices = get_attribute(m, :ambient_space_models_of_g4_fluxes_indices)::Vector{Tuple{Int64, Int64}}
   list_of_divisor_pairs_to_be_considered = Oscar._ambient_space_divisor_pairs_to_be_considered(m)
 
 
@@ -262,7 +264,7 @@ function well_quantized_ambient_space_models_of_g4_fluxes(m::AbstractFTheoryMode
 
     # Cover all other case with generic, but potentially painfully slow methodology.
     tds = torusinvariant_prime_divisors(ambient_space(m))
-    cds = [cohomology_class(tds[i]) for i in 1:length(tds)]
+    cds = [cohomology_class(td) for td in tds]
     pt_class = cohomology_class(anticanonical_divisor_class(ambient_space(m)))
     for i in 1:length(ambient_space_flux_candidates_basis)
       condition = Vector{ZZRingElem}()
@@ -328,7 +330,7 @@ function well_quantized_ambient_space_models_of_g4_fluxes(m::AbstractFTheoryMode
 
 
   # (10) Finally, return the result
-  return res
+  return res::Tuple{QQMatrix, QQMatrix}
 
 end
 
@@ -435,7 +437,7 @@ julia> passes_verticality_checks(qsm_g4_candidate)
 true
 ```
 """
-function well_quantized_and_vertical_ambient_space_models_of_g4_fluxes(m::AbstractFTheoryModel; check::Bool = true)::Tuple{QQMatrix, QQMatrix}
+function well_quantized_and_vertical_ambient_space_models_of_g4_fluxes(m::AbstractFTheoryModel; check::Bool = true)
 
   # (1) Entry checks
   @req base_space(m) isa NormalToricVariety "Computation of well-quantized G4-fluxes only supported for toric base and ambient spaces"
@@ -445,7 +447,7 @@ function well_quantized_and_vertical_ambient_space_models_of_g4_fluxes(m::Abstra
     @req is_simplicial(ambient_space(m)) "Computation of well-quantized G4-fluxes only supported for simplicial toric ambient space"
   end
   if has_attribute(m, :well_quantized_and_vertical_ambient_space_models_of_g4_fluxes)
-    return get_attribute(m, :well_quantized_and_vertical_ambient_space_models_of_g4_fluxes)
+    return get_attribute(m, :well_quantized_and_vertical_ambient_space_models_of_g4_fluxes)::Tuple{QQMatrix, QQMatrix}
   end
 
 
@@ -466,20 +468,22 @@ function well_quantized_and_vertical_ambient_space_models_of_g4_fluxes(m::Abstra
 
 
   # (3) Are intersection numbers known?
-  inter_dict = Dict{NTuple{4, Int64}, ZZRingElem}()
-  s_inter_dict = Dict{String, ZZRingElem}()
-  if has_attribute(m, :inter_dict)
-    inter_dict = get_attribute(m, :inter_dict)
-  end
-  if has_attribute(m, :s_inter_dict)
-    s_inter_dict = get_attribute(m, :s_inter_dict)
-  end
+  inter_dict = if has_attribute(m, :inter_dict)
+    get_attribute(m, :inter_dict)
+  else
+    Dict{NTuple{4, Int64}, ZZRingElem}()
+  end::Dict{NTuple{4, Int64}, ZZRingElem}
+  s_inter_dict = if has_attribute(m, :s_inter_dict)
+    get_attribute(m, :s_inter_dict)
+  else
+    Dict{String, ZZRingElem}()
+  end::Dict{String, ZZRingElem}
 
 
   # (4) Obtain critical information - this may take significant time!
   ambient_space_flux_candidates_basis = ambient_space_models_of_g4_fluxes(m, check = check)
   list_of_base_divisor_pairs_to_be_considered = Oscar._ambient_space_base_divisor_pairs_to_be_considered(m)
-  ambient_space_flux_candidates_basis_indices = get_attribute(m, :ambient_space_models_of_g4_fluxes_indices)
+  ambient_space_flux_candidates_basis_indices = get_attribute(m, :ambient_space_models_of_g4_fluxes_indices)::Vector{Tuple{Int64, Int64}}
   list_of_divisor_pairs_to_be_considered = Oscar._ambient_space_divisor_pairs_to_be_considered(m)
 
 
@@ -515,7 +519,7 @@ function well_quantized_and_vertical_ambient_space_models_of_g4_fluxes(m::Abstra
 
     # Cover all other case with generic, but potentially painfully slow methodology.
     tds = torusinvariant_prime_divisors(ambient_space(m))
-    cds = [cohomology_class(tds[i]) for i in 1:length(tds)]
+    cds = [cohomology_class(td) for td in tds]
     pt_class = cohomology_class(anticanonical_divisor_class(ambient_space(m)))
     for i in 1:length(ambient_space_flux_candidates_basis)
 
@@ -582,7 +586,7 @@ function well_quantized_and_vertical_ambient_space_models_of_g4_fluxes(m::Abstra
 
     # Cover all other case with generic, but potentially painfully slow methodology.
     tds = torusinvariant_prime_divisors(ambient_space(m))
-    cds = [cohomology_class(tds[i]) for i in 1:length(tds)]
+    cds = [cohomology_class(td) for td in tds]
     pt_class = cohomology_class(anticanonical_divisor_class(ambient_space(m)))
     for i in 1:length(ambient_space_flux_candidates_basis)
       condition = Vector{ZZRingElem}()
@@ -637,7 +641,7 @@ function well_quantized_and_vertical_ambient_space_models_of_g4_fluxes(m::Abstra
 
 
   # (12) Finally, return the result
-  return res
+  return res::Tuple{QQMatrix, QQMatrix}
 
 end
 
@@ -752,7 +756,7 @@ julia> breaks_non_abelian_gauge_group(qsm_g4_candidate)
 false
 ```
 """
-function well_quantized_and_vertical_and_no_non_abelian_gauge_group_breaking_ambient_space_models_of_g4_fluxes(m::AbstractFTheoryModel; check::Bool = true)::Tuple{QQMatrix, QQMatrix}
+function well_quantized_and_vertical_and_no_non_abelian_gauge_group_breaking_ambient_space_models_of_g4_fluxes(m::AbstractFTheoryModel; check::Bool = true)
 
   # (1) Entry checks
   @req base_space(m) isa NormalToricVariety "Computation of well-quantized G4-fluxes only supported for toric base and ambient spaces"
@@ -762,7 +766,7 @@ function well_quantized_and_vertical_and_no_non_abelian_gauge_group_breaking_amb
     @req is_simplicial(ambient_space(m)) "Computation of well-quantized G4-fluxes only supported for simplicial toric ambient space"
   end
   if has_attribute(m, :well_quantized_and_vertical_and_no_non_abelian_gauge_group_breaking_ambient_space_models_of_g4_fluxes)
-    return get_attribute(m, :well_quantized_and_vertical_and_no_non_abelian_gauge_group_breaking_ambient_space_models_of_g4_fluxes)
+    return get_attribute(m, :well_quantized_and_vertical_and_no_non_abelian_gauge_group_breaking_ambient_space_models_of_g4_fluxes)::Tuple{QQMatrix, QQMatrix}
   end
 
 
@@ -783,25 +787,27 @@ function well_quantized_and_vertical_and_no_non_abelian_gauge_group_breaking_amb
 
 
   # (3) Are intersection numbers known?
-  inter_dict = Dict{NTuple{4, Int64}, ZZRingElem}()
-  s_inter_dict = Dict{String, ZZRingElem}()
-  if has_attribute(m, :inter_dict)
-    inter_dict = get_attribute(m, :inter_dict)
-  end
-  if has_attribute(m, :s_inter_dict)
-    s_inter_dict = get_attribute(m, :s_inter_dict)
-  end
+  inter_dict = if has_attribute(m, :inter_dict)
+    get_attribute(m, :inter_dict)
+  else
+    Dict{NTuple{4, Int64}, ZZRingElem}()
+  end::Dict{NTuple{4, Int64}, ZZRingElem}
+  s_inter_dict = if has_attribute(m, :s_inter_dict)
+    get_attribute(m, :s_inter_dict)
+  else
+    Dict{String, ZZRingElem}()
+  end::Dict{String, ZZRingElem}
 
 
   # (4) Obtain critical information - this may take significant time!
   ambient_space_flux_candidates_basis = ambient_space_models_of_g4_fluxes(m, check = check)
   list_of_base_divisor_pairs_to_be_considered = Oscar._ambient_space_base_divisor_pairs_to_be_considered(m)
-  ambient_space_flux_candidates_basis_indices = get_attribute(m, :ambient_space_models_of_g4_fluxes_indices)
+  ambient_space_flux_candidates_basis_indices = get_attribute(m, :ambient_space_models_of_g4_fluxes_indices)::Vector{Tuple{Int64, Int64}}
   list_of_divisor_pairs_to_be_considered = Oscar._ambient_space_divisor_pairs_to_be_considered(m)
 
 
   # (5) The following is fragile, but hopefully is a starting point
-  exceptional_divisor_positions = findall(x -> occursin(r"^e\d+$", x), string.(gS))
+  exceptional_divisor_positions = findall(x -> occursin(r"^e\d+$", x), string.(symbols(S)))
 
 
   # (6) Work out the relevant intersection numbers to tell if a flux is vertical
@@ -845,7 +851,7 @@ function well_quantized_and_vertical_and_no_non_abelian_gauge_group_breaking_amb
 
     # Cover all other case with generic, but potentially painfully slow methodology.
     tds = torusinvariant_prime_divisors(ambient_space(m))
-    cds = [cohomology_class(tds[i]) for i in 1:length(tds)]
+    cds = [cohomology_class(td) for td in tds]
     pt_class = cohomology_class(anticanonical_divisor_class(ambient_space(m)))
     for i in 1:length(ambient_space_flux_candidates_basis)
 
@@ -926,7 +932,7 @@ function well_quantized_and_vertical_and_no_non_abelian_gauge_group_breaking_amb
 
     # Cover all other case with generic, but potentially painfully slow methodology.
     tds = torusinvariant_prime_divisors(ambient_space(m))
-    cds = [cohomology_class(tds[i]) for i in 1:length(tds)]
+    cds = [cohomology_class(td) for td in tds]
     pt_class = cohomology_class(anticanonical_divisor_class(ambient_space(m)))
     for i in 1:length(ambient_space_flux_candidates_basis)
       condition = Vector{ZZRingElem}()
@@ -981,6 +987,6 @@ function well_quantized_and_vertical_and_no_non_abelian_gauge_group_breaking_amb
 
 
   # (12) Finally, return the result
-  return res
+  return res::Tuple{QQMatrix, QQMatrix}
 
 end

experimental/FTheoryTools/src/HypersurfaceModels/methods.jl

@@ -120,7 +120,7 @@ function tune(h::HypersurfaceModel, input_sections::Dict{String, <:Any}; complet
   # 2. Compute the new hypersurface equation
   parametrized_hypersurface_equation = hypersurface_equation_parametrization(h)
   R = parent(parametrized_hypersurface_equation)
-  vars = [string(k) for k in symbols(R)]
+  vars = string.(symbols(R))
   S = cox_ring(ambient_space(h))
   images = [k in secs_names ? eval_poly(string(explicit_secs[k]), S) : k == "Kbar" ? eval_poly("0", S) : eval_poly(k, S) for k in vars]
   map = hom(R, S, images; check=false)

experimental/FTheoryTools/src/auxiliary.jl

@@ -225,13 +225,13 @@ function _kodaira_type(id::MPolyIdeal{<:MPolyRingElem}, ords::Tuple{Int64, Int64
     d = discriminant(w)
 
     # For now, we explicitly require that the gauge ideal is principal
-    @req (length(gens(id)) == 1) "Gauge ideal is not principal"
+    @req (ngens(id) == 1) "Gauge ideal is not principal"
 
     # Over concrete bases, we randomly reduce the polynomials defining the gauge
     # divisor to only two variables so that the is_radical check is faster. This
     # could give an incorrect result (radical or not), so we actually try this
     # five times and see if we get agreement among all of the results
-    num_gens = length(gens(parent(f)))
+    num_gens = ngens(parent(f))
     gauge2s, f2s, g2s, d2s = [], [], [], []
     if rand_seed != nothing
       Random.seed!(rand_seed)