[FTheoryTools] Code improvements

Co-authored-by: Max Horn <max@quendi.de>

Author: HereAround

experimental/FTheoryTools/src/FamilyOfG4Fluxes/attributes.jl

@@ -155,7 +155,7 @@ function d3_tadpole_constraint(fgs::FamilyOfG4Fluxes; check::Bool = true)
   if arxiv_doi(m) == "10.48550/arXiv.1511.03209"
     S = cox_ring(ambient_space(m))
     gS = gens(cox_ring(ambient_space(m)))
-    linear_relations = matrix(QQ, matrix(ZZ, rays(ambient_space(m))))
+    linear_relations = matrix(QQ, rays(ambient_space(m)))
     scalings = [c.coeff for c in S.d]
     mnf = Oscar._minimal_nonfaces(ambient_space(m))
     sr_ideal_pos = [Vector{Int}(Polymake.row(mnf, i)) for i in 1:Polymake.nrows(mnf)]
@@ -173,8 +173,7 @@ function d3_tadpole_constraint(fgs::FamilyOfG4Fluxes; check::Bool = true)
   numb_rat_parameters = ncols(matrix_rational(fgs))
 
   # Create a polynomial ring with parameters ai for the integral_parameters and ri for the rational parameters
-  gens_strings = vcat([["a$(k)" for k in 1:numb_int_parameters], ["r$(k)" for k in 1:numb_rat_parameters]]...)
-  amb_ring, gens = polynomial_ring(QQ, gens_strings)
+  amb_ring, my_gens = polynomial_ring(QQ, "a#" => 1:numb_int_parameters, "r#" => 1: numb_rat_parameters)
 
   # Extract ambient space basis of G4-flux candidates used to express flux family in
   basis = ambient_space_models_of_g4_fluxes(m, check = check)
@@ -207,7 +206,8 @@ function d3_tadpole_constraint(fgs::FamilyOfG4Fluxes; check::Bool = true)
       for l1 in 1:length(basis)
         for l2 in 1:length(basis)
 
-          gen1[l1] * gen2[l2] == 0 && continue
+          val = gen1[l1] * gen2[l2]
+          is_zero(val) && continue
 
           my_tuple = Tuple(sort([basis_indices[l1]..., basis_indices[l2]...]))
 
@@ -219,13 +219,13 @@ function d3_tadpole_constraint(fgs::FamilyOfG4Fluxes; check::Bool = true)
             end        
           end
 
-          inter_number += gen1[l1] * gen2[l2] * change
+          inter_number += val * change
 
         end
       end
 
       # Update the D3-tadpole constraint polynomial
-      tadpole_constraint_polynomial += inter_number * gens[k1] * gens[k2]
+      tadpole_constraint_polynomial += inter_number * my_gens[k1] * my_gens[k2]
 
     end
   end

experimental/FTheoryTools/src/FamilyOfG4Fluxes/special_constructors.jl

@@ -8,7 +8,7 @@ properties.
 This family is modelled by the restriction of cohomology classes on the toric
 ambient space to the hypersurface in question. In the toric ambient space,
 those cohomology classes are vertical, i.e. are of the form $a \wedge b$ for
-$a,b \in H^(1,1)(X_\Sigma)$ with $X_\Sigma$. Note that this does NOT mean that 
+$a,b \in H^(1,1)(X_\Sigma)$ with $X_\Sigma$. Note that this does NOT mean that
 they are vertical on the hypersurface, which defines the actual F-theory
 geometry. We further subject this family to the consistency conditions for
 being well-quantized. Unless explicitly asked differently, it is this family of
@@ -159,7 +159,7 @@ function well_quantized_ambient_space_models_of_g4_fluxes(m::AbstractFTheoryMode
   # (2) Compute data, that is frequently used by the sophisticated intersection product below
   S = cox_ring(ambient_space(m))
   gS = gens(cox_ring(ambient_space(m)))
-  linear_relations = matrix(QQ, matrix(ZZ, rays(ambient_space(m))))
+  linear_relations = matrix(QQ, rays(ambient_space(m)))
   scalings = [c.coeff for c in S.d]
   mnf = Oscar._minimal_nonfaces(ambient_space(m))
   sr_ideal_pos = [Vector{Int}(Polymake.row(mnf, i)) for i in 1:Polymake.nrows(mnf)]
@@ -400,7 +400,7 @@ function well_quantized_and_vertical_ambient_space_models_of_g4_fluxes(m::Abstra
   # (2) Compute data, that is frequently used by the sophisticated intersection product below
   S = cox_ring(ambient_space(m))
   gS = gens(cox_ring(ambient_space(m)))
-  linear_relations = matrix(QQ, matrix(ZZ, rays(ambient_space(m))))
+  linear_relations = matrix(QQ, rays(ambient_space(m)))
   scalings = [c.coeff for c in S.d]
   mnf = Oscar._minimal_nonfaces(ambient_space(m))
   sr_ideal_pos = [Vector{Int}(Polymake.row(mnf, i)) for i in 1:Polymake.nrows(mnf)]
@@ -735,7 +735,7 @@ function well_quantized_and_vertical_and_no_non_abelian_gauge_group_breaking_amb
   # (2) Compute data, that is frequently used by the sophisticated intersection product below
   S = cox_ring(ambient_space(m))
   gS = gens(cox_ring(ambient_space(m)))
-  linear_relations = matrix(QQ, matrix(ZZ, rays(ambient_space(m))))
+  linear_relations = matrix(QQ, rays(ambient_space(m)))
   scalings = [c.coeff for c in S.d]
   mnf = Oscar._minimal_nonfaces(ambient_space(m))
   sr_ideal_pos = [Vector{Int}(Polymake.row(mnf, i)) for i in 1:Polymake.nrows(mnf)]

experimental/FTheoryTools/src/G4Fluxes/attributes.jl

@@ -105,10 +105,6 @@ function d3_tadpole_constraint(gf::G4Flux; check::Bool = true)
   cy = polynomial(cohomology_class(toric_divisor_class(ambient_space(m), degree(hypersurface_equation(m)))))
   numb = QQ(euler_characteristic(m; check = check)//24 - 1//2*integrate(cohomology_class(ambient_space(m), polynomial(cohomology_class(gf)) * polynomial(cohomology_class(gf)) * cy); check = check))
   set_attribute!(gf, :d3_tadpole_constraint, numb)
-  if numb >= 0 && is_integer(numb)
-    set_attribute!(gf, :passes_tadpole_cancellation_check, true)
-  else
-    set_attribute!(gf, :passes_tadpole_cancellation_check, false)
-  end
+  set_attribute!(gf, :passes_tadpole_cancellation_check, (numb >= 0 && is_integer(numb)))
   return numb::QQFieldElem
 end

experimental/FTheoryTools/src/G4Fluxes/properties.jl

@@ -183,10 +183,7 @@ G4-flux candidate
   @req base_space(m) isa NormalToricVariety "Tadpole cancellation checks for G4-flux currently supported only for toric base"
   @req ambient_space(m) isa NormalToricVariety "Tadpole cancellation checks for G4-flux currently supported only for toric ambient space"
   numb = d3_tadpole_constraint(g4, check = false)
-  if numb >= 0 && is_integer(numb)
-    return true
-  end
-  return false
+  return numb >= 0 && is_integer(numb)
 end