[FTheoryTools] Consolidate and improve docstring for special_flux_fam…

…ily and make various functions internal

Bug fix in attribute setter of flux instances

experimental/FTheoryTools/docs/src/g4.md

@@ -150,12 +150,5 @@ the non-abelian gauge group.
 For these families, we support the following constructor. Please note that this method may take a long
 time to execute for involved geometries $\widehat{Y}_4$.
 ```@docs
-well_quantized_ambient_space_models_of_g4_fluxes(m::AbstractFTheoryModel; check::Bool = true)
-well_quantized_and_vertical_ambient_space_models_of_g4_fluxes(m::AbstractFTheoryModel; check::Bool = true)
-well_quantized_and_vertical_and_no_non_abelian_gauge_group_breaking_ambient_space_models_of_g4_fluxes(m::AbstractFTheoryModel; check::Bool = true)
-```
-We understand that these function names are very long. For this reason, we also support the following
-convenience method:
-```@docs
 special_flux_family(m::AbstractFTheoryModel; vert::Bool = false, not_breaking::Bool = false, check::Bool = true)
 ```

experimental/FTheoryTools/src/FamilyOfG4Fluxes/methods.jl

@@ -57,13 +57,19 @@ function flux_instance(fgs::FamilyOfG4Fluxes, int_combination::ZZMatrix, rat_com
   set_attribute!(flux, :rat_combination, rat_combination)
   set_attribute!(flux, :g4_flux_family, fgs)
   if has_attribute(fgs, :is_well_quantized)
-    set_attribute!(flux, :passes_elementary_quantization_checks, is_well_quantized(fgs))
+    if is_well_quantized(fgs)
+      set_attribute!(flux, :passes_elementary_quantization_checks, true)
+    end
   end
   if has_attribute(fgs, :is_vertical)
-    set_attribute!(flux, :passes_verticality_checks, is_well_quantized(fgs))
+    if is_vertical(fgs)
+      set_attribute!(flux, :passes_verticality_checks, true)
+    end
   end
   if has_attribute(fgs, :breaks_non_abelian_gauge_group)
-    set_attribute!(flux, :breaks_non_abelian_gauge_group, breaks_non_abelian_gauge_group(fgs))
+    if !breaks_non_abelian_gauge_group(fgs)
+      set_attribute!(flux, :breaks_non_abelian_gauge_group, false)
+    end
   end
   return flux
 end