FTheoryTools: Extend CI tests (#4784)

Author: HereAround

experimental/FTheoryTools/test/QSMs.jl

@@ -29,3 +29,41 @@ g4_exp = flux_instance(fg_not_breaking, [3], [])
   @test euler_characteristic(qsm_model) == integrate((3 * Kbar * (4 * c2_B + 5 * Kbar^2)) * V * cy)
   @test d3_tadpole_constraint(g4_exp) == 12 + 5//8 * Kbar3 - 45//(2 * Kbar3)
 end
+
+@testset "Advanced intersection theory and QSM-fluxes" begin
+  qsm_model = literature_model(arxiv_id = "1903.00009", model_parameters = Dict("k" => 4))
+  h22_converter_dict = converter_dict_h22_ambient(qsm_model, check = false)
+  coh_ring = cohomology_ring(ambient_space(qsm_model), check = false)
+  coh_ring_gens = gens(coh_ring)
+  for (key, value) in h22_converter_dict
+    obj1 = coh_ring_gens[key[1]] * coh_ring_gens[key[2]]
+    obj2 = sum(value[k][1] * coh_ring_gens[value[k][2][1]] * coh_ring_gens[value[k][2][2]] for k in 1:length(value))
+    @test obj1 == obj2
+  end
+  qsm_g4_flux = qsm_flux(qsm_model)
+  h22_basis = basis_of_h22_hypersurface_indices(qsm_model, check = false)
+  flux_poly_str = string(polynomial(cohomology_class(qsm_g4_flux)))
+  ring = base_ring(parent(polynomial(cohomology_class(qsm_g4_flux))))
+  flux_poly = Oscar.eval_poly(flux_poly_str, ring)
+  coeffs = collect(coefficients(flux_poly))
+  raw_exps = collect(exponents(flux_poly))
+  massaged_exps = [length(pos) == 1 ? (pos[1], pos[1]) : Tuple(sort(pos)) for pos in (findall(!=(0), mon) for mon in raw_exps)]
+  flux_vector = fill(QQ(0), length(h22_basis))
+  for (i, exp_pair) in enumerate(massaged_exps)
+    idx = findfirst(==(exp_pair), h22_basis)
+    flux_vector[idx] = coeffs[i]
+  end
+  flux_vector = transpose(matrix(QQ, [flux_vector]))
+  fg = special_flux_family(qsm_model; not_breaking = true, check = false, algorithm = "special")
+  @test ncols(matrix_integral(fg)) == 1
+  @test nrows(matrix_integral(fg)) == nrows(matrix_rational(fg))
+  @test unique(offset(fg)) == [0]
+  M1 = matrix_integral(fg)
+  M2 = matrix_rational(fg)
+  large_M = hcat(M1, M2)
+  @test rank(large_M) == minimum(size(large_M))
+  solution = solve(large_M, flux_vector, side = :right)
+  @test is_integer(solution[1])
+  reconstructed_flux = flux_instance(fg, matrix(ZZ, [[solution[1]]]), solution[2:end,:])
+  @test cohomology_class(qsm_g4_flux) == cohomology_class(reconstructed_flux)
+end