Additional zero section functionality

Added zero_section_index and fixed some previous typos.

experimental/FTheoryTools/docs/src/literature.md

@@ -101,7 +101,7 @@ following methods:
 * `has_weighted_resolution_generating_sections(m::AbstractFTheoryModel)`,
 * `has_weighted_resolution_zero_sections(m::AbstractFTheoryModel)`,
 * `has_zero_section(m::AbstractFTheoryModel)`,
-* `has_zero_section_coordinates(m::AbstractFTheoryModel)`,
+* `has_zero_section_class(m::AbstractFTheoryModel)`,
 * `has_gauge_algebra(m::AbstractFTheoryModel)`,
 * `has_global_gauge_quotients(m::AbstractFTheoryModel)`.
 

experimental/FTheoryTools/src/AbstractFTheoryModels/attributes.jl

@@ -1044,8 +1044,8 @@ end
 
 Return the zero section class of a model as a cohomology class in the toric ambient space.
 If no zero section class is known, an error is raised.
-This information is not typically available for
-Weierstrass and global Tate models, whose zero section classs are known.
+This information is always available for
+Weierstrass and global Tate models, whose zero section classes are known.
 
 ```jldoctest; setup = :(Oscar.LazyArtifacts.ensure_artifact_installed("QSMDB", Oscar.LazyArtifacts.find_artifacts_toml(Oscar.oscardir)))
 julia> qsm_model = literature_model(arxiv_id = "1903.00009", model_parameters = Dict("k" => 4))
@@ -1061,6 +1061,36 @@ function zero_section_class(m::AbstractFTheoryModel)
 end
 
 
+@doc raw"""
+    zero_section_index(m::AbstractFTheoryModel)
+
+Return the index of the generator of the Cox ring of the ambient space, whose corresponding vanishing locus defines the zero section of a model.
+If no zero section class is known, an error is raised. This attribute is always set simultaneously with zero_section_class.
+This information is always available for
+Weierstrass and global Tate models, whose zero section classes are known.
+
+```jldoctest
+julia> B3 = projective_space(NormalToricVariety, 3)
+Normal toric variety
+
+julia> Kbar = anticanonical_divisor_class(B3)
+Divisor class on a normal toric variety
+
+julia> foah15_B3 = literature_model(arxiv_id = "1408.4808", equation = "3.190", type = "hypersurface", base_space = B3, defining_classes = Dict("s7" => Kbar, "s9" => Kbar))
+Construction over concrete base may lead to singularity enhancement. Consider computing singular_loci. However, this may take time!
+
+Hypersurface model over a concrete base
+
+julia> zero_section_index(foah15_B3)
+5
+```
+"""
+function zero_section_index(m::AbstractFTheoryModel)
+  @req has_zero_section_class(m) "No zero section class stored for this model"
+  return get_attribute(m, :zero_section_index)::Int
+end
+
+
 @doc raw"""
     gauge_algebra(m::AbstractFTheoryModel)
 

experimental/FTheoryTools/src/AbstractFTheoryModels/methods.jl

@@ -647,6 +647,7 @@ function set_zero_section_class(m::AbstractFTheoryModel, desired_value::String)
   cox_gens = string.(gens(cox_ring(ambient_space(m))))
   @req desired_value in cox_gens "Specified zero section is invalid"
   index = findfirst(==(desired_value), cox_gens)
+  set_attribute!(m, :zero_section_index => index::Int)
   set_attribute!(m, :zero_section_class => cohomology_class(divs[index]))
 end
 

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-10-WSF.json

@@ -54,7 +54,7 @@
             [-1,  0,  1,  2, -1, 0, -1],
             [-1, -1, -1, -1,  0, 0,  1]
         ],
-        "zero_section": ["0", "0", "1"]
+        "zero_section": ["1", "1", "0"]
     },
     "associated_models": [
         "model1408_4808-1-WSF.json",

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-10.json

@@ -62,6 +62,7 @@
             [-1, 1, 0, 0, 0, 0]
         ],
         "hypersurface_equation": "s1*e1^2*e2^4*e3^6*u^3 + s2*e1^2*e2^3*e3^4*u^2*v + s3*e1^2*e2^2*e3^2*u*v^2 + s4*e1^2*e2*v^3 + s5*e1*e2^2*e3^3*u^2*w + s6*e1*e2*e3*u*v*w + s8*u*w^2",
+        "zero_section_class": "e3",
         "zero_section": ["s4", "1", "1", "1", "-s8", "0"]
     },
     "associated_models": [

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-11-WSF.json

@@ -55,7 +55,7 @@
             [-1,  0,  1, -1, 0, 0],
             [-1, -1, -1,  0, 0, 1]
         ],
-        "zero_section": ["0", "0", "1"],
+        "zero_section": ["1", "1", "0"],
         "generating_sections": [
             [
                 "1//12*(12*s1^2*s9^6 + s9^5*(8*s2*s5^2 - 12*s1*s6*s5) + s5^2*s6^2*s9^4)", 

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-11.json

@@ -63,6 +63,7 @@
             [ 1,  1, 0, 0, 0, 0, 0]
         ],
         "hypersurface_equation": "s1*e1^2*e2^2*e3*e4^4*u^3 + s2*e1*e2^2*e3^2*e4^2*u^2*v + s3*e2^2*e3^3*u*v^2 + s5*e1^2*e2*e4^3*u^2*w + s6*e1*e2*e3*e4*u*v*w + s9*e1*v*w^2",
+        "zero_section_class": "v",
         "zero_section": ["1", "0", "s5", "1", "1", "-s5", "1"],
         "generating_sections": [
             ["s9", "1", "1", "-s3", "1", "1", "0"]

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-12-WSF.json

@@ -55,7 +55,7 @@
             [-1,  0, -1, 0, 1, 0],
             [-1, -1,  0, 0, 0, 1]
         ],
-        "zero_section": ["0", "0", "1"],
+        "zero_section": ["1", "1", "0"],
         "generating_sections": [
             [
                 "1//12*(s6^2 - 4*s5*s7 - 4*s2*s9)", 

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-12.json

@@ -63,6 +63,7 @@
             [1, 1, 0, 0, 0, 0, 0]
         ],
         "hypersurface_equation": "s1*e1^2*e2^2*e3*e4*u^3 + s2*e1*e2^2*e3^2*u^2*v + s5*e1^2*e2*e4^2*u^2*w + s6*e1*e2*e3*e4*u*v*w + s7*e2*e3^2*v^2*w + s9*e1*e4^2*v*w^2",
+        "zero_section_class": "u",
         "zero_section": ["0", "1", "1", "s7", "-s9", "1", "1"],
         "generating_sections": [
             ["1", "s5", "1", "1", "-s9", "0", "1"],

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-13-WSF.json

@@ -55,7 +55,7 @@
             [-1,  0,  1, 0, 0],
             [-1, -1, -1, 0, 1]
         ],
-        "zero_section": ["0", "0", "1"],
+        "zero_section": ["1", "1", "0"],
         "torsion_sections": [
             ["1//12*(s6^2 - 4*s2*s9)", "0", "1"]
         ]

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-13.json

@@ -63,6 +63,7 @@
             [1,  1, 0, 0, 0, 0, 0, 0]
         ],
         "hypersurface_equation": "s1*e1^2*e2^2*e3*e5^4*u^3 + s2*e1*e2^2*e3^2*e4^2*e5^2*u^2*v + s3*e2^2*e3^3*e4^4*u*v^2 + s6*e1*e2*e3*e4*e5*u*v*w + s9*e1*v*w^2",
+        "zero_section_class": "e4",
         "zero_section": ["1", "s1", "1", "1", "1", "-s9", "0", "1"],
         "torsion_sections": [
             ["s9", "1", "1", "-s3", "1", "1", "1", "0"]

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-14-WSF.json

@@ -55,7 +55,7 @@
             [-1, -1, 0, 1, 0],
             [-1,  0, 0, 0, 1]
         ],
-        "zero_section": ["0", "0", "1"],
+        "zero_section": ["1", "1", "0"],
         "generating_sections": [
             [
                 "1//12*(12*s1^2*s9^6 - s5^2*s9^4*( - s6^2 + 4*s5*s7) - 12*s1*s5*s6*s9^5)", 

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-14.json

@@ -63,6 +63,7 @@
             [1, 1, 0, 0, 0, 0, 0, 0]
         ],
         "hypersurface_equation": "s1*e1^2*e2^2*e3*e4*u^3 + s5*e1^2*e2*e4^2*e5^2*u^2*w + s6*e1*e2*e3*e4*e5*u*v*w + s7*e2*e3^2*v^2*w + s9*e1*e4^2*e5^3*v*w^2",
+        "zero_section_class": "u",
         "zero_section": ["0", "1", "1", "s7", "-s9", "1", "1", "1"],
         "generating_sections": [
             ["1", "1", "s1", "1", "1", "1", "-s7", "0"]

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-15-WSF.json

@@ -55,7 +55,7 @@
             [0, -1, 0, 1, 0],
             [-1,  0, 0, 0, 1]
         ],
-        "zero_section": ["0", "0", "1"],
+        "zero_section": ["1", "1", "0"],
         "generating_sections": [
             ["1//12*(8*s2*s5^2*s9^5 - s5^2*s9^4*( - s6^2 + 4*s5*s7))", " -1//2*s2*s5^3*s6*s9^7", "s5*s9^2"]
         ],

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-15.json

@@ -63,6 +63,7 @@
             [1, 1, 0, 0, 0, 0, 0, 0]
         ],
         "hypersurface_equation": "s2*e1*e2^2*e3^2*u^2*v + s5*e1^2*e2*e4^2*u^2*w + s6*e1*e2*e3*e4*e5*u*v*w + s7*e2*e3^2*e5^2*v^2*w + s9*e1*e4^2*e5^2*v*w^2",
+        "zero_section_class": "u",
         "zero_section": ["0", "1", "1", "s7", "-s9", "1", "1", "1"],
         "generating_sections": [
             ["1", "1", "s2", "-s7", "1", "1", "0", "1"]

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-16-WSF.json

@@ -55,7 +55,7 @@
             [-1, 0, 1, 0],
             [-1, 0, 0, 1]
         ],
-        "zero_section": ["0", "0", "1"],
+        "zero_section": ["1", "1", "0"],
         "torsion_sections": [
             ["1//12*s6^2", "1//2*s1*s7*s9", "1"],
             ["1//12*s6^2", "-1//2*s1*s7*s9", "1"]

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-16.json

@@ -63,6 +63,7 @@
             [1, 1, 0, 0, 0, 0, 0, 0, 0]
         ],
         "hypersurface_equation": "s1*e1^2*e2^2*e3*e4*u^3 + s6*e1*e2*e3*e4*e5*e6*u*v*w + s7*e2*e3^2*e6^3*v^2*w + s9*e1*e4^2*e5^3*v*w^2",
+        "zero_section_class": "u",
         "zero_section": ["0", "1", "1", "s7", "-s9", "1", "1", "1", "1"],
         "torsion_sections": [
             ["1", "1", "s1", "1", "1", "1", "-s7", "0", "1"],

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-3-WSF.json

@@ -54,7 +54,7 @@
             [-1,  0,  1,  2, -1, 0, 1, -1, 0],
             [-1, -1, -1, -1,  0, 0, 0, 1, 1]
         ],
-        "zero_section": ["0", "0", "1"],
+        "zero_section": ["1", "1", "0"],
         "generating_sections": [
             [
                 "1//12*(12*s1^2*s9^6 + 4*(2*s2*(s5^2 - 3*s1*s8) - 3*s1*s5*s6)*s9^5 + ((s6^2 - 4*s5*s7)*s5^2 + 12*(s2^2 + 2*s1*s3)*s8^2 - 4*(4*s3*s5^2 + s2*s6*s5 - 3*s1*(s6^2 + 2*s5*s7))*s8)*s9^4 - 2*s8*( - 4*(s6*s7 + 3*s4*s8)*s5^2 + (s6^3 - 10*s3*s8*s6 + 4*s2*s7*s8)*s5 + 2*s8*(9*s1*s6*s7 + 6*s1*s4*s8 + s2*(s6^2 + 6*s3*s8)))*s9^3 + s8^2*(s6^4 - 2*s5*s7*s6^2 - 8*s5^2*s7^2 + 12*(s3^2 + 2*s2*s4)*s8^2 - 4*(9*s4*s5*s6 - s7*(5*s2*s6 + 6*s1*s7) + s3*(s6^2 + 2*s5*s7))*s8)*s9^2 - 2*s8^3*(12*s3*s4*s8^2 + 2*(s7*(s3*s6 + 4*s2*s7) - 3*s4*(s6^2 + 2*s5*s7))*s8 + s6*s7*(s6^2 - 4*s5*s7))*s9 + s8^4*((s6^2 - 4*s5*s7)*s7^2 + 4*(2*s3*s7 - 3*s4*s6)*s8*s7 + 12*s4^2*s8^2))",

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-3.json

@@ -62,6 +62,7 @@
             [1, 1, 0, 0]
         ],
         "hypersurface_equation": "s1*u^3*e1^2 + s2*u^2*v*e1^2 + s3*u*v^2*e1^2 + s4*v^3*e1^2 + s5*u^2*w*e1 + s6*u*v*w*e1 + s7*v^2*w*e1 + s8*u*w^2 + s9*v*w^2",
+        "zero_section_class": "e1",
         "zero_section": ["s9", "-s8", "1", "0"],
         "generating_sections": [
             ["-s9", "s8", "s1 * s9^3 - s4 * s8^3 + s3 * s9 * s8^2 - s2 * s9^2 * s8", "s7 * s8^2 - s6 * s9 * s8 + s5 * s9^2"]

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-5-WSF.json

@@ -54,7 +54,7 @@
             [-1,  0,  1, -1, 0, 1, -1, 0],
             [-1, -1, -1,  0, 0, 0, 1, 1]
         ],
-        "zero_section": ["0", "0", "1"],
+        "zero_section": ["1", "1", "0"],
         "generating_sections": [
             [
                 "1//12*(s6^2 - 4*s5*s7 + 8*s3*s8 - 4*s2*s9)",

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-5.json

@@ -62,6 +62,7 @@
             [1, 1, 0, 0, 0]
         ],
         "hypersurface_equation": "s1*e2^2*e1^2*u^3 + s2*e2^2*e1*u^2*v + s3*e2^2*u*v^2 + s5*e2*e1^2*u^2*w + s6*e2*e1*u*v*w + s7*e2*v^2*w + s8*e1^2*u*w^2 + s9*e1*v*w^2",
+        "zero_section_class": "e2",
         "zero_section": ["s9", "-s8", "1", "1", "0"],
         "generating_sections": [
             ["s7", "1", "-s3", "0", "1"],

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-6-WSF.json

@@ -55,7 +55,7 @@
             [-1,  0,  1,  2, -1, 0, 1, -1],
             [-1, -1, -1, -1,  0, 0, 0, 1]
         ],
-        "zero_section": ["0", "0", "1"],
+        "zero_section": ["1", "1", "0"],
         "generating_sections": [
             [
                 "1//12*(s8^4*(12*s4^2*s8^2 - s7^2*( - s6^2 + 4*s5*s7) + s7*s8*(8*s3*s7 - 12*s4*s6)))",

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-6.json

@@ -63,6 +63,7 @@
             [1,  1, 0, 0, 0]
         ],
         "hypersurface_equation": "s1*e1^2*e2^4*u^3 + s2*e1^2*e2^3*u^2*v + s3*e1^2*e2^2*u*v^2 + s4*e1^2*e2*v^3 + s5*e1*e2^2*u^2*w + s6*e1*e2*u*v*w + s7*e1*v^2*w + s8*u*w^2",
+        "zero_section_class": "e2",
         "zero_section": ["-s7", "1", "s8", "1", "0"],
         "generating_sections": [
             ["0", "1", "s4", "1", "-s7"]

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-7-WSF.json

@@ -54,7 +54,7 @@
             [0,  1, -1, 0, 1, -1, 0],
             [-1, -1,  0, 0, 0, 1, 1]
         ],
-        "zero_section": ["0", "0", "1"],
+        "zero_section": ["1", "1", "0"],
         "generating_sections": [
             [
                 "1//12*(s6^2*s7^2 - 4*s5*s7^3 + 8*s3*s7^2*s8 - 12*s3*s6*s7*s9 + 8*s2*s7^2*s9 + 12*s3^2*s9^2)", 

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-7.json

@@ -62,6 +62,7 @@
             [1, 1, 0, 0, 0, 0]
         ],
         "hypersurface_equation": "s2*e1*e3^2*u^2*v + s3*e2*e3^2*u*v^2 + s5*e1^2*e3*u^2*w + s6*e1*e2*e3*u*v*w + s7*e2^2*e3*v^2*w  + s8*e1^2*e2*u*w^2 + s9*e1*e2^2*w^2*v",
+        "zero_section_class": "u",
         "zero_section": ["0", "1", "1", "s7", "1", "-s9"],
         "generating_sections": [
             ["s7", "1", "-s3", "0", "1", "1"],

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-8-WSF.json

@@ -55,7 +55,7 @@
             [-1,  0,  1, -1, 0, 1, -1],
             [-1, -1, -1,  0, 0, 0, 1]
         ],
-        "zero_section": ["0", "0", "1"],
+        "zero_section": ["1", "1", "0"],
         "generating_sections": [
             [
                 "1//12*( - s8^4*(s7^2*( - s6^2 + 4*s5*s7) - 8*s3*s7^2*s8))", 

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-8.json

@@ -63,6 +63,7 @@
             [-1,  1, 0, 0, 0, 0]
         ],
         "hypersurface_equation": "s1*e1^2*e2^4*e3^2*u^3 + s2*e1^2*e2^3*e3*u^2*v + s3*e1^2*e2^2*u*v^2 + s5*e1*e2^2*e3^2*u^2*w + s6*e1*e2*e3*u*v*w +  s7*e1*v^2*w + s8*e3^2*u*w^2",
+        "zero_section_class": "e2",
         "zero_section": ["s7", "1", "1", "-s8", "0", "1"],
         "generating_sections": [
             ["s7", "1", "-s3", "1", "1", "0"]

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-9-WSF.json

@@ -55,7 +55,7 @@
             [-1,  0,  1, -1, 0, 1, 0],
             [-1, -1, -1,  0, 0, 0, 1]
         ],
-        "zero_section": ["0", "0", "1"],
+        "zero_section": ["1", "1", "0"],
         "generating_sections": [
             [
                 "1//12*(s6^2 - 4*s5*s7 - 4*s2*s9)", 

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-9.json

@@ -63,6 +63,7 @@
             [1, 1, 0, 0, 0, 0]
         ],
         "hypersurface_equation": "s1*e1^2*e2^2*e3*u^3 + s2*e1*e2^2*e3^2*u^2*v + s3*e2^2*e3^3*u*v^2 + s5*e1^2*e2*u^2*w + s6*e1*e2*e3*u*v*w + s7*e2*e3^2*v^2*w + s9*e1*v*w^2",
+        "zero_section_class": "u",
         "zero_section": ["0", "1", "1", "s7", "-s9", "1"],
         "generating_sections": [
             ["1", "s5", "1", "1", "-s9", "0"],

experimental/FTheoryTools/src/exports.jl

@@ -221,3 +221,4 @@ export well_quantized_ambient_space_models_of_g4_fluxes
 export well_quantized_and_vertical_ambient_space_models_of_g4_fluxes
 export zero_section
 export zero_section_class
+export zero_section_index