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[FTheoryTools] Added additional zero section functionality #4343

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Nov 26, 2024
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[FTheoryTools] Added additional zero section functionality #4343

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2 changes: 1 addition & 1 deletion experimental/FTheoryTools/docs/src/literature.md
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Expand Up @@ -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)`.

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34 changes: 32 additions & 2 deletions experimental/FTheoryTools/src/AbstractFTheoryModels/attributes.jl
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Expand Up @@ -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))
Expand All @@ -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)

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1 change: 1 addition & 0 deletions experimental/FTheoryTools/src/AbstractFTheoryModels/methods.jl
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Expand Up @@ -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

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2 changes: 1 addition & 1 deletion experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-10-WSF.json
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Expand Up @@ -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",
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1 change: 1 addition & 0 deletions experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-10.json
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Expand Up @@ -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": [
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2 changes: 1 addition & 1 deletion experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-11-WSF.json
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Expand Up @@ -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)",
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1 change: 1 addition & 0 deletions experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-11.json
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Expand Up @@ -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"]
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2 changes: 1 addition & 1 deletion experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-12-WSF.json
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Expand Up @@ -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)",
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1 change: 1 addition & 0 deletions experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-12.json
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Expand Up @@ -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"],
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2 changes: 1 addition & 1 deletion experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-13-WSF.json
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Expand Up @@ -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"]
]
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1 change: 1 addition & 0 deletions experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-13.json
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Expand Up @@ -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"]
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2 changes: 1 addition & 1 deletion experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-14-WSF.json
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Expand Up @@ -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)",
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1 change: 1 addition & 0 deletions experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-14.json
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Expand Up @@ -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"]
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2 changes: 1 addition & 1 deletion experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-15-WSF.json
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Expand Up @@ -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"]
],
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1 change: 1 addition & 0 deletions experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-15.json
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Expand Up @@ -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"]
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2 changes: 1 addition & 1 deletion experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-16-WSF.json
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Expand Up @@ -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"]
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1 change: 1 addition & 0 deletions experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-16.json
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Expand Up @@ -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"],
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2 changes: 1 addition & 1 deletion experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-3-WSF.json
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Expand Up @@ -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))",
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1 change: 1 addition & 0 deletions experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-3.json
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Expand Up @@ -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"]
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2 changes: 1 addition & 1 deletion experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-5-WSF.json
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Expand Up @@ -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)",
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1 change: 1 addition & 0 deletions experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-5.json
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Expand Up @@ -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"],
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2 changes: 1 addition & 1 deletion experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-6-WSF.json
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Expand Up @@ -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)))",
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1 change: 1 addition & 0 deletions experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-6.json
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Expand Up @@ -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"]
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2 changes: 1 addition & 1 deletion experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-7-WSF.json
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Expand Up @@ -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)",
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1 change: 1 addition & 0 deletions experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-7.json
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Expand Up @@ -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"],
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2 changes: 1 addition & 1 deletion experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-8-WSF.json
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Expand Up @@ -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))",
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1 change: 1 addition & 0 deletions experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-8.json
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Expand Up @@ -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"]
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2 changes: 1 addition & 1 deletion experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-9-WSF.json
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Expand Up @@ -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)",
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1 change: 1 addition & 0 deletions experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-9.json
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Expand Up @@ -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"],
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1 change: 1 addition & 0 deletions experimental/FTheoryTools/src/exports.jl
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Expand Up @@ -219,3 +219,4 @@ export weighted_resolutions
export weights
export zero_section
export zero_section_class
export zero_section_index
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