Merge branch 'master' into mh/gap-4.13

Project.toml

@@ -25,22 +25,22 @@ UUIDs = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"
 cohomCalg_jll = "5558cf25-a90e-53b0-b813-cadaa3ae7ade"
 
 [compat]
-AbstractAlgebra = "0.40.8"
+AbstractAlgebra = "0.41.3"
 AlgebraicSolving = "0.4.11"
 Distributed = "1.6"
 DocStringExtensions = "0.8, 0.9"
 GAP = "0.11.0"
-Hecke = "0.30.11"
+Hecke = "0.31.3"
 JSON = "^0.20, ^0.21"
 JSON3 = "1.13.2"
 LazyArtifacts = "1.6"
-Nemo = "0.43.3"
+Nemo = "0.44.0"
 Pkg = "1.6"
 Polymake = "0.11.14"
 Random = "1.6"
 RandomExtensions = "0.4.3"
 Serialization = "1.6"
-Singular = "0.22.4"
+Singular = "0.23.0"
 TOPCOM_jll = "0.17.8"
 UUIDs = "1.6"
 cohomCalg_jll = "0.32.0"

docs/src/CommutativeAlgebra/rings.md

@@ -405,7 +405,7 @@ julia> R, (x, y) = polynomial_ring(QQ, ["x", "y"])
 (Multivariate polynomial ring in 2 variables over QQ, QQMPolyRingElem[x, y])
 
 julia> B = MPolyBuildCtx(R)
-Builder for an element of Multivariate polynomial ring in 2 variables over QQ
+Builder for an element of multivariate polynomial ring
 
 julia> for i = 1:5 push_term!(B, QQ(i), [i, i-1]) end
 

docs/src/NumberTheory/galois.md

@@ -96,10 +96,10 @@ julia> F, a = function_field(x^6 + 108*t^2 + 108*t + 27);
 
 julia> subfields(F)
 4-element Vector{Any}:
- (Function Field over Rational field with defining polynomial a^3 + 54*t + 27, (1//12*_a^4 + (3//2*t + 3//4)*_a)//(t + 1//2))
- (Function Field over Rational field with defining polynomial a^2 + 108*t^2 + 108*t + 27, _a^3)
- (Function Field over Rational field with defining polynomial a^3 - 108*t^2 - 108*t - 27, -_a^2)
- (Function Field over Rational field with defining polynomial a^3 - 54*t - 27, (-1//12*_a^4 + (3//2*t + 3//4)*_a)//(t + 1//2))
+ (Function Field over QQ with defining polynomial a^3 + 54*t + 27, (1//12*_a^4 + (3//2*t + 3//4)*_a)//(t + 1//2))
+ (Function Field over QQ with defining polynomial a^2 + 108*t^2 + 108*t + 27, _a^3)
+ (Function Field over QQ with defining polynomial a^3 - 108*t^2 - 108*t - 27, -_a^2)
+ (Function Field over QQ with defining polynomial a^3 - 54*t - 27, (-1//12*_a^4 + (3//2*t + 3//4)*_a)//(t + 1//2))
 
 julia> galois_group(F)
 (Permutation group of degree 6 and order 6, Galois context for s^6 + 108*t^2 + 540*t + 675)

experimental/FTheoryTools/docs/src/hypersurface.md

@@ -76,7 +76,7 @@ Completeness is an expensive check. Therefore, we provide an optional argument w
  demonstrate this:
 ```@docs
 hypersurface_model(base::NormalToricVariety; completeness_check::Bool = true)
-hypersurface_model(base::NormalToricVariety, fiber_ambient_space::NormalToricVariety, D1::ToricDivisorClass, D2::ToricDivisorClass; completeness_check::Bool = true)
+hypersurface_model(base::NormalToricVariety, fiber_ambient_space::NormalToricVariety, fiber_twist_divisor_classes::Vector{ToricDivisorClass}; completeness_check::Bool = true)
 ```
 
 ### A (covered) scheme as base space
@@ -88,8 +88,9 @@ This functionality does not yet exist.
 This method constructs a hypersurface model over a base space, where
 this base space is not (fully) specified. We currently provide the following constructors:
 ```@docs
-hypersurface_model(auxiliary_base_vars::Vector{String}, auxiliary_base_grading::Matrix{Int64}, d::Int, fiber_ambient_space::NormalToricVariety, D1::Vector{Int64}, D2::Vector{Int64}, p::MPolyRingElem)
+hypersurface_model(auxiliary_base_vars::Vector{String}, auxiliary_base_grading::Matrix{Int64}, d::Int, fiber_ambient_space::NormalToricVariety, fiber_twist_divisor_classes::Vector{Vector{Int64}}, p::MPolyRingElem)
 ```
+For convenience, the fiber_twist_divisor_classes can also be provided as `ZZMatrix`.
 
 ### Standard constructions
 

experimental/FTheoryTools/src/HypersurfaceModels/constructors.jl

@@ -23,12 +23,13 @@ function hypersurface_model(base::NormalToricVariety; completeness_check::Bool =
   set_coordinate_names(fiber_ambient_space, ["x", "y", "z"])
   D1 = 2 * anticanonical_divisor_class(base)
   D2 = 3 * anticanonical_divisor_class(base)
-  return hypersurface_model(base, fiber_ambient_space, D1, D2; completeness_check = completeness_check)
+  D3 = trivial_divisor_class(base)
+  return hypersurface_model(base, fiber_ambient_space, [D1, D2, D3]; completeness_check = completeness_check)
 end
 
 
 @doc raw"""
-    hypersurface_model(base::NormalToricVariety, fiber_ambient_space::NormalToricVariety, D1::ToricDivisorClass, D2::ToricDivisorClass; completeness_check::Bool = true)
+    hypersurface_model(base::NormalToricVariety, fiber_ambient_space::NormalToricVariety, fiber_twist_divisor_classes::Vector{ToricDivisorClass}; completeness_check::Bool = true)
 
 Construct a hypersurface model, for which the user can specify a fiber ambient space
 as well as divisor classes of the toric base space, in which the first two homogeneous
@@ -50,11 +51,14 @@ Divisor class on a normal toric variety
 julia> D2 = 3 * anticanonical_divisor_class(base)
 Divisor class on a normal toric variety
 
-julia> hypersurface_model(base, fiber_ambient_space, D1, D2; completeness_check = false)
+julia> D3 = trivial_divisor_class(base)
+Divisor class on a normal toric variety
+
+julia> hypersurface_model(base, fiber_ambient_space, [D1, D2, D3]; completeness_check = false)
 Hypersurface model over a concrete base
 ```
 """
-function hypersurface_model(base::NormalToricVariety, fiber_ambient_space::NormalToricVariety, D1::ToricDivisorClass, D2::ToricDivisorClass; completeness_check::Bool = true)
+function hypersurface_model(base::NormalToricVariety, fiber_ambient_space::NormalToricVariety, fiber_twist_divisor_classes::Vector{ToricDivisorClass}; completeness_check::Bool = true)
   # Consistency checks
   gens_base_names = [string(g) for g in gens(cox_ring(base))]
   gens_fiber_names = [string(g) for g in gens(cox_ring(fiber_ambient_space))]
@@ -66,8 +70,8 @@ function hypersurface_model(base::NormalToricVariety, fiber_ambient_space::Norma
   end
 
   # Compute an ambient space
-  ambient_space = _ambient_space(base, fiber_ambient_space, D1, D2)
-  
+  ambient_space = _ambient_space(base, fiber_ambient_space, fiber_twist_divisor_classes)
+
   # Construct the model
   hypersurface_equation = generic_section(anticanonical_bundle(ambient_space))
   explicit_model_sections = Dict{String, MPolyRingElem}()
@@ -95,19 +99,18 @@ end
 
 
 @doc raw"""
-    hypersurface_model(auxiliary_base_vars::Vector{String}, auxiliary_base_grading::Matrix{Int64}, d::Int, fiber_ambient_space::NormalToricVariety, D1::Vector{Int64}, D2::Vector{Int64}, p::MPolyRingElem)
+    hypersurface_model(auxiliary_base_vars::Vector{String}, auxiliary_base_grading::Matrix{Int64}, d::Int, fiber_ambient_space::NormalToricVariety, fiber_twist_divisor_classes::Vector{Vector{Int64}}, p::MPolyRingElem)
 
 This method constructs a hypersurface model over a base space that is not
 fully specified. In the background, we construct a family of spaces to represent
 the base space. This method requires the following information:
 1. The names of the homogeneous coordinates of the coordinate ring of the generic member
 of the family of bsae spaces.
 2. The grading of the coordinate ring of the generic member of the family of base spaces.
-3. The weights corresponding to the divisor class `D_1` of the coordinate ring under which the first fiber coordinate transforms.
-4. The weights corresponding to the divisor class `D_2` of the coordinate ring under which the first fiber coordinate transforms.
-5. The dimension of the generic member of the family of base spaces.
-6. The fiber ambient space.
-7. The hypersurface equation.
+3. The weights telling us how the fiber ambient space coordinates transform under the base.
+4. The dimension of the generic member of the family of base spaces.
+5. The fiber ambient space.
+6. The hypersurface equation.
 
 Note that many studies in the literature use the class of the anticanonical bundle
 in their analysis. We anticipate this by adding this class as a variable of the
@@ -144,6 +147,11 @@ julia> D2 = [6,0]
  6
  0
 
+julia> D3 = [0,0]
+2-element Vector{Int64}:
+ 0
+ 0
+ 
 julia> d = 3
 3
 
@@ -158,13 +166,17 @@ julia> auxiliary_ambient_ring, (a1, a21, a32, a43, a65, w, x, y, z)  = QQ["a1",
 julia> p = x^3 - y^2 - x * y * z * a1 + x^2 * z^2 * a21 * w - y * z^3 * a32 * w^2 + x * z^4 * a43 * w^3 + z^6 * a65 * w^5
 -a1*x*y*z + a21*w*x^2*z^2 - a32*w^2*y*z^3 + a43*w^3*x*z^4 + a65*w^5*z^6 + x^3 - y^2
 
-julia> h = hypersurface_model(auxiliary_base_vars, auxiliary_base_grading, d, fiber_ambient_space, D1, D2, p)
+julia> h = hypersurface_model(auxiliary_base_vars, auxiliary_base_grading, d, fiber_ambient_space, [D1, D2, D3], p)
 Assuming that the first row of the given grading is the grading under Kbar
 
 Hypersurface model over a not fully specified base
 ```
 """
-function hypersurface_model(auxiliary_base_vars::Vector{String}, auxiliary_base_grading::Matrix{Int64}, d::Int, fiber_ambient_space::NormalToricVariety, D1::Vector{Int64}, D2::Vector{Int64}, p::MPolyRingElem)
+function hypersurface_model(auxiliary_base_vars::Vector{String}, auxiliary_base_grading::Matrix{Int64}, d::Int, fiber_ambient_space::NormalToricVariety, fiber_twist_divisor_classes::Vector{Vector{Int64}}, p::MPolyRingElem)
+  return hypersurface_model(auxiliary_base_vars, auxiliary_base_grading, d, fiber_ambient_space, transpose(matrix(ZZ, fiber_twist_divisor_classes)), p)
+end
+
+function hypersurface_model(auxiliary_base_vars::Vector{String}, auxiliary_base_grading::Matrix{Int64}, d::Int, fiber_ambient_space::NormalToricVariety, fiber_twist_divisor_classes::ZZMatrix, p::MPolyRingElem)
 
   # Compute simple information
   gens_fiber_names = [string(g) for g in gens(cox_ring(fiber_ambient_space))]
@@ -182,8 +194,8 @@ function hypersurface_model(auxiliary_base_vars::Vector{String}, auxiliary_base_
   @vprint :FTheoryModelPrinter 0 "Assuming that the first row of the given grading is the grading under Kbar\n\n"
 
   # Construct the spaces
-  (S, auxiliary_base_space, auxiliary_ambient_space) = _construct_generic_sample(auxiliary_base_grading, auxiliary_base_vars, d, fiber_ambient_space, D1, D2)
-  
+  (S, auxiliary_base_space, auxiliary_ambient_space) = _construct_generic_sample(auxiliary_base_grading, auxiliary_base_vars, d, fiber_ambient_space, fiber_twist_divisor_classes)
+
   # Map p to coordinate ring of ambient space
   gens_S = gens(S)
   image_list = Vector{MPolyRingElem}()

experimental/FTheoryTools/src/LiteratureModels/Models/model1109_3454.json

@@ -38,16 +38,16 @@
     },
     "model_data": {
         "base_dim": 3,
-        "model_sections": ["w"],
-        "base_coordinates": ["w", "a1", "a21", "a32", "a43"],
+        "divisors_user_must_specify": ["w"],
+        "divisors_parametrized_by_user_specified_divisors": ["a1", "a21", "a32", "a43"],
         "a1": "a1",
         "a2": "a21*w",
         "a3": "a32*w^2",
         "a4": "a43*w^3",
         "a6": "0",
-        "auxiliary_base_grading": [
-            [0, 1, 2, 3, 4],
-            [1, 0, -1, -2, -3]
+        "parametrization_of_parametrized_divisors_by_Kbar_and_user_specified_divisors": [
+            [1, 2, 3, 4],
+            [0, -1, -2, -3]
         ],
         "generating_sections": [["0", "0", "1"]],
         "resolutions": [

experimental/FTheoryTools/src/LiteratureModels/Models/model1208_2695-1.json

@@ -39,18 +39,20 @@
     },
     "model_data": {
         "base_dim": 2,
-        "model_sections": ["b"],
-        "base_coordinates": ["b", "c0", "c1", "c2", "c3"],
-        "auxiliary_base_grading": [
-            [0, 4, 3, 2, 1],
-            [1, -2, -1, 0, 1]
+        "divisors_user_must_specify": ["b"],
+        "divisors_parametrized_by_user_specified_divisors": ["c0", "c1", "c2", "c3"],
+        "parametrization_of_parametrized_divisors_by_Kbar_and_user_specified_divisors": [
+            [4, 3, 2, 1],
+            [-2, -1, 0, 1]
         ],
         "fiber_ambient_space_rays": [[-2, -1], [1, 0], [0, 1]],
         "fiber_ambient_space_max_cones": [[1, 2], [1, 3], [2, 3]],
         "fiber_ambient_space_coordinates": ["u", "w", "v"],
         "fiber_ambient_space_name": "P^{(1, 2, 1)}",
-        "D1": [-1, 1],
-        "D2": [0, 1],
+        "fiber_twist_matrix": [
+            [-1, 0, 0],
+            [1, 1, 0]
+        ],
         "hypersurface_equation": "w^2 + b * v^2 * w - u * (c0 * u^3 + c1 * u^2 * v + c2 * u * v^2 + c3 * v^3)",
         "zero_section": ["0", "1", "0"],
         "generating_sections": [["0", "1", "-b"]]

experimental/FTheoryTools/src/LiteratureModels/Models/model1208_2695-2.json

@@ -39,13 +39,13 @@
     },
     "model_data": {
         "base_dim": 2,
-        "model_sections": ["b"],
-        "base_coordinates": ["b", "c0", "c1", "c2", "c3"],
+        "divisors_user_must_specify": ["b"],
+        "divisors_parametrized_by_user_specified_divisors": ["c0", "c1", "c2", "c3"],
         "f": "c1 * c3 - b^2 * c0 - 1//3 * c2^2",
         "g": "c0 * c3^2 - 1//3 * c1 * c2 * c3 + 2//27 * c2^3 - 2//3 * b^2 * c0 * c2 + 1//4 * b^2 * c1^2",
-        "auxiliary_base_grading": [
-            [0, 4, 3, 2, 1],
-            [1, -2, -1, 0, 1]
+        "parametrization_of_parametrized_divisors_by_Kbar_and_user_specified_divisors": [
+            [4, 3, 2, 1],
+            [-2, -1, 0, 1]
         ],
         "generating_sections": [
             [

experimental/FTheoryTools/src/LiteratureModels/Models/model1212_2949-1.json

@@ -40,16 +40,16 @@
     "model_parameters": ["k"],
     "model_data": {
         "base_dim": 3,
-        "model_sections": ["ζ0"],
-        "base_coordinates": ["ζ0", "b1", "b2", "b3", "b4", "b6"],
+        "divisors_user_must_specify": ["ζ0"],
+        "divisors_parametrized_by_user_specified_divisors": ["b1", "b2", "b3", "b4", "b6"],
         "a1": "b1",
         "a2": "b2*ζ0",
         "a3": "b3*ζ0^k",
         "a4": "b4*ζ0^(k + 1)",
         "a6": "b6*ζ0^(2*k + 1)",
-        "auxiliary_base_grading": [
-            [0, 1, 2, 3, 4, 6],
-            [1, 0, -1, "-k", "-(k + 1)", "-(2*k + 1)"]
+        "parametrization_of_parametrized_divisors_by_Kbar_and_user_specified_divisors": [
+            [1, 2, 3, 4, 6],
+            [0, -1, "-k", "-(k + 1)", "-(2*k + 1)"]
         ],
         "resolutions": [
             [

experimental/FTheoryTools/src/LiteratureModels/Models/model1212_2949-2.json

@@ -40,16 +40,16 @@
     "model_parameters": ["k"],
     "model_data": {
         "base_dim": 3,
-        "model_sections": ["ζ0"],
-        "base_coordinates": ["ζ0", "b1", "b2", "b3", "b4", "b6"],
+        "divisors_user_must_specify": ["ζ0"],
+        "divisors_parametrized_by_user_specified_divisors": ["b1", "b2", "b3", "b4", "b6"],
         "a1": "b1",
         "a2": "b2*ζ0",
         "a3": "b3*ζ0^k",
         "a4": "b4*ζ0^k",
         "a6": "b6*ζ0^(2*k)",
-        "auxiliary_base_grading": [
-            [0, 1, 2, 3, 4, 6],
-            [1, 0, -1, "-k", "-k", "-2*k"]
+        "parametrization_of_parametrized_divisors_by_Kbar_and_user_specified_divisors": [
+            [1, 2, 3, 4, 6],
+            [0, -1, "-k", "-k", "-2*k"]
         ],
         "resolutions": [
             [

experimental/FTheoryTools/src/LiteratureModels/Models/model1212_2949-3.json

@@ -40,16 +40,16 @@
     "model_parameters": ["k"],
     "model_data": {
         "base_dim": 3,
-        "model_sections": ["ζ0"],
-        "base_coordinates": ["ζ0", "b1", "b2", "b3", "b4", "b6"],
+        "divisors_user_must_specify": ["ζ0"],
+        "divisors_parametrized_by_user_specified_divisors": ["b1", "b2", "b3", "b4", "b6"],
         "a1": "b1*ζ0",
         "a2": "b2*ζ0",
         "a3": "b3*ζ0^k",
         "a4": "b4*ζ0^(k + 1)",
         "a6": "b6*ζ0^(2*k + 1)",
-        "auxiliary_base_grading": [
-            [0, 1, 2, 3, 4, 6],
-            [1, -1, -1, "-k", "-(k + 1)", "-(2*k + 1)"]
+        "parametrization_of_parametrized_divisors_by_Kbar_and_user_specified_divisors": [
+            [1, 2, 3, 4, 6],
+            [-1, -1, "-k", "-(k + 1)", "-(2*k + 1)"]
         ],
         "resolutions": [
             [

experimental/FTheoryTools/src/LiteratureModels/Models/model1212_2949-4.json

@@ -41,16 +41,16 @@
     "model_parameters": ["k"],
     "model_data": {
         "base_dim": 3,
-        "model_sections": ["ζ0"],
-        "base_coordinates": ["ζ0", "b1", "b2", "b3", "b4"],
+        "divisors_user_must_specify": ["ζ0"],
+        "divisors_parametrized_by_user_specified_divisors": ["b1", "b2", "b3", "b4"],
         "a1": "b1*ζ0",
         "a2": "b2*ζ0",
         "a3": "b3*ζ0^(k + 1)",
         "a4": "b4*ζ0^(k + 1)",
         "a6": "0",
-        "auxiliary_base_grading": [
-            [0, 1, 2, 3, 4],
-            [1, -1, -1, "-(k + 1)", "-(k + 1)"]
+        "parametrization_of_parametrized_divisors_by_Kbar_and_user_specified_divisors": [
+            [1, 2, 3, 4],
+            [-1, -1, "-(k + 1)", "-(k + 1)"]
         ],
         "generating_sections": [["0", "0", "1"]],
         "resolutions": [

experimental/FTheoryTools/src/LiteratureModels/Models/model1212_2949-5.json

@@ -39,16 +39,16 @@
     },
     "model_data": {
         "base_dim": 3,
-        "model_sections": ["ζ0"],
-        "base_coordinates": ["ζ0", "b1", "b2", "b3", "b4", "b6"],
+        "divisors_user_must_specify": ["ζ0"],
+        "divisors_parametrized_by_user_specified_divisors": ["b1", "b2", "b3", "b4", "b6"],
         "a1": "b1*ζ0",
         "a2": "b2*ζ0^2",
         "a3": "b3*ζ0^2",
         "a4": "b4*ζ0^3",
         "a6": "b6*ζ0^5",
-        "auxiliary_base_grading": [
-            [0, 1, 2, 3, 4, 6],
-            [1, -1, -2, -2, -3, -5]
+        "parametrization_of_parametrized_divisors_by_Kbar_and_user_specified_divisors": [
+            [1, 2, 3, 4, 6],
+            [-1, -2, -2, -3, -5]
         ],
         "resolutions": [
             [

experimental/FTheoryTools/src/LiteratureModels/Models/model1212_2949-6.json

@@ -39,16 +39,16 @@
     },
     "model_data": {
         "base_dim": 3,
-        "model_sections": ["ζ0"],
-        "base_coordinates": ["ζ0", "b1", "b2", "b3", "b4", "b6"],
+        "divisors_user_must_specify": ["ζ0"],
+        "divisors_parametrized_by_user_specified_divisors": ["b1", "b2", "b3", "b4", "b6"],
         "a1": "b1*ζ0",
         "a2": "b2*ζ0^2",
         "a3": "b3*ζ0^3",
         "a4": "b4*ζ0^3",
         "a6": "b6*ζ0^5",
-        "auxiliary_base_grading": [
-            [0, 1, 2, 3, 4, 6],
-            [1, -1, -2, -3, -3, -5]
+        "parametrization_of_parametrized_divisors_by_Kbar_and_user_specified_divisors": [
+            [1, 2, 3, 4, 6],
+            [-1, -2, -3, -3, -5]
         ],
         "resolutions": [
             [