Merge branch 'master' into lg/mul

Project.toml

@@ -26,18 +26,18 @@ UUIDs = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"
 cohomCalg_jll = "5558cf25-a90e-53b0-b813-cadaa3ae7ade"
 
 [compat]
-AbstractAlgebra = "0.32.5"
-AlgebraicSolving = "0.3.3"
+AbstractAlgebra = "0.33.0"
+AlgebraicSolving = "0.3.6"
 DocStringExtensions = "0.8, 0.9"
 GAP = "0.9.4"
 Hecke = "0.22.4"
 JSON = "^0.20, ^0.21"
-Nemo = "0.36.1"
+Nemo = "0.37.1"
 Polymake = "0.11.6"
 Preferences = "1"
 RandomExtensions = "0.4.3"
 RecipesBase = "1.2.1"
-Singular = "0.18.10"
+Singular = "0.18.17"
 TOPCOM_jll = "0.17.8"
 cohomCalg_jll = "0.32.0"
 julia = "1.6"

docs/doc.main

@@ -193,6 +193,8 @@
         "AlgebraicGeometry/ToricVarieties/AlgebraicCycles.md",
         "AlgebraicGeometry/ToricVarieties/ToricMorphisms.md",
         "AlgebraicGeometry/ToricVarieties/ToricSchemes.md",
+        "AlgebraicGeometry/ToricVarieties/ToricIdealSheaves.md",
+        "AlgebraicGeometry/ToricVarieties/BlowdownMorphisms.md",
      ],
      "Tropical Geometry" => [
         "AlgebraicGeometry/TropicalGeometry/intro.md",

docs/src/AlgebraicGeometry/ToricVarieties/BlowdownMorphisms.md

@@ -0,0 +1,81 @@
+```@meta
+CurrentModule = Oscar
+```
+
+# Toric Blowdown Morphisms (Experimental)
+
+It is a common goal in algebraic geometry to resolve singularities. Certainly, (sub)varieties of
+toric varieties are no exception and we provide a growing set of functionality for such tasks.
+
+In general, resolutions need not be toric. Indeed, some of the functionality below requires
+fully-fledge schemes machinery, which -- as of this writing (October 2023) -- is still in
+Oscar's experimental state. For this reason, the methods below should be considered experimental.
+
+
+## Constructors
+
+Blowups of toric varieties are obtained from star subdivisions of polyhedral fans. In the most general form,
+a star subdivision is defined by a new primitive element in the fan. Below, we refer to this new primitive
+element as `new_ray`. In addition to this `new_ray`, our design of toric blowdown morphisms requires an
+underlying toric morphism. With an eye towards covered schemes as possible return value, any toric blowdown
+morphism must also know (to compute) its blowup center in the form of an ideal sheaf. The following constructor
+allows to set this ideal sheaf center upon construction:
+- `toric_blowdown_morphism(bl::ToricMorphism, new_ray::AbstractVector{<:IntegerUnion}, center::IdealSheaf)`
+The "working-horse" constructor however is the following:
+- `toric_blowdown_morphism(Y::NormalToricVariety, new_ray::AbstractVector{<:IntegerUnion}, coordinate_name::String, set_attributes::Bool)`
+This constructor will, among others, construct the underlying toric morphism. In addition, we can then specify
+a name for the coordinate in the Cox ring that is assigned to `new_ray`.
+
+
+
+## Blowdown morphisms from blowing up toric varieties
+
+The following methods blow up toric varieties. The center of the blowup can be provided in different formats.
+We discuss the methods in ascending generality.
+
+For our most specialized blow-up method, we focus on the n-th cone in the fan of the variety `v` in question.
+This cone need not be maximal! The ensuing star subdivision will subdivide this cone about its "diagonal"
+(the sum of all its rays). The result of this will always be a toric variety:
+```@docs
+blow_up(v::NormalToricVarietyType, n::Int; coordinate_name::String = "e", set_attributes::Bool = true)
+```
+More generally, we can provide a primitive element in the fan of the variety in question. The resulting
+star subdivision leads to a polyhedral fan, or put differently, the blow-up along this center is always toric:
+```@docs
+blow_up(v::NormalToricVarietyType, new_ray::AbstractVector{<:IntegerUnion}; coordinate_name::String = "e", set_attributes::Bool = true)
+```
+Finally, and most generally, we encode the blowup center by a homogeneous ideal in the Cox ring.
+Such blowups center may easily lead to non-toric blowups, i.e. the return value of the following method
+could well be non-toric.
+```@docs
+blow_up(v::NormalToricVarietyType, I::MPolyIdeal; coordinate_name::String = "e", set_attributes::Bool = true)
+```
+
+
+## Attributes
+
+```@docs
+underlying_morphism(bl::ToricBlowdownMorphism)
+index_of_new_ray(bl::ToricBlowdownMorphism)
+center(bl::ToricBlowdownMorphism)
+exceptional_divisor(bl::ToricBlowdownMorphism)
+```
+Based on `underlying_morphism`, also the following attributes of toric morphisms are supported for toric
+blowdown morphisms:
+- `grid_morphism(bl::ToricBlowdownMorphism)`,
+- `morphism_on_torusinvariant_weil_divisor_group(bl::ToricBlowdownMorphism)`,
+- `morphism_on_torusinvariant_cartier_divisor_group(bl::ToricBlowdownMorphism)`,
+- `morphism_on_class_group(bl::ToricBlowdownMorphism)`,
+- `morphism_on_picard_group(bl::ToricBlowdownMorphism)`.
+The total and strict transform of ideal sheaves along toric blowdown morphisms can be computed:
+```@docs
+total_transform(f::AbsSimpleBlowdownMorphism, II::IdealSheaf)
+```
+
+
+## Arithmetics
+
+Toric blowdown morphisms can be added, subtracted and multiplied by rational numbers. The results of such
+operations will be toric morphisms, i.e. no longer attributed to the blowup of a certain locus. Arithmetics
+among toric blowdown morphisms and general toric morphisms is also supported, as well as equality for toric
+blowdown morphisms.

docs/src/AlgebraicGeometry/ToricVarieties/NormalToricVarieties.md

@@ -92,9 +92,6 @@ normal_toric_varieties_from_glsm(charges::ZZMatrix; set_attributes::Bool = true)
 ### Further Constructions
 
 ```@docs
-blow_up(v::NormalToricVarietyType, I::MPolyIdeal; coordinate_name::String = "e", set_attributes::Bool = true)
-blow_up(v::NormalToricVarietyType, new_ray::AbstractVector{<:IntegerUnion}; coordinate_name::String = "e", set_attributes::Bool = true)
-blow_up(v::NormalToricVarietyType, n::Int; coordinate_name::String = "e", set_attributes::Bool = true)
 Base.:*(v::NormalToricVarietyType, w::NormalToricVarietyType; set_attributes::Bool = true)
 proj(E::ToricLineBundle...)
 total_space(E::ToricLineBundle...)

docs/src/AlgebraicGeometry/ToricVarieties/ToricIdealSheaves.md

@@ -0,0 +1,14 @@
+```@meta
+CurrentModule = Oscar
+```
+
+
+# Toric Ideal Sheaves (Experimental)
+
+Ideal sheaves on toric varieties are currently in experimental state.
+Currently, we support the following functionality. Note that, as of
+October 2023, this is limited to smooth toric varieties.
+```@docs
+ideal_sheaf(td::ToricDivisor)
+ideal_sheaf(X::NormalToricVariety, I::MPolyIdeal)
+```

docs/src/AlgebraicGeometry/ToricVarieties/ToricLineBundles.md

@@ -41,8 +41,9 @@ Equality of toric line bundles can be tested via `==`.
 To check if a toric line bundle is trivial, one can invoke `is_trivial`. Beyond this,
 we support the following properties of toric line bundles:
 ```@docs
-is_basepoint_free(l::ToricLineBundle)
 is_ample(l::ToricLineBundle)
+is_basepoint_free(l::ToricLineBundle)
+is_immaculate(l::ToricLineBundle)
 is_very_ample(l::ToricLineBundle)
 ```
 

docs/src/AlgebraicGeometry/ToricVarieties/ToricSchemes.md

@@ -2,7 +2,7 @@
 CurrentModule = Oscar
 ```
 
-# Introduction
+# Toric Schemes
 
 Toric varieties are special instances of schemes. As such, all scheme functionality is
 available to toric varieties.

docs/src/AlgebraicGeometry/ToricVarieties/cohomCalg.md

@@ -46,5 +46,5 @@ Beyond this, we support the following attributes for vanishing sets:
 ```@docs
 toric_variety(tvs::ToricVanishingSet)
 polyhedra(tvs::ToricVanishingSet)
-cohomology_index(tvs::ToricVanishingSet)
+cohomology_indices(tvs::ToricVanishingSet)
 ```

docs/src/Combinatorics/matroids.md

@@ -26,7 +26,7 @@ matroid_from_circuits(circuits::AbstractVector{T}, nelements::IntegerUnion) wher
 matroid_from_hyperplanes(hyperplanes::AbstractVector{T}, nelements::IntegerUnion) where T<:GroundsetType
 matroid_from_matrix_columns(A::MatrixElem; check::Bool=true)
 matroid_from_matrix_rows(A::MatrixElem, ; check::Bool=true)
-cycle_matroid(g::Graph)
+cycle_matroid
 bond_matroid(g::Graph)
 cocycle_matroid(g::Graph)
 Matroid(pm_matroid::Polymake.BigObjectAllocated, E::GroundsetType=Vector{Integer}(1:pm_matroid.N_ELEMENTS))

docs/src/NumberTheory/galois.md

@@ -88,7 +88,7 @@ Over the rational function field, we can also compute the monodromy group:
 DocTestFilters = r"Galois context\(.*\]\)"
 ```
 ```jldoctest galqt; setup = :(using Oscar, Random ; Random.seed!(1))
-julia> Qt, t = RationalFunctionField(QQ, "t");
+julia> Qt, t = rational_function_field(QQ, "t");
 
 julia> Qtx, x = Qt["x"];
 
@@ -233,7 +233,7 @@ is now a polynomial with integer coefficients. Thus the bound needs
 to bound the degree as well as the coefficient size.
 
 ```jldoctest
-julia> Qt,t = RationalFunctionField(QQ, "t");
+julia> Qt,t = rational_function_field(QQ, "t");
 
 julia> Qtx, x = Qt["x"];
 

experimental/Experimental.jl

@@ -68,4 +68,12 @@ include("Schemes/duValSing.jl")
 include("Schemes/elliptic_surface.jl")
 include("Schemes/MorphismFromRationalFunctions.jl")
 
+include("Schemes/ToricIdealSheaves/auxiliary.jl")
+include("Schemes/ToricIdealSheaves/constructors.jl")
+
+include("Schemes/ToricBlowups/types.jl")
+include("Schemes/ToricBlowups/constructors.jl")
+include("Schemes/ToricBlowups/attributes.jl")
+include("Schemes/ToricBlowups/methods.jl")
+
 include("ExteriorAlgebra/ExteriorAlgebra.jl")

experimental/GModule/Brueckner.jl

@@ -67,7 +67,7 @@ function reps(K, G::Oscar.GAPGroup)
         @hassert :BruecknerSQ 2 Oscar.GrpCoh.is_consistent(rh)
         l = Oscar.GModuleFromGap.hom_base(r, rh)
         @assert length(l) <= 1
-        Y = mat(action(r, preimage(ms, h^p)))
+        Y = matrix(action(r, preimage(ms, h^p)))
         if length(l) == 1
           # The representation extends from the subgroup,
           # all these extensions are pairwise inequivalent.
@@ -128,7 +128,7 @@ function reps(K, G::Oscar.GAPGroup)
             z = zero_matrix(K, dim(F), dim(F))
             for j=1:p
               Y = action(r, g)
-              m = mat(Y)
+              m = matrix(Y)
               z[(j-1)*n+1:j*n, (j-1)*n+1:j*n] = m
               push!(conjreps[j], hom(M, M, m))
               g = preimage(ms, ms(g)^h)
@@ -282,7 +282,7 @@ function Oscar.dual(h::Map{<:AbstractAlgebra.FPModule{ZZRingElem}, <:AbstractAlg
   A = domain(h)
   B = codomain(h)
   @assert is_free(A) && is_free(B)
-  return hom(B, A, transpose(mat(h)))
+  return hom(B, A, transpose(matrix(h)))
 end
 
 function coimage(h::Map)

experimental/GModule/Cohomology.jl

@@ -354,7 +354,7 @@ end
 
 function Oscar.direct_sum(M::AbstractAlgebra.Generic.DirectSumModule{T}, N::AbstractAlgebra.Generic.DirectSumModule{T}, mp::Vector{AbstractAlgebra.Generic.ModuleHomomorphism{T}})  where T
   @assert length(M.m) == length(mp) == length(N.m)
-  return hom(M, N, cat(map(mat, mp)..., dims = (1,2)))
+  return hom(M, N, cat(map(matrix, mp)..., dims = (1,2)))
 end
 
 function Oscar.direct_product(C::GModule...; task::Symbol = :none)
@@ -713,7 +713,7 @@ end
    - issubset yields (for GrpAb) only true/ false, not the map
    - is_subgroup cannot apply to modules
    - quo does ONLY work if B is a direct submodule of A (Z-modules)
-   - mat or matrix is used to get "the matrix" from a hom
+   - matrix is used to get "the matrix" from a hom
    - zero_hom/ zero_obj/ identity_hom is missing
    - Janko-Module-Homs have different types, they probably need to
      come under a common abstract type or be more selective
@@ -1591,7 +1591,7 @@ function Oscar.hom(V::Module, W::Module, v::MatElem; check::Bool = true)
   return Generic.ModuleHomomorphism(V, W, v)
 end
 function Oscar.inv(M::Generic.ModuleHomomorphism)
-  return hom(codomain(M), domain(M), inv(mat(M)))
+  return hom(codomain(M), domain(M), inv(matrix(M)))
 end
 
 function Oscar.direct_product(M::Module...; task::Symbol = :none)
@@ -1608,18 +1608,18 @@ function Oscar.direct_product(M::Module...; task::Symbol = :none)
   error("illegal task")
 end
 
-Base.:*(a::T, b::Generic.ModuleHomomorphism{T}) where {T} = hom(domain(b), codomain(b), a * mat(b))
-Base.:*(a::T, b::Generic.ModuleIsomorphism{T}) where {T} = hom(domain(b), codomain(b), a * mat(b))
-Base.:+(a::Generic.ModuleHomomorphism, b::Generic.ModuleHomomorphism) = hom(domain(a), codomain(a), mat(a) + mat(b))
-Base.:-(a::Generic.ModuleHomomorphism, b::Generic.ModuleHomomorphism) = hom(domain(a), codomain(a), mat(a) - mat(b))
-Base.:-(a::Generic.ModuleHomomorphism) = hom(domain(a), codomain(a), -mat(a))
+Base.:*(a::T, b::Generic.ModuleHomomorphism{T}) where {T} = hom(domain(b), codomain(b), a * matrix(b))
+Base.:*(a::T, b::Generic.ModuleIsomorphism{T}) where {T} = hom(domain(b), codomain(b), a * matrix(b))
+Base.:+(a::Generic.ModuleHomomorphism, b::Generic.ModuleHomomorphism) = hom(domain(a), codomain(a), matrix(a) + matrix(b))
+Base.:-(a::Generic.ModuleHomomorphism, b::Generic.ModuleHomomorphism) = hom(domain(a), codomain(a), matrix(a) - matrix(b))
+Base.:-(a::Generic.ModuleHomomorphism) = hom(domain(a), codomain(a), -matrix(a))
 
-function Oscar.mat(M::FreeModuleHom{FreeMod{QQAbElem}, FreeMod{QQAbElem}})
+function Oscar.matrix(M::FreeModuleHom{FreeMod{QQAbElem}, FreeMod{QQAbElem}})
   return M.matrix
 end
 
 function ==(a::Union{Generic.ModuleHomomorphism, Generic.ModuleIsomorphism}, b::Union{Generic.ModuleHomomorphism, Generic.ModuleIsomorphism})
-  return mat(a) == mat(b)
+  return matrix(a) == matrix(b)
 end
 
 function Oscar.id_hom(A::AbstractAlgebra.FPModule)