polyhedral_fan: Adapt order of arguments, see #3054

Author: lkastner

docs/src/AlgebraicGeometry/ToricVarieties/NormalToricVarieties.md

@@ -29,9 +29,7 @@ affine_normal_toric_variety(v::NormalToricVariety)
 ### Normal Toric Varieties
 
 ```@docs
-normal_toric_variety(rays::AbstractCollection[RayVector], max_cones::Vector{Vector{Int64}}; non_redundant::Bool = false)
-normal_toric_variety(PF::PolyhedralFan)
-normal_toric_variety(P::Polyhedron)
+normal_toric_variety
 ```
 
 ### Famous Toric Vareties

experimental/FTheoryTools/src/auxiliary.jl

@@ -22,7 +22,7 @@ function _auxiliary_base_space(auxiliary_base_variable_names::Vector{String}, au
   if dim(auxiliary_base_space) != d
     integral_rays = matrix(ZZ, rays(variety))
     new_max_cones = IncidenceMatrix(cones(variety, d))
-    auxiliary_base_space = normal_toric_variety(integral_rays, new_max_cones; non_redundant = true)
+    auxiliary_base_space = normal_toric_variety(new_max_cones, integral_rays; non_redundant = true)
   end
 
   # Set attributes of this base space and return it
@@ -81,7 +81,7 @@ function _ambient_space(base::NormalToricVariety, fiber_ambient_space::NormalTor
   ambient_space_max_cones = IncidenceMatrix(vcat(ambient_space_max_cones...))
 
   # Construct the ambient space
-  ambient_space = normal_toric_variety(ambient_space_rays, ambient_space_max_cones; non_redundant = true)
+  ambient_space = normal_toric_variety(ambient_space_max_cones, ambient_space_rays; non_redundant = true)
 
   # Compute torusinvariant weil divisor group and the class group
   ambient_space_torusinvariant_weil_divisor_group = free_abelian_group(nrows(ambient_space_rays))
@@ -198,7 +198,7 @@ function sample_toric_variety()
           [5, 11, 12], [5, 6, 32], [5, 6, 12], [4, 31, 32], [4, 10, 11], [4, 5, 32],
           [4, 5, 11], [3, 30, 31], [3, 9, 10], [3, 4, 31], [3, 4, 10], [2, 29, 30],
           [2, 8, 9], [2, 3, 30], [2, 3, 9], [1, 8, 29], [1, 2, 29], [1, 2, 8]])
-  return normal_toric_variety(rays, cones)
+  return normal_toric_variety(cones, rays)
 end
 
 

src/AlgebraicGeometry/ToricVarieties/AlgebraicCycles/special_attributes.jl

@@ -27,7 +27,7 @@ true
 julia> ngens(chow_ring(p2))
 3
 
-julia> v = normal_toric_variety([[1, 0], [0, 1], [-1, -1]], [[1], [2], [3]])
+julia> v = normal_toric_variety(IncidenceMatrix([[1], [2], [3]]), [[1, 0], [0, 1], [-1, -1]])
 Normal toric variety
 
 julia> is_complete(v)

src/AlgebraicGeometry/ToricVarieties/CohomologyClasses/methods.jl

@@ -58,9 +58,9 @@ julia> m = 2;
 
 julia> ray_generators = [e1, -e1, e2, e3, - e2 - e3 - m * e1];
 
-julia> max_cones = [[1,3,4], [1,3,5], [1,4,5], [2,3,4], [2,3,5], [2,4,5]];
+julia> max_cones = IncidenceMatrix([[1,3,4], [1,3,5], [1,4,5], [2,3,4], [2,3,5], [2,4,5]]);
 
-julia> X = normal_toric_variety(ray_generators, max_cones; non_redundant = true)
+julia> X = normal_toric_variety(max_cones, ray_generators; non_redundant = true)
 Normal toric variety
 
 julia> cox_ring(X)

src/AlgebraicGeometry/ToricVarieties/NormalToricVarieties/constructors.jl

@@ -63,7 +63,7 @@ end
 
 
 @doc raw"""
-    normal_toric_variety(rays::AbstractCollection[RayVector], max_cones::IncidenceMatrix; non_redundant::Bool = false)
+    normal_toric_variety(max_cones::IncidenceMatrix, rays::AbstractCollection[RayVector]; non_redundant::Bool = false)
 
 Construct a normal toric variety $X$ by providing the rays and maximal cones
 as vector of vectors. By default, this method assumes that the input is not
@@ -82,23 +82,23 @@ julia> ray_generators = [[1,0], [0, 1], [-1, 5], [0, -1]]
  [-1, 5]
  [0, -1]
 
-julia> max_cones = [[1, 2], [2, 3], [3, 4], [4, 1]]
-4-element Vector{Vector{Int64}}:
- [1, 2]
- [2, 3]
- [3, 4]
- [4, 1]
+julia> max_cones = IncidenceMatrix([[1, 2], [2, 3], [3, 4], [4, 1]])
+4×4 IncidenceMatrix
+[1, 2]
+[2, 3]
+[3, 4]
+[1, 4]
 
-julia> normal_toric_variety(ray_generators, max_cones)
+julia> normal_toric_variety(max_cones, ray_generators)
 Normal toric variety
 
-julia> normal_toric_variety(ray_generators, max_cones; non_redundant = true)
+julia> normal_toric_variety(max_cones, ray_generators; non_redundant = true)
 Normal toric variety
 ```
 """
-normal_toric_variety(rays::AbstractCollection[RayVector], max_cones::Vector{Vector{Int64}}; non_redundant::Bool = false) = normal_toric_variety(rays, IncidenceMatrix(max_cones); non_redundant = non_redundant)
-function normal_toric_variety(rays::AbstractCollection[RayVector], max_cones::IncidenceMatrix; non_redundant::Bool = false)
-  fan = polyhedral_fan(rays, max_cones; non_redundant=non_redundant)
+normal_toric_variety(max_cones::Vector{Vector{Int64}}, rays::AbstractCollection[RayVector]; non_redundant::Bool = false) = normal_toric_variety(IncidenceMatrix(max_cones), rays; non_redundant)
+function normal_toric_variety(max_cones::IncidenceMatrix, rays::AbstractCollection[RayVector]; non_redundant::Bool = false)
+  fan = polyhedral_fan(max_cones, rays; non_redundant)
   return normal_toric_variety(fan)
 end
 

src/AlgebraicGeometry/ToricVarieties/NormalToricVarieties/standard_constructions.jl

@@ -80,8 +80,8 @@ Normal toric variety
 """
 function hirzebruch_surface(::Type{NormalToricVariety}, r::Int)
   fan_rays = [1 0; 0 1; -1 r; 0 -1]
-  cones = [[1, 2], [2, 3], [3, 4], [4, 1]]
-  variety = normal_toric_variety(fan_rays, cones; non_redundant = true)
+  cones = IncidenceMatrix([[1, 2], [2, 3], [3, 4], [4, 1]])
+  variety = normal_toric_variety(cones, fan_rays; non_redundant = true)
   set_attribute!(variety, :torusinvariant_weil_divisor_group, free_abelian_group(4))
   set_attribute!(variety, :class_group, free_abelian_group(2))
   weights = matrix(ZZ, [1 0; 0 1; 1 0; r 1])
@@ -126,7 +126,7 @@ function del_pezzo_surface(::Type{NormalToricVariety}, b::Int)
     fan_rays = [1 0; 0 1; -1 -1; 1 1; 0 -1; -1 0]
     cones = IncidenceMatrix([[1, 4], [2, 4], [1, 5], [5, 3], [2, 6], [6, 3]])
   end
-  variety = normal_toric_variety(fan_rays, cones; non_redundant = true)
+  variety = normal_toric_variety(cones, fan_rays; non_redundant = true)
   set_attribute!(variety, :torusinvariant_weil_divisor_group, free_abelian_group(b+3))
   set_attribute!(variety, :class_group, free_abelian_group(b+1))
   if b == 1
@@ -245,7 +245,7 @@ function normal_toric_variety_from_star_triangulation(P::Polyhedron)
   integral_rays = vcat([pts[k,:] for k in 2:nrows(pts)])
 
   # construct the variety
-  return normal_toric_variety(integral_rays, max_cones; non_redundant = true)
+  return normal_toric_variety(max_cones, integral_rays; non_redundant = true)
 end
 
 
@@ -298,7 +298,7 @@ function normal_toric_varieties_from_star_triangulations(P::Polyhedron)
   max_cones = [IncidenceMatrix([[c[i]-1 for i in 2:length(c)] for c in t]) for t in trias]
 
   # construct the varieties
-  return [normal_toric_variety(integral_rays, cones; non_redundant = true) for cones in max_cones]
+  return [normal_toric_variety(cones, integral_rays; non_redundant = true) for cones in max_cones]
 end
 
 
@@ -341,7 +341,7 @@ function normal_toric_variety_from_glsm(charges::ZZMatrix)
   # construct varieties
   triang = _find_full_star_triangulation(pts)
   max_cones = IncidenceMatrix([[c[i]-1 for i in 2:length(c)] for c in triang])
-  variety = normal_toric_variety(integral_rays, max_cones; non_redundant = true)
+  variety = normal_toric_variety(max_cones, integral_rays; non_redundant = true)
 
   # set the attributes and return the variety
   set_attribute!(variety, :torusinvariant_weil_divisor_group, G1)
@@ -408,7 +408,7 @@ function normal_toric_varieties_from_glsm(charges::ZZMatrix)
   # construct varieties
   integral_rays = vcat([pts[k,:] for k in 2:nrows(pts)])
   max_cones = [IncidenceMatrix([[c[i]-1 for i in 2:length(c)] for c in t]) for t in star_triangulations(pts; full = true)]
-  varieties = [normal_toric_variety(integral_rays, cones; non_redundant = true) for cones in max_cones]
+  varieties = [normal_toric_variety(cones, integral_rays; non_redundant = true) for cones in max_cones]
 
   # set the map from Div_T -> Cl to the desired matrix
   for v in varieties

src/AlgebraicGeometry/ToricVarieties/Proj/constructors.jl

@@ -76,7 +76,7 @@ function _proj_and_total_space(is_proj::Bool, E::Vector{T}) where T <: Union{Tor
 
   total_rays_gens = vcat([modified_ray_gens[ray] for ray in rays(v)], [vcat(ray_vector(zeros(Int64, dim(v))), l[i]) for i in eachindex(E)])
 
-  return normal_toric_variety(polyhedral_fan(total_rays_gens, IncidenceMatrix(new_maximal_cones)))
+  return normal_toric_variety(polyhedral_fan(IncidenceMatrix(new_maximal_cones), total_rays_gens))
 end
 
 function _m_sigma(sigma::Cone{QQFieldElem}, pol_sigma::Cone{QQFieldElem}, D::Union{ToricDivisor, ToricLineBundle})::RayVector{QQFieldElem}

src/AlgebraicGeometry/ToricVarieties/ToricMorphisms/standard_constructions.jl

@@ -16,7 +16,7 @@ Toric morphism
     mapping_matrix = matrix(ZZ, rays(variety))
     max_cones_for_cox_variety = ray_indices(maximal_cones(variety))
     rays_for_cox_variety = matrix(ZZ, [[if i==j 1 else 0 end for j in 1:nrays(variety)] for i in 1:nrays(variety)])
-    cox_variety = normal_toric_variety(polyhedral_fan(rays_for_cox_variety, max_cones_for_cox_variety))
+    cox_variety = normal_toric_variety(polyhedral_fan(max_cones_for_cox_variety, rays_for_cox_variety))
     return toric_morphism(cox_variety, mapping_matrix, variety)
 end
 

src/PolyhedralGeometry/PolyhedralFan/constructors.jl

@@ -45,7 +45,7 @@ julia> R = [1 0; 1 1; 0 1; -1 0; 0 -1];
 
 julia> IM=IncidenceMatrix([[1,2],[2,3],[3,4],[4,5],[1,5]]);
 
-julia> PF=polyhedral_fan(R,IM)
+julia> PF=polyhedral_fan(IM, R)
 Polyhedral fan in ambient dimension 2
 ```
 
@@ -57,17 +57,17 @@ julia> L = [0 1 0];
 
 julia> IM = IncidenceMatrix([[1],[2]]);
 
-julia> PF=polyhedral_fan(R, L, IM)
+julia> PF=polyhedral_fan(IM, R, L)
 Polyhedral fan in ambient dimension 3
 
 julia> lineality_dim(PF)
 1
 ```
 """
 function polyhedral_fan(f::scalar_type_or_field,
+                        Incidence::IncidenceMatrix,
                         Rays::AbstractCollection[RayVector], 
-                        LS::Union{AbstractCollection[RayVector], Nothing},
-                        Incidence::IncidenceMatrix; 
+                        LS::Union{AbstractCollection[RayVector], Nothing};
                         non_redundant::Bool = false)
   parent_field, scalar_type = _determine_parent_and_scalar(f, Rays, LS)
   RM = unhomogenized_matrix(Rays)
@@ -90,9 +90,9 @@ function polyhedral_fan(f::scalar_type_or_field,
     ), parent_field)
   end
 end
-polyhedral_fan(f::scalar_type_or_field, Rays::AbstractCollection[RayVector], Incidence::IncidenceMatrix; non_redundant::Bool = false) = polyhedral_fan(f, Rays, nothing, Incidence; non_redundant=non_redundant)
-polyhedral_fan(Rays::AbstractCollection[RayVector], LS::Union{AbstractCollection[RayVector], Nothing}, Incidence::IncidenceMatrix; non_redundant::Bool = false) = polyhedral_fan(QQFieldElem, Rays, LS, Incidence; non_redundant = non_redundant)
-polyhedral_fan(Rays::AbstractCollection[RayVector], Incidence::IncidenceMatrix; non_redundant::Bool = false) = polyhedral_fan(QQFieldElem, Rays, Incidence; non_redundant = non_redundant)
+polyhedral_fan(f::scalar_type_or_field, Incidence::IncidenceMatrix, Rays::AbstractCollection[RayVector]; non_redundant::Bool = false) = polyhedral_fan(f, Incidence, Rays, nothing; non_redundant)
+polyhedral_fan(Incidence::IncidenceMatrix, Rays::AbstractCollection[RayVector], LS::Union{AbstractCollection[RayVector], Nothing}; non_redundant::Bool = false) = polyhedral_fan(QQFieldElem, Incidence, Rays, LS; non_redundant)
+polyhedral_fan(Incidence::IncidenceMatrix, Rays::AbstractCollection[RayVector]; non_redundant::Bool = false) = polyhedral_fan(QQFieldElem, Incidence, Rays; non_redundant)
 
 """
     pm_object(PF::PolyhedralFan)
@@ -117,10 +117,10 @@ function polyhedral_fan(cones::AbstractVector{Cone{T}}; non_redundant::Bool=fals
 end
 
 #Same construction for when the user gives Matrix{Bool} as incidence matrix
-polyhedral_fan(f::scalar_type_or_field, Rays::AbstractCollection[RayVector], LS::AbstractCollection[RayVector], Incidence::Matrix{Bool}) =
-  polyhedral_fan(f, Rays, LS, IncidenceMatrix(Polymake.IncidenceMatrix(Incidence)))
-polyhedral_fan(f::scalar_type_or_field, Rays::AbstractCollection[RayVector], Incidence::Matrix{Bool}) =
-  polyhedral_fan(f, Rays, IncidenceMatrix(Polymake.IncidenceMatrix(Incidence)))
+polyhedral_fan(f::scalar_type_or_field, Incidence::Matrix{Bool}, Rays::AbstractCollection[RayVector], LS::AbstractCollection[RayVector]) =
+  polyhedral_fan(f, IncidenceMatrix(Polymake.IncidenceMatrix(Incidence)), Rays, LS)
+polyhedral_fan(f::scalar_type_or_field, Incidence::Matrix{Bool}, Rays::AbstractCollection[RayVector]) =
+  polyhedral_fan(f, IncidenceMatrix(Polymake.IncidenceMatrix(Incidence)), Rays)
 
 polyhedral_fan(C::Cone{T}) where T<:scalar_types = polyhedral_fan([C])
 

src/PolyhedralGeometry/PolyhedralFan/properties.jl

@@ -230,7 +230,7 @@ Return the dimension of `PF`.
 This fan in the plane contains a 2-dimensional cone and is thus 2-dimensional
 itself.
 ```jldoctest
-julia> PF = polyhedral_fan([1 0; 0 1; -1 -1], IncidenceMatrix([[1, 2], [3]]));
+julia> PF = polyhedral_fan(IncidenceMatrix([[1, 2], [3]]), [1 0; 0 1; -1 -1]);
 
 julia> dim(PF)
 2
@@ -247,7 +247,7 @@ Return the number of maximal cones of `PF`.
 The cones given in this construction are non-redundant. Thus there are two
 maximal cones.
 ```jldoctest
-julia> PF = polyhedral_fan([1 0; 0 1; -1 -1], IncidenceMatrix([[1, 2], [3]]));
+julia> PF = polyhedral_fan(IncidenceMatrix([[1, 2], [3]]), [1 0; 0 1; -1 -1]);
 
 julia> n_maximal_cones(PF)
 2
@@ -264,7 +264,7 @@ Return the number of cones of `PF`.
 The cones given in this construction are non-redundant. There are six
 cones in this fan.
 ```jldoctest
-julia> PF = polyhedral_fan([1 0; 0 1; -1 -1], IncidenceMatrix([[1, 2], [3]]))
+julia> PF = polyhedral_fan(IncidenceMatrix([[1, 2], [3]]), [1 0; 0 1; -1 -1])
 Polyhedral fan in ambient dimension 2
 
 julia> n_cones(PF)
@@ -386,7 +386,7 @@ This fan consists of two cones, one containing all the points with $y ≤ 0$ and
 one containing all the points with $y ≥ 0$. The fan's lineality is the common
 lineality of these two cones, i.e. in $x$-direction.
 ```jldoctest
-julia> PF = polyhedral_fan([1 0; 0 1; -1 0; 0 -1], IncidenceMatrix([[1, 2, 3], [3, 4, 1]]))
+julia> PF = polyhedral_fan(IncidenceMatrix([[1, 2, 3], [3, 4, 1]]), [1 0; 0 1; -1 0; 0 -1])
 Polyhedral fan in ambient dimension 2
 
 julia> lineality_space(PF)
@@ -441,7 +441,7 @@ Determine whether `PF` is smooth.
 Even though the cones of this fan cover the positive orthant together, one of
 these und thus the whole fan is not smooth.
 ```jldoctest
-julia> PF = polyhedral_fan([0 1; 2 1; 1 0], IncidenceMatrix([[1, 2], [2, 3]]));
+julia> PF = polyhedral_fan(IncidenceMatrix([[1, 2], [2, 3]]), [0 1; 2 1; 1 0]);
 
 julia> is_smooth(PF)
 false
@@ -457,7 +457,7 @@ Determine whether `PF` is regular, i.e. the normal fan of a polytope.
 # Examples
 This fan is not complete and thus not regular.
 ```jldoctest
-julia> PF = polyhedral_fan([1 0; 0 1; -1 -1], IncidenceMatrix([[1, 2], [3]]));
+julia> PF = polyhedral_fan(IncidenceMatrix([[1, 2], [3]]), [1 0; 0 1; -1 -1]);
 
 julia> is_regular(PF)
 false
@@ -473,7 +473,7 @@ Determine whether `PF` is pure, i.e. all maximal cones have the same dimension.
 
 # Examples
 ```jldoctest
-julia> PF = polyhedral_fan([1 0; 0 1; -1 -1], IncidenceMatrix([[1, 2], [3]]));
+julia> PF = polyhedral_fan(IncidenceMatrix([[1, 2], [3]]), [1 0; 0 1; -1 -1]);
 
 julia> is_pure(PF)
 false
@@ -490,7 +490,7 @@ dimension.
 
 # Examples
 ```jldoctest
-julia> PF = polyhedral_fan([1 0; 0 1; -1 -1], IncidenceMatrix([[1, 2], [3]]));
+julia> PF = polyhedral_fan(IncidenceMatrix([[1, 2], [3]]), [1 0; 0 1; -1 -1]);
 
 julia> is_fulldimensional(PF)
 true