Merge branch 'master' into th/buuuump

docs/src/AlgebraicGeometry/ToricVarieties/ToricLineBundles.md

@@ -31,6 +31,7 @@ the inverse by invoking `inv`.
 anticanonical_bundle(v::NormalToricVarietyType)
 canonical_bundle(v::NormalToricVarietyType)
 structure_sheaf(v::NormalToricVarietyType)
+trivial_line_bundle(v::NormalToricVarietyType)
 ```
 
 

experimental/IntersectionTheory/src/IntersectionTheory.jl

@@ -7,6 +7,7 @@ import ..Oscar: basis, betti, chow_ring, codomain, degree, det, dim, domain, dua
 import ..Oscar.AbstractAlgebra: combinations
 import ..Oscar.AbstractAlgebra.Generic: FunctionalMap
 import..Oscar: pullback, pushforward, base, OO, product, compose
+import ..Oscar: trivial_line_bundle
 
 export a_hat_genus
 export abstract_bundle

src/AlgebraicGeometry/ToricVarieties/Proj/constructors.jl

@@ -106,7 +106,7 @@ This function computes the total space of a direct sum of line bundles or diviso
 Please see [OM78](@cite) for more background information.
 
 # Examples
-Let us construct the toric Calabi-Yau varieties given by the total space of ``\mathcal{O}_{\mathbb{P}^1}(2)\oplus\mathcal{O}_{\mathbb{P}^1}(-4))`` and ``\omega_{\mathbb{P}^2}``.
+Let us construct the toric Calabi-Yau varieties given by the total space of ``\mathcal{O}_{\mathbb{P}^1}(2)\oplus\mathcal{O}_{\mathbb{P}^1}(-4)`` and ``\omega_{\mathbb{P}^2}``.
 ```jldoctest
 julia> P1 = projective_space(NormalToricVariety, 1);
 

src/AlgebraicGeometry/ToricVarieties/ToricLineBundles/standard_constructions.jl

@@ -6,7 +6,6 @@
     structure_sheaf(v::NormalToricVarietyType)
 
 Construct the structure sheaf of a normal toric variety.
-For convenience, we also support `structure_sheaf(variety)`.
 
 # Examples
 ```jldoctest
@@ -24,7 +23,6 @@ Toric line bundle on a normal toric variety
     anticanonical_bundle(v::NormalToricVarietyType)
 
 Construct the anticanonical bundle of a normal toric variety.
-For convenience, we also support `anticanonical_bundle(variety)`.
 
 # Examples
 ```jldoctest
@@ -42,7 +40,6 @@ Toric line bundle on a normal toric variety
     canonical_bundle(v::NormalToricVarietyType)
 
 Construct the canonical bundle of a normal toric variety.
-For convenience, we also support `canonical_bundle(variety)`.
 
 # Examples
 ```jldoctest
@@ -54,3 +51,23 @@ Toric line bundle on a normal toric variety
 ```
 """
 @attr ToricLineBundle canonical_bundle(v::NormalToricVarietyType) = inv(anticanonical_bundle(v))
+
+
+@doc raw"""
+    trivial_line_bundle(v::NormalToricVarietyType)
+
+Construct the trivial line bundle on a normal toric variety.
+
+# Examples
+```jldoctest
+julia> v = projective_space(NormalToricVariety, 2)
+Normal toric variety
+
+julia> l = trivial_line_bundle(v)
+Toric line bundle on a normal toric variety
+
+julia> is_trivial(l)
+true
+```
+"""
+@attr ToricLineBundle trivial_line_bundle(v::NormalToricVarietyType) = toric_line_bundle(v, trivial_divisor(v))

src/TropicalGeometry/matrix.jl

@@ -41,3 +41,36 @@ function det(A::Matrix{<:TropicalSemiringElem})
   @req 0 < nrows(A) == ncols(A) "Non-square or empty matrix"
   return det(matrix(parent(first(A)),A))
 end
+
+@doc raw"""
+    is_tropically_generic(A::MatrixElem{<:TropicalSemiringElem})
+
+Check if a collection of vectors in the tropical torus (given as rows of a matrix `A`) are in tropical general position.
+
+# Examples
+```jldoctest
+julia> A = matrix(tropical_semiring(),[1 0;0 1])
+[(1)   (0)]
+[(0)   (1)]
+
+julia> is_tropically_generic(A)
+true
+```
+"""
+function is_tropically_generic(A::MatrixElem{<:TropicalSemiringElem})
+  function helper(A,C,B)
+    for b in subsets(C,B)
+      Polymake.tropical.tsgn(A[b,:]) == 0 && return false
+    end
+    return true
+  end
+  nca = ncols(A)
+  nra = nrows(A)
+  if nca == nra
+    return Polymake.tropical.tsgn(A) != 0
+  elseif nra>nca
+    return helper(A,nra,nca)
+  else 
+    return helper(transpose(A),nca,nra)
+  end
+end

src/exports.jl

@@ -882,6 +882,7 @@ export is_total
 export is_transitive
 export is_transverse_intersection
 export is_trivial
+export is_tropically_generic
 export is_two_sided
 export is_unipotent
 export is_unit
@@ -1478,6 +1479,7 @@ export transportation_polytope
 export trivial_character
 export trivial_divisor
 export trivial_divisor_class
+export trivial_line_bundle
 export trivial_morphism
 export trivial_subgroup, has_trivial_subgroup, set_trivial_subgroup
 export tropical_matrix

test/TropicalGeometry/matrix.jl

@@ -9,3 +9,11 @@
     end
 
 end
+
+@testset "tropical general position" begin
+  A = matrix(tropical_semiring(),[1 0;0 1])
+  @test is_tropically_generic(A) == true
+  A = matrix(tropical_semiring(max),[1 5;0 0;0 0])
+  @test is_tropically_generic(A) == false
+  @test is_tropically_generic(transpose(A)) == false
+end