ToricVarieties bugfix: is_effective(ToricDivisor)

It checks if a divisor is lin. equivalent to an effective divisor.
But it should check if the divisor is effective.

docs/src/ToricVarieties/ToricDivisorClasses.md

@@ -43,6 +43,10 @@ Equality of toric divisor classes can be tested via `==`.
 
 To check if a toric divisor class is trivial, one can invoke `is_trivial`.
 
+```@docs
+is_effective(tdc::ToricDivisorClass)
+```
+
 
 ## Attributes
 

docs/src/ToricVarieties/ToricDivisors.md

@@ -57,6 +57,7 @@ is_ample(td::ToricDivisor)
 is_basepoint_free(td::ToricDivisor)
 is_cartier(td::ToricDivisor)
 is_effective(td::ToricDivisor)
+is_linearly_equivalent_to_effective_toric_divisor(td::ToricDivisor)
 is_integral(td::ToricDivisor)
 is_nef(td::ToricDivisor)
 is_prime(td::ToricDivisor)

src/ToricVarieties/ToricDivisorClasses/properties.jl

@@ -1,2 +1,30 @@
 @attr Bool is_trivial(tdc::ToricDivisorClass) = iszero(divisor_class(tdc))
 export is_trivial
+
+
+@doc Markdown.doc"""
+    is_effective(tdc::ToricDivisorClass)
+
+Determines whether the toric divisor class `tdc` is effective, that is if a toric divisor
+in this divisor class is linearly equivalent to an effective toric divisor.
+
+# Examples
+```jldoctest
+julia> P2 = projective_space(NormalToricVariety,2)
+A normal, non-affine, smooth, projective, gorenstein, fano, 2-dimensional toric variety without torusfactor
+
+julia> tdc = ToricDivisorClass(P2, [1])
+A divisor class on a normal toric variety
+
+julia> is_effective(tdc)
+true
+
+julia> tdc2 = ToricDivisorClass(P2, [-1])
+A divisor class on a normal toric variety
+
+julia> is_effective(tdc2)
+false
+```
+"""
+@attr Bool is_effective(tdc::ToricDivisorClass) = is_effective(toric_divisor(tdc))
+export is_effective

src/ToricVarieties/ToricDivisors/properties.jl

@@ -67,24 +67,55 @@ export is_basepoint_free
 @doc Markdown.doc"""
     is_effective(td::ToricDivisor)
 
-Determine whether the toric divisor `td` is effective.
+Determine whether the toric divisor `td` is effective,
+i.e. if all of its coefficients are non-negative.
 
 # Examples
 ```jldoctest
-julia> F4 = hirzebruch_surface(4)
-A normal, non-affine, smooth, projective, gorenstein, non-fano, 2-dimensional toric variety without torusfactor
+julia> P2 = projective_space(NormalToricVariety,2)
+A normal, non-affine, smooth, projective, gorenstein, fano, 2-dimensional toric variety without torusfactor
 
-julia> td = ToricDivisor(F4, [1,0,0,0])
-A torus-invariant, prime divisor on a normal toric variety
+julia> td = ToricDivisor(P2, [1,-1,0])
+A torus-invariant, non-prime divisor on a normal toric variety
 
 julia> is_effective(td)
+false
+
+julia> td2 = ToricDivisor(P2, [1,2,3])
+A torus-invariant, non-prime divisor on a normal toric variety
+
+julia> is_effective(td2)
 true
 ```
 """
-@attr Bool is_effective(td::ToricDivisor) = pm_tdivisor(td).EFFECTIVE
+@attr Bool is_effective(td::ToricDivisor) = all(c -> (c >= 0), coefficients(td))
 export is_effective
 
 
+@doc Markdown.doc"""
+    is_linearly_equivalent_to_effective_toric_divisor(td::ToricDivisor)
+
+Determine whether the toric divisor `td` is linearly equivalent to an effective toric divisor.
+
+# Examples
+```jldoctest
+julia> P2 = projective_space(NormalToricVariety,2)
+A normal, non-affine, smooth, projective, gorenstein, fano, 2-dimensional toric variety without torusfactor
+
+julia> td = ToricDivisor(P2, [1,-1,0])
+A torus-invariant, non-prime divisor on a normal toric variety
+
+julia> is_effective(td)
+false
+
+julia> is_linearly_equivalent_to_effective_toric_divisor(td)
+true
+```
+"""
+@attr Bool is_linearly_equivalent_to_effective_toric_divisor(td::ToricDivisor) = pm_tdivisor(td).EFFECTIVE
+export is_linearly_equivalent_to_effective_toric_divisor
+
+
 @doc Markdown.doc"""
     is_integral(td::ToricDivisor)
 

test/ToricVarieties/divisor_classes.jl

@@ -2,19 +2,24 @@
 
     F5 = NormalToricVariety([[1, 0], [0, 1], [-1, 5], [0, -1]], [[1, 2], [2, 3], [3, 4], [4, 1]])
     dP3 = NormalToricVariety([[1, 0], [1, 1], [0, 1], [-1, 0], [-1, -1], [0, -1]], [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 1]])
+    P2 = projective_space(NormalToricVariety,2)
     DC = ToricDivisorClass(F5, [fmpz(0), fmpz(0)])
     DC2 = ToricDivisorClass(F5, [1, 2])
     DC3 = ToricDivisorClass(dP3, [4, 3, 2, 1])
     DC4 = canonical_divisor_class(dP3)
     DC5 = anticanonical_divisor_class(dP3)
     DC6 = trivial_divisor_class(dP3)
-
+    DC7 = ToricDivisorClass(P2, [1])
+    DC8 = ToricDivisorClass(P2, [-1])
+
     @testset "Basic properties" begin
         @test is_trivial(toric_divisor(DC2)) == false
         @test rank(parent(divisor_class(DC2))) == 2
         @test dim(toric_variety(DC2)) == 2
+        @test is_effective(DC7) == true
+        @test is_effective(DC8) == false
     end
-
+    
     @testset "Arithmetic" begin
         @test is_trivial(fmpz(2)*DC+DC2) == false
         @test is_trivial(2*DC-DC2) == false

test/ToricVarieties/divisors.jl

@@ -2,13 +2,17 @@
 
     F5 = NormalToricVariety([[1, 0], [0, 1], [-1, 5], [0, -1]], [[1, 2], [2, 3], [3, 4], [4, 1]])
     dP3 = NormalToricVariety([[1, 0], [1, 1], [0, 1], [-1, 0], [-1, -1], [0, -1]], [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 1]])
+    P2 = projective_space(NormalToricVariety,2)
     D=ToricDivisor(F5, [0, 0, 0, 0])
     D2 = DivisorOfCharacter(F5, [1, 2])
     D3 = ToricDivisor(dP3, [1, 0, 0, 0, 0, 0])
     D4 = canonical_divisor(dP3)
     D5 = anticanonical_divisor(dP3)
     D6 = trivial_divisor(dP3)
-
+    D7 = ToricDivisor(P2, [1,1,0])
+    D8 = ToricDivisor(P2, [1,-1,0])
+    D9 = ToricDivisor(P2, [0,-1,0])
+
     @testset "Should fail" begin
         @test_throws ArgumentError ToricDivisor(F5, [0, 0, 0])
         @test_throws ArgumentError D+D3
@@ -43,6 +47,11 @@
         @test is_prime(D2) == false
         @test coefficients(D2) == [1, 2, 9, -2]
         @test is_prime(D3) == true
+        @test is_effective(D7) ==  true
+        @test is_effective(D8) ==  false
+        @test is_linearly_equivalent_to_effective_toric_divisor(D7) == true
+        @test is_linearly_equivalent_to_effective_toric_divisor(D8) == true
+        @test is_linearly_equivalent_to_effective_toric_divisor(D9) == false
     end
 
     @testset "Arithmetic" begin