TropicalGeometry: tests for varieties and bugfixes

oscar-system · Oct 19, 2023 · 7071095 · 7071095
1 parent cbc4697
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Showing 4 changed files with 46 additions and 86 deletions.
diff --git a/src/TropicalGeometry/linear_space.jl b/src/TropicalGeometry/linear_space.jl
@@ -240,8 +240,7 @@ Min tropical linear space
 
 ```
 """
-function tropical_linear_space(A::Union{Matrix{T},MatElem{T}};
-                               weighted_polyhedral_complex_only::Bool=false) where T <: TropicalSemiringElem
+function tropical_linear_space(A::Union{Matrix{T},MatElem{T}}; weighted_polyhedral_complex_only::Bool=false) where {T<:TropicalSemiringElem}
     # convert to Oscar matrix (necessary for AbstractAlgebra.minors)
     if A isa Matrix
         A = matrix(parent(first(A)),A)
@@ -278,8 +277,11 @@ Min tropical linear space
 
 ```
 """
-function tropical_linear_space(A::MatElem, nu::TropicalSemiringMap;
+function tropical_linear_space(A::MatElem, nu::Union{Nothing,TropicalSemiringMap}=nothing;
                                weighted_polyhedral_complex_only::Bool=false)
+    # initialise nu as the trivial valuation if not specified by user
+    isnothing(nu) && (nu=tropical_semiring_map(coefficient_ring(f)))
+
     n = max(nrows(A), ncols(A))
     k = min(nrows(A), ncols(A))
     plueckerIndices = AbstractAlgebra.combinations(1:n,k)
@@ -315,8 +317,11 @@ Min tropical linear space
 
 ```
 """
-function tropical_linear_space(I::MPolyIdeal, nu::TropicalSemiringMap;
+function tropical_linear_space(I::MPolyIdeal, nu::Union{Nothing,TropicalSemiringMap}=nothing;
                                weighted_polyhedral_complex_only::Bool=false)
+    # initialise nu as the trivial valuation if not specified by user
+    isnothing(nu) && (nu=tropical_semiring_map(coefficient_ring(f)))
+
     x = gens(base_ring(I))
     G = gens(I)
     macaulayMatrix = matrix([[coeff(g,xi) for xi in x] for g in G])

diff --git a/src/TropicalGeometry/variety.jl b/src/TropicalGeometry/variety.jl
@@ -312,7 +312,7 @@ function tropical_variety_binomial(I::MPolyIdeal,nu::TropicalSemiringMap; weight
     ###
     G = groebner_basis(I,complete_reduction=true)
     A = matrix(ZZ,[first(collect(expv))-last(collect(expv)) for expv in exponents.(G)])
-    b = [ QQ(nu(first(collect(coeff))/last(collect(coeff)))) for coeff in coefficients.(G)]
+    b = [ QQ(nu(last(collect(coeff))/first(collect(coeff)))) for coeff in coefficients.(G)]
 
     ###
     # Compute tropical variety multiplicity

diff --git a/test/TropicalGeometry/hypersurface.jl b/test/TropicalGeometry/hypersurface.jl
diff --git a/test/TropicalGeometry/variety.jl b/test/TropicalGeometry/variety.jl
@@ -1,44 +1,44 @@
 @testset "src/TropicalGeometry/{variety,hypersurface,curve,linear_space}.jl" begin
 
-    # no dedicated tests for variety.jl
-    # will be tested inside the following testsets
-
-    @testset "hypersurface.jl" begin
-        # semiring min
-        T = tropical_semiring()
-        R,(x,y) = T["x","y"]
-        f = x^3+y^3+1*x*y+0
-        TropH = tropical_hypersurface(f)
-        S,(x,y) = QQ["x","y"];
-        TropV = first(tropical_variety(ideal(S,[x^3+y^3+1]))) # default trivial valuation, min convention
-        @test issetequal(vertices_and_rays(TropH),vertices_and_rays(TropV))
-        @test n_maximal_polyhedra(TropH)==3
-
-        # semiring max
-        T = tropical_semiring(max)
-        R,(x,y) = T["x","y"]
-        f = x^3+y^3+(-1)*x*y+0
-        TropH = tropical_hypersurface(f)
-        S,(x,y) = QQ["x","y"];
-        nu = tropical_semiring_map(QQ,max)
-        TropV = first(tropical_variety(ideal(S,[x^3+y^3+1]),nu))
-        @test issetequal(vertices_and_rays(TropH),vertices_and_rays(TropV))
-        @test n_maximal_polyhedra(TropH)==3
+    # constructing various tropicalizations two ways
+    # and comparing their results
+    @testset "hypersurface and linear spaces" begin
+        R,(x,y,z) = QQ["x","y","z"]
+        f = x+2*y+4*z
+        nu = tropical_semiring_map(QQ,2)
+        TropH = tropical_hypersurface(f,nu)
+        TropL = tropical_linear_space(ideal(R,f),nu)
+        @test issetequal(maximal_polyhedra(TropH),maximal_polyhedra(TropL))
+        nu = tropical_semiring_map(QQ,2,max)
+        TropH = tropical_hypersurface(f,nu)
+        TropL = tropical_linear_space(ideal(R,f),nu)
+        @test issetequal(maximal_polyhedra(TropH),maximal_polyhedra(TropL))
+    end
 
-        # trivial, min
-        R,(x,y) = QQ["x","y"]
-        f = x^3+y^3+x*y+0
-        TropH = tropical_hypersurface(f)
-        TropV = first(tropical_variety(f))
-        issetequal(vertices_and_rays(TropH),vertices_and_rays(TropV))
-        n_maximal_polyhedra(TropH)==3
+    @testset "binomial ideals and linear spaces" begin
+        R,(x,y,z,w) = QQ["x","y","z","w"]
+        I = ideal(R,[x+2*y,z+4*w])
+        nu = tropical_semiring_map(QQ,2)
+        TropV = first(tropical_variety(I,nu))
+        TropL = tropical_linear_space(I,nu)
+        @test issetequal(maximal_polyhedra(TropV),maximal_polyhedra(TropL))
+        nu = tropical_semiring_map(QQ,2,max)
+        TropV = first(tropical_variety(I,nu))
+        TropL = tropical_linear_space(I,nu)
+        @test issetequal(maximal_polyhedra(TropV),maximal_polyhedra(TropL))
+    end
 
-        # trivial, max
-        nu = tropical_semiring_map(QQ,max)
+    @testset "hypersurface and binomial ideals" begin
+        R,(x,y,z) = QQ["x","y","z"]
+        f = x*y*z+2
+        nu = tropical_semiring_map(QQ,2)
+        TropH = tropical_hypersurface(f,nu)
+        TropV = first(tropical_variety(ideal(R,f),nu))
+        @test issetequal(maximal_polyhedra(TropH),maximal_polyhedra(TropV))
+        nu = tropical_semiring_map(QQ,2,max)
+        TropV = first(tropical_variety(ideal(R,f),nu))
         TropH = tropical_hypersurface(f,nu)
-        TropV = first(tropical_variety(f,nu))
-        issetequal(vertices_and_rays(TropH),vertices_and_rays(TropV))
-        n_maximal_polyhedra(TropH)==3
+        @test issetequal(maximal_polyhedra(TropH),maximal_polyhedra(TropV))
     end
 
 end