TropicalGeometry: tropical linear spaces from graphs

docs/src/TropicalGeometry/linear_space.md

@@ -18,6 +18,7 @@ In addition to converting from `TropicalVariety`, objects of type `TropicalLinea
 4. matrices over a field and a tropical semiring map.
     - if matrix over `QQ` and tropical semiring map is trivial, uses an implementation of Rincon's algorithm [Rin13](@cite) in `polymake`
     - for general input, computes minors and uses constructor (2.)
+5. graphs
 ```@docs
 tropical_linear_space
 ```

src/TropicalGeometry/linear_space.jl

@@ -365,6 +365,34 @@ function tropical_linear_space(I::MPolyIdeal, nu::Union{Nothing,TropicalSemiring
 end
 
 
+@doc raw"""
+    tropical_linear_space(G::Graph, nu::TropicalSemiringMap; weighted_polyhedral_complex_only::Bool=false)
+
+Return the Bergman fan of the graphic matroid of `G` as a tropical linear space, the tropical semiring map `nu` is used to fix the convention.  If `weighted_polyhedral_complex==true`, will not cache any extra information.
+
+# Examples
+```jldoctest
+julia> G = complete_graph(4)
+Undirected graph with 4 nodes and the following edges:
+(2, 1)(3, 1)(3, 2)(4, 1)(4, 2)(4, 3)
+
+julia> tropical_linear_space(G)
+Min tropical linear space
+
+```
+"""
+function tropical_linear_space(G::Graph, nu::Union{Nothing,TropicalSemiringMap}=nothing; weighted_polyhedral_complex_only::Bool=false)
+    M = zero_matrix(QQ,nv(G),ne(G))
+    for (i,edge) in enumerate(edges(G))
+        M[src(edge),i] = 1
+        M[dst(edge),i] = -1
+    end
+    TropG = tropical_linear_space(M,nu;weighted_polyhedral_complex_only=weighted_polyhedral_complex_only)
+    if !weighted_polyhedral_complex_only
+        set_attribute!(TropG,:graph,G)
+    end
+    return TropG
+end
 
 ###############################################################################
 #

test/TropicalGeometry/linear_space.jl

@@ -32,4 +32,10 @@
         @test issetequal(plueckerVector,tropical_pluecker_vector(TropL))
     end
 
+    @testset "tropical linear space from graphs" begin
+        G = complete_graph(3)
+        TropG = tropical_linear_space(G)
+        @test f_vector(TropG) == [0,1,3]
+    end
+
 end