TropicalGeometry: added stable intersection linear spaces

src/TropicalGeometry/intersection.jl

@@ -37,9 +37,14 @@ function intersect_stably(TropV1::TropicalVarietySupertype{minOrMax,true}, TropV
     # return Sigma12,mults12
 end
 
+# SUGGESTION: Add this to PolyhedralGeometry
+function isempty(sigma::Polyhedron)
+    return dim(sigma)<0
+end
+
 function intersect_after_perturbation(sigma1::Polyhedron, sigma2::Polyhedron, perturbation::Vector{Int})
 
-    if dim(intersect(sigma1,sigma2))<0
+    if isempty(intersect(sigma1,sigma2))
         return false
     end
 
@@ -85,3 +90,32 @@ function tropical_intersection_multiplicity(sigma1::Polyhedron,sigma2::Polyhedro
     snfB12 = snf(vcat(B1,B2))
     return abs(prod([snfB12[i,i] for i in 1:ncols(snfB12)]))
 end
+
+
+# Todo: make this use algebraic_pluecker_vector if available
+# Problem: the +/- in the formula of speyers paper
+function intersect_stably(TropL1::TropicalLinearSpace{minOrMax,true}, TropL2::TropicalLinearSpace{minOrMax,true}) where minOrMax
+
+    plueckerIndices12 = Vector{Int}[]
+    plueckerVector12 = TropicalSemiringElem{typeof(minOrMax)}[]
+    d = codim(TropL1)+codim(TropL2)
+
+    for (I1,p1) in zip(pluecker_indices(TropL1),tropical_pluecker_vector(TropL1))
+        for (I2,p2) in zip(pluecker_indices(TropL2),tropical_pluecker_vector(TropL2))
+            I12 = intersect(I1,I2)
+            if length(I12)>d
+                continue
+            end
+
+            i = searchsortedfirst(plueckerIndices12,I12)
+            if i<=length(plueckerIndices12) && plueckerIndices12[i]==I12
+                plueckerVector12[i] += p1*p2
+            else
+                insert!(plueckerIndices12,i,I12)
+                insert!(plueckerVector12,i,p1*p2)
+            end
+        end
+    end
+
+    return tropical_linear_space(plueckerIndices12,plueckerVector12)
+end