Added a symmetry test for maximal cones of trop(CM2)

(currently fails for n=5)

Author: Anton Leykin

Rigidity/CayleyMenger-tests.m2

@@ -9,3 +9,35 @@ maximalCones = apply(maximalPairs,
     p->apply(raysOfTreePairCone(p_0,p_1),v->v_GIndices));
 assert(toString max maximalPairs == "{x_1*x_2*x_3*x_4+x_1*x_2*x_3+x_1*x_2, x_1*x_2*x_3*x_4+x_1*x_3+x_2*x_4}")
 ///
+
+TEST ///
+permutationOfDoubleIndices = (p,G) -> apply(G, l->position(G,l' -> sort p_l' == l))
+checkInvariance = perm -> (
+    n := #perm;
+    G := subsets(1..n,2);
+    GIndices := edgeListToIndices(G,n);
+    maximalPairs := maximalTreePairs(n);
+    maximalCones = apply(maximalPairs,
+	p->apply(raysOfTreePairCone(p_0,p_1),v->v_GIndices));
+    lookupSet = maximalCones/toCompare//set;
+    p := permutationOfDoubleIndices(perm,apply(G,p->p-{1,1})); -- need to decrease indices by 1
+    wrong := select(#maximalCones, i->(
+	    c := maximalCones#i;
+	    c' := c/(r->r_p);
+	    not member(toCompare c', lookupSet)
+	    ));
+    wrong
+    )
+
+perm = {3,0,1,2}
+toCompare = set; -- comparison as sets holds for n=4
+wrong = checkInvariance perm
+assert isEmpty wrong
+
+-* FAILS!!!
+perm = {4,0,1,2,3}
+toCompare = c -> mingens image transpose matrix(QQ,c);
+wrong = checkInvariance perm
+assert isEmpty wrong
+*-
+///

Rigidity/Examples/tropCM2-examples.m2

@@ -1,16 +1,25 @@
-
+-----------------------------
+-- maximal cones
+-----------------------------
 n=5;
 G={{1,2},{2,3},{3,4},{1,4},{1,5},{2,5},{3,5},{4,5}};
 
---n=7;
---G={{1,5},{1,6},{1,7},{2,5},{2,6},{2,7},{3,5},{3,6},{3,7},{4,5},{4,6},{4,7}};
+-* ... one may pick one of these ... 
+n=6;
+G=subsets(1..n,2) -- takes long time
+
+n=7;
+G={{1,5},{1,6},{1,7},{2,5},{2,6},{2,7},{3,5},{3,6},{3,7},{4,5},{4,6},{4,7}};
+*-
 
 GIndices=edgeListToIndices(G,n);
-maximalPairs = maximalTreePairs(n);
-maximalCones = apply(maximalPairs,
+time maximalPairs = maximalTreePairs(n);
+time maximalCones = apply(maximalPairs,
     p->apply(raysOfTreePairCone(p_0,p_1),v->v_GIndices));
 
-
+----------------------------
+-- cones to complete
+----------------------------
 n=4;
 G={{1,2},{2,3},{3,4},{1,4}};
 GIndices=edgeListToIndices(G,n);