Stable intersection not contained in set-theoretic intersection
Posted: 11 Jun 2021, 13:03
Hi,
I have a question about the "intersect" and "set_theoretic_intersection" commands in polymake. I made an example down below with two tropical hypersurfaces in R^{4}. Polymake then tells me that their stable intersection is two-dimensional, whereas their set-theoretic intersection is one-dimensional. Is polymake by any chance removing a lineality space in the set-theoretic intersection or?
The corresponding code is as follows:
Thanks in advance!
I have a question about the "intersect" and "set_theoretic_intersection" commands in polymake. I made an example down below with two tropical hypersurfaces in R^{4}. Polymake then tells me that their stable intersection is two-dimensional, whereas their set-theoretic intersection is one-dimensional. Is polymake by any chance removing a lineality space in the set-theoretic intersection or?
The corresponding code is as follows:
Code: Select all
application "tropical";
$f1 = toTropicalPolynomial("min(a+b+c-20,b+c+w+5,d+2*b+1,c+2*w)", qw( a b c d w ));
$f2 = toTropicalPolynomial("min(2*a+b-5,a+b+w+3,2*b+w-2,b+c+w+10)", qw( a b c d w ));
$V1 = new Hypersurface<Min>(POLYNOMIAL=>$f1);
$V2 = new Hypersurface<Min>(POLYNOMIAL=>$f2);
$W12 = set_theoretic_intersection($V1,$V2);
$V12 = intersect($V1,$V2);
print $W12->DIM;
print $V12->DIM;
Thanks in advance!