Here is an example that I would be interested in printing, a faithful tropicalization of a plane quartic curve that cannot be faithfully tropicalized if embedded into the plane (because the edge lengths violates some inequalities in https://arxiv.org/abs/1409.4395):

Code: Select all

```
application "tropical";
$f = toTropicalPolynomial("max(y,z,w+0*x)");
$Vf = new Hypersurface<Max>(POLYNOMIAL=>$f);
$g = toTropicalPolynomial("max((-18)+4w+0z,(-6)+x+3w,2x+2w,(-24)+4x,(-11)+y+3w,x+y+2w,2x+y+w,(-8)+2y+2w,(-3)+x+2y+w,2x+2y,(-12)+3y+w,(-8)+x+3y,(-18)+4y)");
$Vg = new Hypersurface<Max>(POLYNOMIAL=>$g);
$g1 = toTropicalPolynomial("max((-8)+4w+0y,x+3w,(-24)+4x,(-8)+z+3w,x+z+2w,(-2)+2x+z+w,(-8)+2z+2w,(-3)+x+2z+w,2x+2z,(-12)+3z+w,(-8)+x+3z,(-18)+4z)");
$Vg1 = new Hypersurface<Max>(POLYNOMIAL=>$g1);
$Vgg1 = set_theoretic_intersection($Vg,$Vg1);
$Wgg1 = new Cycle<Max>(VERTICES=>thomog($Vgg1->VERTICES), MAXIMAL_POLYTOPES=>$Vgg1->MAXIMAL_POLYTOPES);
$Vfgg1 = set_theoretic_intersection($Vf,$Wgg1);
$Wfgg1 = new Cycle<Max>(VERTICES=>thomog($Vfgg1->VERTICES), MAXIMAL_POLYTOPES=>$Vfgg1->MAXIMAL_POLYTOPES);
visualize_in_surface($Vf,$Wfgg1);
```