Computing Tropical Curves via Homotopy Continuation

Abstract

Exploiting a connection between amoebas and tropical curves, we devise a method for computing tropical curves using numerical algebraic geometry and give an implementation. As an application, we use this technique to compute Newton polygons of A-polynomials of knots.

2000 AMS Subject Classification::

• 14T05
• 14Q05

Keywords:

• tropical curves
• homotopy continuation
• numerical algebraic geometry
• tropical geometry