Computing tropical curves via homotopy continuation
Computing tropical curves via homotopy continuation
Anders Jensen, Anton Leykin, and Josephine Yu
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.
- Paper: arXiv.
- Software:
- download and install Macaulay2 (works with version 1.6), PHCpack (2.3.93), and Bertini (1.4),
- make sure these are "on the PATH",
- clone Macaulay2 source code from the github repository antonleykin/M2 (branch NTG):
git clone -b NTG https://github.com/antonleykin/M2.git
In particular, this branch (of the M2 fork) includes NumericalTropicalGeometry.m2.
- make sure M2 packages are loading from the M2/Macaulay2/packages/ directory of the source code above: change "path", e.g.
path = {"directory-where-you-cloned/M2/Macaulay2/packages/"} | path
If you wish to have the line above automatically executed at the beginning of every M2 session, edit init.m2 (located in ~/.Macaulay2/ on Linux systems).
- Examples from the paper: