TropAJ: Tropical Abel--Jacobi Transform of Metric Graphs

TropAJ is a Python repository for computing the tropical Abel--Jacobi transform of a metric graph and tropical distances on its tropical Jacobian. This repository also contains source codes for experiments in the paper

Computing the Tropical Abel--Jacobi Transform and Tropical Distances for Metric Graphs

Tutorial

Some tutorials about the tropical Abel--Jacobi transform and this repository are included in notebooks.

Package Dependence

The repository depends on several Python libraries from different scientific fields. For your purpose it is not necessary to install all of them.

• The computation of tropical Abel--Jacobi transform depends on NetworkX;
• The computation of tropical polarization distance depends on fplll and G6K (not available on Windows system);
• The computation of Foster--Zhang distance depends on Pyomo, and any MIP solver (in the paper, Cbc, Ipopt, GLPK, SCIP are tested).

Usage

The repository is organized as follows:

• src contains modules for tropical transform and tropical distances:
  • mgraph.py: metric graph class, with functions for operations on metric graphs and computations of the tropical Abel--Jacobi transform
  • tropdist: functions for computations of tropical distances
• notebooks contains jupyter notebook tutorials:
  • tropical transform: tutorial of tropical Abel--Jacobi transform
  • tropical distances: tutorial of tropical distances on the tropical Jacobian
• scripts contains source codes for experiments in the original paper:
  • fplll_l2_dist.py: computation using fplll
  • g6k_l2_dist.py: computation using g6k
  • fs_dist.py: computation using MIP solvers
  • babai_dist_time.py and babai_dist_error.py: computation using Babai's algorithms
• data contains numerical outputs of experiments in the original paper

Academic Use

You can use the following BibTex entry:

@misc{cao2025computingtropicalabeljacobitransform,
      title={Computing the Tropical Abel--Jacobi Transform and Tropical Distances for Metric Graphs}, 
      author={Yueqi Cao and Anthea Monod},
      year={2025},
      eprint={2504.11619},
      archivePrefix={arXiv},
      primaryClass={math.AG},
      url={https://arxiv.org/abs/2504.11619}, 
}

Contact

If you are interested in this work, or if you find any bug in the code, please contact y.cao21@imperial.ac.uk