Computing tropical ranks
The code on this page computes tropical ranks with respect to various tropical varieties. Since it relies on external programs in order to do the actual computational work, you will need to install extra software.
- In order to compute the rank of a matrix with respect to a classical linear space:
- In order to compute the chromatic numbers of the deficiency graph, you will
- Smallk (It should be relatively easy to modify the code for to use a different graph coloring program.)
Download the scripts:
- rank.py: Computes ranks.
- findtreerank.py: Random search to find dissimilarity matrices with large tree rank based on the chromatic number of their deficiency graph.
- paper.sh: Shell script for verifying the computation claims from the paper "Three notions of tropical rank for symmetric matrices." Requires rank.py.
The algorithm for computing the rank of classical secant varieties is implicit in the paper "Tropical secant varieties of linear spaces" by Mike Develin. The construction of deficiency graph is described in "Three notions of tropical rank for symmetric matrices" by Dustin Cartwright and Melody Chan.