In this work we consider the matrices M whose entries are constant degree polynomials. One again wants to compute the rank of M over the rational function field F(x1,x2,...,xn). This can be used to compute the transcendence degree of any set of constant degree polynomials by using the Jacobian criterion. We describe a deterministic PTAS for the rank of M (when the entries of M are constant degree polynomials). This naturally generalizes the results of BJP17.
This is based on joint work with Vishwas Bhargava (Rutgers University), Markus Bläser (Saarland University) and Anurag Pandey (Max-Planck-Institut für Informatik).
[BJP17] : Markus Bläser, Gorav Jindal, and Anurag Pandey. Greedy strikes again: A deterministic PTAS for commutative rank of matrix spaces. In Proc. 32nd IEEE Conf. on Computational Complexity (CCC'17), volume 79 of LIPIcs, pages 33:1-33:16. IEEE Comp. Soc. Press, 2017.