Tropical Differential Gröbner Bases

Abstract

In this paper, the concept of tropical differential Grobner basis is introduced, which is a natural generalization of the tropical Grobner basis to the recently introduced tropical differential algebra. Like the differential Grobner basis, the tropical differential Grobner basis generally contains an infinite number of elements. We give a Buchberger style criterion for the tropical differential Grobner basis. For differential ideals generated by homogeneous linear differential polynomials with constant coefficients, we give a complete algorithm to compute the finite tropical differential Grobner basis.