A Gr\"obner basis computation for the Weyl algebra with respect to a tropical term order and by using a homogenization-dehomogenization technique is sufficiently sluggish. A significant number of reductions to zero occur. To improve the computation, a tropical F5 algorithm is developed for this context. As a member of the family of signature-based algorithms, this algorithm keeps track of where Weyl algebra elements come from to anticipate reductions to zero. The total order for ordering module monomials or signatures in this paper is designed as close as possible to the definition of the tropical term order. As in Vaccon et al. (2021), this total order is not compatible with the tropical term order.

翻译：针对Weyl代数在热带项序下采用齐次化-去齐次化技术的Gröbner基计算存在效率显著低下的问题，其间会产生大量零化约化。为提升计算性能，本文在该背景下提出了一种热带F5算法。作为签名基算法族成员，该算法通过追踪Weyl代数元素的来源以预判零化约化。本文对模单项或签名进行排序所采用的全序，被设计为尽可能贴近热带项序的定义方式。与Vaccon等人(2021)的研究一致，该全序与热带项序并不相容。