On affine tropical F5 algorithms

Let K be a field equipped with valuation. Tropical varieties over can defined theory of Gröbner bases taking into account the valuation K. Because use valuation, tropical has proved to provide settings for computations polynomial rings p-adic that are more stable than classical bases. Beforehand, these strategies were only available homogeneous polynomials. In this article, we extend F5 strategy new definition in an affine setting. We also competitor adaptation F4 computations. numerical examples illustrate time-complexity and stability algorithm. its merits as first step before FGLM algorithm compute (classical) lex p-adics.