Tropical geometry is a combinatorial counterpart of algebraic geometry, transforming polynomials into piecewise linear functions and their solutions (varieties) into polyhedral fans. This transformation is intricately linked to the concept of Grobner bases, which provide a powerful tool in computational algebra. Specifically, all possible Grobner bases of an ideal are encoded within a polyhedral fan, with the tropical variety appearing as a subfan. Despite its significance, the computational complexity of tropical varieties often limits computations to small-scale instances. In this talk, we introduce a geometric approach that enables the effective computation of various points within tropical varieties. One application of this method is the computation of toric degenerations, which are important objects in algebraic geometry. These degenerations can be modeled on polytopes, and there exists a dictionary between their geometric properties and the combinatorial invariants of the corresponding polytopes. This dictionary can be extended from toric varieties to arbitrary varieties through toric degenerations.

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