Computing of tropical sequences associated with Somos sequences in the Gfan package
Abstract
This paper examines tropical recurrent sequences associated with Somos sequences. The classical Somos sequences have applications in the theory of elliptic curves. Due to the Laurent character of the classical sequences, a pattern can be inferred between the classical sequences and their tropical counterparts.
The greatest interest is the increase in the dimension of the solution space of tropical sequences depending on the length of the final sequence. For a set of tropical sequences described by tropical recurrence relations, D.Yu.Grigoriev put forward a hypothesis about the stabilization of the maximum dimensions of the components of the corresponding tropical prevarieties. This hypothesis has been proven for tropical linear recurrent sequences. As part of this work, for tropical recurrent sequences associated with the sequences Somos-4 and Somos-5, the corresponding tropical prevarieties were investigated using the Gfan package in order to test Grigoriev's hypothesis.
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