Computing Tropical Varieties over Fields with Valuation
نویسندگان
چکیده
We show how tropical varieties of ideals I E K[x] over a field K with non-trivial valuation can always be traced back to tropical varieties of ideals π−1I E RJtK[x] over some dense subring R in its ring of integers. Moreover, for homogeneous ideals, we present algorithms on how the latter can be computed in finite time, provided that π−1I is generated by elements in R[t, x]. While doing so, we also comment on the computation of the Gröbner polytope structure and p-adic Gröbner bases using our framework.
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