Computing tropical varieties over fields with valuation

Computing tropical varieties involves a lot of computation in commutative algebra. However, while existing well-established tools of computer algebra come in handy where the valuation can be ignored, they prove to be, at first glance, insufficient where the valuation cannot be ignored. Therefore, recent works, most notably those by Diane Maclagan and Andrew Chan, have been modifying these classical algorithms in order to cope with the new setting.

This talk will present an alternative approach to the dilemma. We will show that a tropical variety of a polynomial ideal over a field with valuation is always isomorphic to the intersection of a tropical variety of another ideal over a ring without valuation and a hyperplane. Computing the tropical variety of the new ideal, albeit more complex than the
original ideal, can in turn be done via the classical means of computer algebra.