Metric invariants of tropical conics and factorization of degree–two homogeneous tropical polynomials in three variables

  • M. Ansola
  • Published 2008

Abstract

To every tropical conic we associate a certain non–negative symmetric 3 × 3 real matrix. The non–diagonal entries of this matrix are metric invariants of the given tropical conic, up to translation. There exist proper and improper tropical conics, pairs of lines being a particular sort of the latter. We characterize those tropical conics whose associated matrix is tropically singular. Again, pairs of lines are among the latter. A tropical conic is defined by an arbitrary degree–two homogeneous tropical polynomial in three variables. The conic is a tree of a very particular kind. Given such a tree, we give a procedure to obtain a defining tropical polynomial. Finally, we give criteria to decide whether a tropical degree–two homogeneous polynomial in three variables is reducible and, if so, we find a factorization. 2000 Math. Subj. Class.: 05C05; 12K99

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Cite this paper

@inproceedings{Ansola2008MetricIO, title={Metric invariants of tropical conics and factorization of degree–two homogeneous tropical polynomials in three variables}, author={M. Ansola}, year={2008} }