English

Tropical Newton-Puiseux polynomials

Algebraic Geometry 2018-11-08 v3

Abstract

We introduce tropical Newton-Puiseux polynomials admitting rational exponents. A resolution of a tropical hypersurface is defined by means of a tropical Newton-Puiseux polynomial. A polynomial complexity algorithm for resolubility of a tropical curve is designed. The complexity of resolubility of tropical prevarieties of arbitrary codimensions is studied. Tropical Newton-Puiseux rational functions are introduced, and we prove that any tropical polynomial has a resolution in tropical Newton-Puiseux rational functions (this can be treated as a tropical analog of the algebraic closedness of the field of Newton-Puiseux series).

Keywords

Cite

@article{arxiv.1704.03842,
  title  = {Tropical Newton-Puiseux polynomials},
  author = {Dima Grigoriev},
  journal= {arXiv preprint arXiv:1704.03842},
  year   = {2018}
}

Comments

Conference Computer Algebra in Scientific Computing, Lille. 2018, Lect. Notes Comput. Sci. vol. 11077

R2 v1 2026-06-22T19:15:55.092Z