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).
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