English

Could Ren\'e Descartes have known this?

Classical Analysis and ODEs 2015-01-06 v1

Abstract

Below we discuss the partition of the space of real univariate polynomials according to the number of positive and negative roots and signs of the coefficients. We present several series of non-realizable combinations of signs together with the numbers of positive and negative roots. We provide a detailed information about possible non-realizable combinations as above up to degree 8 as well as a general conjecture about such combinations.

Keywords

Cite

@article{arxiv.1501.00856,
  title  = {Could Ren\'e Descartes have known this?},
  author = {Jens Forsgard and Vladimir P. Kostov and Boris Shapiro},
  journal= {arXiv preprint arXiv:1501.00856},
  year   = {2015}
}

Comments

15 pages, no figures

R2 v1 2026-06-22T07:51:06.965Z