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.
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