Could René Descartes have known this?

2015/01/05 by Forsgard, Jens, Kostov, Vladimir P., Shapiro, Boris
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Primary 26C10 #Secondary 30C15

paper · doi:10.48550/arxiv.1501.00856

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.

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