New Complexity Bounds for Certain Real Fewnomial Zero Sets

d Abstract) Frederic Bihan∗ Joel Gomez† Andrew Niles‡ J. Maurice Rojas§ January 24, 2007 Rojas dedicates this paper to his friend, Professor Tien-Yien Li. Consider real bivariate polynomials f and g, respectively having 3 and m monomial terms. We prove that for all m≥3, there are systems of the form (f, g) having exactly 2m − 1 roots in the positive quadrant. Even examples with m=4 having 7 positive roots were unknown before this paper, so we detail an explicit example of this form. We also present an O(n11 ) upper bound for the number of diffeotopy types of the real zero set of an n-variate polynomial with n + 4 monomial terms.

• Type: Journal
• Year: 2007
• Where: CORR
• Authors: Joel Gomez, Andrew Niles, J. Maurice Rojas
• Keywords: CORR 2007, Education, Frederic Bihan∗ Joel, Gomez Andrew Niles‡, Real Bivariate Polynomials