Counting Isolated Roots of Trinomial Systems in the Plane and Beyond
| dc.creator | Li, Tien-Yien | |
| dc.creator | Rojas, J. Maurice | |
| dc.creator | Wang, Xiaoshen | |
| dc.date | 2000-08-09 | |
| dc.date | 2001-05-29 | |
| dc.date.accessioned | 2026-07-07T04:36:42Z | |
| dc.date.available | 2026-07-07T04:36:42Z | |
| dc.description | We prove that any pair of bivariate trinomials has at most 5 isolated roots in the positive quadrant. The best previous upper bounds independent of the polynomial degrees counted only non-degenerate roots and even then gave much larger bounds, e.g., 248832 via a famous general result of Khovanski. Our bound is sharp, allows real exponents, and extends to certain systems of n-variate fewnomials, giving improvements over earlier bounds by a factor exponential in the number of monomials. We also derive new bounds on the number of real connected components of fewnomial hypersurfaces. | |
| dc.description | 18 pages, submitted for publication. Further streamlining and clarifications made. There is also a new figure illustrating the optimality of a variant of Rolles' Theorem we use | |
| dc.identifier | https://arxiv.org/abs/math/0008069 | |
| dc.identifier | http://arxiv.org/abs/math/0008069 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/59698 | |
| dc.subject | Combinatorics | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Primary 34C08; Secondary 14P05,30C15 | |
| dc.title | Counting Isolated Roots of Trinomial Systems in the Plane and Beyond | |
| dc.type | text |