Counting Isolated Roots of Trinomial Systems in the Plane and Beyond

Details Counting Isolated Roots of Trinomial Systems in the Plane and Beyond Counting Isolated Roots of Trinomial Systems in the Plane and Beyond

2000-08-09

arxiv.org/abs/math/0008069v4

Mathematics

Combinatorics

18 pages, submitted for publication. Further streamlining and clarifications made. There is also a new figure illustrating the

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Counting Isolated Roots of Trinomial Systems in the Plane and Beyond does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Counting Isolated Roots of Trinomial Systems in the Plane and Beyond, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Counting Isolated Roots of Trinomial Systems in the Plane and Beyond will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-524247