6 citations · 9 across the 2 of their papers we have counts for
4 papers
First Steps in Algorithmic Fewnomial Theory
Frederic Bihan, J. Maurice Rojas, Casey E. Stella
Fewnomial theory began with explicit bounds -- solely in terms of the number of variables and monomial terms -- on the number of real roots of systems of polynomial equations. Here…
A Direct Ultrametric Approach to Additive Complexity and the Shub-Smale Tau Conjecture
J. Maurice Rojas
The Shub-Smale Tau Conjecture is a hypothesis relating the number of integral roots of a polynomial f in one variable and the Straight-Line Program (SLP) complexity of f. A consequ…
Dedekind Zeta Functions and the Complexity of Hilbert's Nullstellensatz
J. Maurice Rojas
Let HN denote the problem of determining whether a system of multivariate polynomials with integer coefficients has a complex root. It has long been known that HN in P implies P=NP…
Counting Real Connected Components of Trinomial Curve Intersections and m-nomial Hypersurfaces
Tien-Yien Li, J. Maurice Rojas, Xiaoshen Wang
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 were much…