7 citations · 19 across the 4 of their papers we have counts for
7 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…
Additive Complexity and the Roots of Polynomials Over Number Fields and p-adic Fields
J. Maurice Rojas
Consider any nonzero univariate polynomial with rational coefficients, presented as an elementary algebraic expression (using only integer exponents). Letting sigma(f) denotes the…
Finiteness for Arithmetic Fewnomial Systems
J. Maurice Rojas
Suppose L is any finite algebraic extension of either the ordinary rational numbers or the p-adic rational numbers. Also let g_1,...,g_k be polynomials in n variables, with coeffic…