9 citations · 16 across the 8 of their papers we have counts for
8 papers
A-Discriminants for Complex Exponents, and Counting Real Isotopy Types
J. Maurice Rojas, Korben Rusek
We extend the definition of -discriminant varieties, and Kapranov's parametrization of -discriminant varieties, to complex exponents. As an application, w…
Report on "Mathematical Aspects of P vs. NP and its Variants."
Joshua A. Grochow, Korben Rusek
This is a report on a workshop held August 1 to August 5, 2011 at the Institute for Computational and Experimental Research in Mathematics (ICERM) at Brown University, Providence,…
Effective Results on non-Archimedean Tropical Discriminants
Korben Rusek
We study A-discriminants from a non-Archimedean point of view, refining earlier work on the tropical discriminant. In particular, we study the case where is a collection of n+m…
Faster p-adic Feasibility for Certain Multivariate Sparse Polynomials
Martín Avendaño, Ashraf Ibrahim, J. Maurice Rojas +1
We present algorithms revealing new families of polynomials allowing sub-exponential detection of p-adic rational roots, relative to the sparse encoding. For instance, we show that…
Dense Fewnomials
Korben Rusek, Jeanette Shakalli, Frank Sottile
We derive new bounds of fewnomial type for the number of real solutions to systems of polynomials that have structure intermediate between fewnomials and generic (dense) polynomial…
Near NP-Completeness for Detecting p-adic Rational Roots in One Variable
Martin Avendano, Ashraf Ibrahim, J. Maurice Rojas +1
We show that deciding whether a sparse univariate polynomial has a p-adic rational root can be done in NP for most inputs. We also prove a polynomial-time upper bound for trinomial…