Zobrazeno 1 - 10
of 19
pro vyhledávání: '"Rusek, Korben"'
Autor:
Rojas, J. Maurice, Rusek, Korben
We extend the definition of $\mathcal{A}$-discriminant varieties, and Kapranov's parametrization of $\mathcal{A}$-discriminant varieties, to complex exponents. As an application, we study the special case where $\mathcal{A}$ is a fixed real $n\times
Externí odkaz:
http://arxiv.org/abs/1612.03458
Autor:
Rusek, Korben Allen
The motivating question behind this body of research is Smale’s 17th problem: Can a zero of n complex polynomial equations in n unknowns be found approximately, on the average, in polynomial time with a uniform algorithm? While certain aspects and
Externí odkaz:
http://hdl.handle.net/1969.1/150998
Autor:
Grochow, Joshua A., Rusek, Korben
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, Rhode Island, organized by Saugata Basu, Joseph M. Landsberg, and J. M
Externí odkaz:
http://arxiv.org/abs/1203.2888
Autor:
Rusek, Korben
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 $A$ is a collection of n+m+1 points in Z^n in general position, and give an algorithm to compute
Externí odkaz:
http://arxiv.org/abs/1201.6401
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 the case of honest n-variate (n+1)-nomials is doable in NP and, for p
Externí odkaz:
http://arxiv.org/abs/1010.5310
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) polynomials. This uses a modified version of Gale duality for polynomial systems
Externí odkaz:
http://arxiv.org/abs/1010.2962
Publikováno v:
proceedings of International Symposium on Symbolic and Algebraic Computation (ISSAC 2010, July 25-28, 2010, Munchen), pp. 331-338, ACM Press, 2010
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 trinomials with suitably generic p-adic Newton polygon. We thus improve the bes
Externí odkaz:
http://arxiv.org/abs/1001.4252
Withdrawn by the authors due to an error in the proof of the finite field result (Thm. 1.5): The random primes used in the proof need NOT avoid the exceptional primes from Lemma 2.7, thus leaving Thm. 1.5 unproved.
Comment: This paper has been w
Comment: This paper has been w
Externí odkaz:
http://arxiv.org/abs/0711.2562
We present a new, far simpler family of counter-examples to Kushnirenko's Conjecture. Along the way, we illustrate a computer-assisted approach to finding sparse polynomial systems with maximally many real roots, thus shedding light on the nature of
Externí odkaz:
http://arxiv.org/abs/math/0609485
Publikováno v:
In Journal of Symbolic Computation April 2012 47(4):454-479
