Mathematics

New computational mathematics study results from University of California described

  2008 NOV 17 - (VerticalNews.com) -- According to a study from the United States, "Let F-q be the finite field of q elements, where q = p(h). Let f(x) be a polynomial over F-q in n variables with m nonzero terms."

  "Let N(f) denote the number of solutions of f(x) = 0 with coordinates in F-q. In this paper we give a deterministic algorithm which computes the reduction of N(f) modulo p(b) in O(n(8m)((h+b)p)) bit operations," wrote D.Q. Wan and colleagues, University of California.

  The researchers concluded: "This is singly exponential in each of the parameters {h, b, p}, answering affirmatively an open problem proposed by Gopalan, Guruswami, and Lipton."

  Wan and colleagues published their study in Foundations of Computational Mathematics (Modular counting of rational points over finite fields. Foundations of Computational Mathematics, 2008;8(5):597-605).

  For more information, contact D.Q. Wan, University of California, Dept. of Math, Irvine, CA 92697, USA.

  Publisher contact information for the journal Foundations of Computational Mathematics is: Springer, 233 Spring St., New York, NY 10013, USA.

  Keywords: Mathematics, PolynomialComputational Mathematics, University of California.

  This article was prepared by VerticalNews Mathematics editors from staff and other reports. Copyright 2008, VerticalNews Mathematics via VerticalNews.com.