Abstract

It was shown by Bernstein that the number of roots in  of a polynomial system depended only on the Newton polytopes of the system for almost all specializations of the coefficients. This result henceforth is referred to as the BKK bound and it gives an upper bound on the number of roots of a polynomial system. But this bound is only applicable to the systems of polynomials. In this paper, the BBK bound was generalized in certain cases of the systems of B-spline function. For the general case, a conjecture was presented.

Key words: The BKK bound, Newton polytope, B-spline, Minkowski mixed volume.