Solving Degenerate Sparse Polynomial Systems Faster
Abstract
Consider a system F of n polynomial equations in n unknowns, over an algebraically closed field of arbitrary characteristic. We present a fast method to find a point in every irreducible component of the zero set Z of F. Our techniques allow us to sharpen and lower prior complexity bounds for this problem by fully taking into account the monomial term structure. As a corollary of our development we also obtain new explicit formulae for the exact number of isolated roots of F and the intersection multiplicity of the positive-dimensional part of Z. Finally, we present a combinatorial construction of non-degenerate polynomial systems, with specified monomial term structure and maximally many isolated roots, which may be of independent interest.
Cite
@article{arxiv.math/9809071,
title = {Solving Degenerate Sparse Polynomial Systems Faster},
author = {J. Maurice Rojas},
journal= {arXiv preprint arXiv:math/9809071},
year = {2007}
}
Comments
This is the final journal version of math.AG/9702222 (``Toric Generalized Characteristic Polynomials''). This final version is a major revision with several new theorems, examples, and references. The prior results are also significantly improved