Solving Degenerate Sparse Polynomial Systems Faster
<|reference_start|>Solving Degenerate Sparse Polynomial Systems Faster: 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.<|reference_end|>
@article{rojas1998solving,
    title={Solving Degenerate Sparse Polynomial Systems Faster},
    author={J. Maurice Rojas},
    journal={arXiv preprint arXiv:math/9809071},
    year={1998},
    archivePrefix={arXiv},
    eprint={math/9809071},
    primaryClass={math.AG cs.CC cs.NA math.NA}
}