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CORR
1998
Springer

Solving Degenerate Sparse Polynomial Systems Faster

13 years 3 months ago
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 positivedimensional 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.
J. Maurice Rojas
Added 22 Dec 2010
Updated 22 Dec 2010
Type Journal
Year 1998
Where CORR
Authors J. Maurice Rojas
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