Global residues for sparse polynomial systems

Details Global residues for sparse polynomial systems Global residues for sparse polynomial systems

2005-11-28

arxiv.org/abs/math/0511684v2

Mathematics

Algebraic Geometry

Typos corrected, reference added, 13 pages, 5 figures. To appear in JPAA

Scientific paper

We consider families of sparse Laurent polynomials f_1,...,f_n with a finite set of common zeroes Z_f in the complex algebraic n-torus. The global residue assigns to every Laurent polynomial g the sum of its Grothendieck residues over the set Z_f. We present a new symbolic algorithm for computing the global residue as a rational function of the coefficients of the f_i when the Newton polytopes of the f_i are full-dimensional. Our results have consequences in sparse polynomial interpolation and lattice point enumeration in Minkowski sums of polytopes.

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