Global residues for sparse polynomial systems |
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Authors: | Ivan Soprunov |
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Affiliation: | Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA, USA |
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Abstract: | We consider families of sparse Laurent polynomials f1,…,fn with a finite set of common zeros Zf in the torus Tn=(C−{0})n. The global residue assigns to every Laurent polynomial g the sum of its Grothendieck residues over Zf. We present a new symbolic algorithm for computing the global residue as a rational function of the coefficients of the fi when the Newton polytopes of the fi are full-dimensional. Our results have consequences in sparse polynomial interpolation and lattice point enumeration in Minkowski sums of polytopes. |
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Keywords: | Primary 14M25 secondary 52B20 |
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