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Article
Global Residues for Sparse Polynomial Systems
Journal of Pure and Applied Algebra
  • Ivan Soprunov, Cleveland State University
Document Type
Article
Publication Date
4-8-2006
Disciplines
Abstract

We consider families of sparse Laurent polynomials f1, . . . , fn with a finite set of common zeros Z f in the torus Tn = (C − {0})n. The global residue assigns to every Laurent polynomial g the sum of its Grothendieck residues over Z f . 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.

DOI
10.1016/j.jpaa.2006.06.012
Version
Postprint
Creative Commons License
Creative Commons Attribution-Noncommercial-No Derivative Works 4.0
Citation Information
Ivan Soprunov. "Global Residues for Sparse Polynomial Systems" Journal of Pure and Applied Algebra Vol. 209 Iss. 2 (2006) p. 383 - 392 ISSN: 0022-4049
Available at: http://works.bepress.com/ivan-soprunov/16/