Global Residues for Sparse Polynomial Systems

Ivan Soprunov

doi:10.1016/j.jpaa.2006.06.012

Global Residues for Sparse Polynomial Systems

Research output: Contribution to journal › Article › peer-review

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.

Original language	American English
Journal	Journal of Pure and Applied Algebra
Volume	209
DOIs	https://doi.org/10.1016/j.jpaa.2006.06.012
State	Published - Apr 8 2006

Disciplines

Mathematics

Access to Document

10.1016/j.jpaa.2006.06.012License: CC BY

Global Residues for Sparse Polynomial SystemsFinal published version, 1.31 MBLicense: CC BY

Cite this

@article{46e6fed64d4c4b3fa00880a673122a33,

title = "Global Residues for Sparse Polynomial Systems",

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.",

author = "Ivan Soprunov",

year = "2006",

month = apr,

day = "8",

doi = "10.1016/j.jpaa.2006.06.012",

language = "American English",

volume = "209",

journal = "Journal of Pure and Applied Algebra",

}

TY - JOUR

T1 - Global Residues for Sparse Polynomial Systems

AU - Soprunov, Ivan

PY - 2006/4/8

Y1 - 2006/4/8

N2 - 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.

AB - 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.

UR - https://engagedscholarship.csuohio.edu/scimath_facpub/272

U2 - 10.1016/j.jpaa.2006.06.012

DO - 10.1016/j.jpaa.2006.06.012

M3 - Article

VL - 209

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

ER -

Global Residues for Sparse Polynomial Systems

Abstract

Disciplines

Access to Document

Other files and links

Cite this