Counting solutions to binomial complete intersections

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We study the problem of counting the total number of affine solutions of a system of n binomials in n variables over an algebraically closed field of characteristic zero. We show that we may decide in polynomial time if that number is finite. We give a combinatorial formula for computing the total n...

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Detalles Bibliográficos
Autores principales: Cattani, E., Dickenstein, A.
Formato: JOUR
Materias:
# P-complete
Binomial ideal
Complete intersection
Computational methods
Polynomials
Problem solving
Vectors
Binomials
Polynomial time
Algebra
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_0885064X_v23_n1_p82_Cattani
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
Descripción
Sumario:We study the problem of counting the total number of affine solutions of a system of n binomials in n variables over an algebraically closed field of characteristic zero. We show that we may decide in polynomial time if that number is finite. We give a combinatorial formula for computing the total number of affine solutions (with or without multiplicity) from which we deduce that this counting problem is # P-complete. We discuss special cases in which this formula may be computed in polynomial time; in particular, this is true for generic exponent vectors. © 2006 Elsevier Inc. All rights reserved.

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