Counting solutions to binomial complete intersections
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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| Autores principales: | , |
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| Formato: | Artículo publishedVersion |
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2007
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_0885064X_v23_n1_p82_Cattani https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_0885064X_v23_n1_p82_Cattani_oai |
| Aporte de: |
| 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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