Toric laminations, sparse generalized characteristic polynomials, and a refinement of Hilbert’s tenth problem. (English) Zbl 0911.13012
Cucker, Felipe (ed.) et al., Foundations of computational mathematics. Selected papers of a conference, held at IMPA in Rio de Janeiro, Brazil, January 1997. Berlin: Springer. 369-381 (1997).
In order to study the solutions of a polynomial system with a finite number of solutions, one basic technique is univariate reduction. When the system has a special “toric structure” (i.e. when the Newton diagrams of equations have a special shape) it is interesting to device computational techniques taking this special structure into account. This now classical approach is further developed in this paper.
The reference to Hilbert’s tenth problem in the title is totally irrelevant: in the zero dimensional case, Hilbert’s tenth problem is nothing else than deciding whether a polynomial system with a finite number of solutions has an integer solution which can be done by elimination and factorization! I do not think it is a good idea to give to a paper such a misleading title.
For the entire collection see [Zbl 0857.00037].
The reference to Hilbert’s tenth problem in the title is totally irrelevant: in the zero dimensional case, Hilbert’s tenth problem is nothing else than deciding whether a polynomial system with a finite number of solutions has an integer solution which can be done by elimination and factorization! I do not think it is a good idea to give to a paper such a misleading title.
For the entire collection see [Zbl 0857.00037].
Reviewer: M.-F.Roy (Rennes)
MSC:
| 13P05 | Polynomials, factorization in commutative rings |
