Artículo

Heintz, J.; Krick, T.; Puddu, S.; Sabia, J.; Waissbein, A. "Deformation Techniques for Efficient Polynomial Equation Solving" (2000) Journal of Complexity. 16(1):70-109
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Abstract:

Suppose we are given a parametric polynomial equation system encoded by an arithmetic circuit, which represents a generically flat and unramified family of zero-dimensional algebraic varieties. Let us also assume that there is given the complete description of the solution of a particular unramified parameter instance of our system. We show that it is possible to "move" the given particular solution along the parameter space in order to reconstruct - by means of an arithmetic circuit - the coordinates of the solutions of the system for an arbitrary parameter instance. The underlying algorithm is highly efficient, i.e., polynomial in the syntactic description of the input and the following geometric invariants: the number of solutions of a typical parameter instance and the degree of the polynomials occurring in the output. In fact, we prove a slightly more general result, which implies the previous statement by means of a well-known primitive element algorithm. We produce an efficient algorithmic description of the hypersurface obtained projecting polynomially the given generically flat family of varieties into a suitable affine space. © 2000 Academic Press.

Registro:

Documento: Artículo
Título:Deformation Techniques for Efficient Polynomial Equation Solving
Autor:Heintz, J.; Krick, T.; Puddu, S.; Sabia, J.; Waissbein, A.
Filiación:Departamento de Matemática, Fac. de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pab. I, 1428, Buenos Aires, Argentina
Departamento de Matemática, Estadística y Comp., Universidad de Cantabria, Avda. de los Castros s/n, E-39071, Santander, Spain
Palabras clave:Polynomial equation system; arithmetic circuit; shape (or primitive element) lemma; Newton-Hensel iteration
Año:2000
Volumen:16
Número:1
Página de inicio:70
Página de fin:109
DOI: http://dx.doi.org/10.1006/jcom.1999.0529
Handle:http://hdl.handle.net/20.500.12110/paper_0885064X_v16_n1_p70_Heintz
Título revista:Journal of Complexity
Título revista abreviado:J. Complexity
ISSN:0885064X
PDF:https://bibliotecadigital.exactas.uba.ar/download/paper/paper_0885064X_v16_n1_p70_Heintz.pdf
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0885064X_v16_n1_p70_Heintz

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Citas:

---------- APA ----------
Heintz, J., Krick, T., Puddu, S., Sabia, J. & Waissbein, A. (2000) . Deformation Techniques for Efficient Polynomial Equation Solving. Journal of Complexity, 16(1), 70-109.
http://dx.doi.org/10.1006/jcom.1999.0529
---------- CHICAGO ----------
Heintz, J., Krick, T., Puddu, S., Sabia, J., Waissbein, A. "Deformation Techniques for Efficient Polynomial Equation Solving" . Journal of Complexity 16, no. 1 (2000) : 70-109.
http://dx.doi.org/10.1006/jcom.1999.0529
---------- MLA ----------
Heintz, J., Krick, T., Puddu, S., Sabia, J., Waissbein, A. "Deformation Techniques for Efficient Polynomial Equation Solving" . Journal of Complexity, vol. 16, no. 1, 2000, pp. 70-109.
http://dx.doi.org/10.1006/jcom.1999.0529
---------- VANCOUVER ----------
Heintz, J., Krick, T., Puddu, S., Sabia, J., Waissbein, A. Deformation Techniques for Efficient Polynomial Equation Solving. J. Complexity. 2000;16(1):70-109.
http://dx.doi.org/10.1006/jcom.1999.0529