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Abstract:

One may represent polynomials not only by their coefficients but also by arithmetic circuits which evaluate them. This idea allowed in the past fifteen years considerable complexity progress in effective polynomial equation solving. We present a circuit based computation model which captures all known symbolic elimination algorithms in effective Algebraic Geometry and exhibit a class of simple elimination problems which require exponential size circuits to be solved in this model. This implies that the known, circuit based elimination algorithms are already optimal. © 2012 Elsevier Inc. All rights reserved.

Registro:

Documento: Artículo
Título:Software Engineering and complexity in effective Algebraic Geometry
Autor:Heintz, J.; Kuijpers, B.; Rojas Paredes, A.
Filiación:Departamento de Computación, Universidad de Buenos Aires, Ciudad Universitaria, Pab. I, 1428 Buenos Aires, Argentina
CONICET, Ciudad Universitaria, Pab. I, 1428 Buenos Aires, Argentina
Departamento de Matemáticas, Estadística y Computación, Facultad de Ciencias, Universidad de Cantabria, Avda. de los Castros s/n, 39005 Santander, Spain
Database and Theoretical Computer Science Research Group, Hasselt University, Agoralaan, Gebouw D, 3590 Diepenbeek, Belgium
Palabras clave:Branching parsimonious algorithm; Flat family of zero dimensional elimination problems; Isoparametric routine; Robust parameterized arithmetic circuit; Logic circuits; Polynomials; Software engineering; Algebraic geometry; Arithmetic circuit; Computation model; Elimination problem; Iso-parametric; Polynomial equation solving; Geometry
Año:2013
Volumen:29
Número:1
Página de inicio:92
Página de fin:138
DOI: http://dx.doi.org/10.1016/j.jco.2012.04.005
Título revista:Journal of Complexity
Título revista abreviado:J. Complexity
ISSN:0885064X
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0885064X_v29_n1_p92_Heintz

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Citas:

---------- APA ----------
Heintz, J., Kuijpers, B. & Rojas Paredes, A. (2013) . Software Engineering and complexity in effective Algebraic Geometry. Journal of Complexity, 29(1), 92-138.
http://dx.doi.org/10.1016/j.jco.2012.04.005
---------- CHICAGO ----------
Heintz, J., Kuijpers, B., Rojas Paredes, A. "Software Engineering and complexity in effective Algebraic Geometry" . Journal of Complexity 29, no. 1 (2013) : 92-138.
http://dx.doi.org/10.1016/j.jco.2012.04.005
---------- MLA ----------
Heintz, J., Kuijpers, B., Rojas Paredes, A. "Software Engineering and complexity in effective Algebraic Geometry" . Journal of Complexity, vol. 29, no. 1, 2013, pp. 92-138.
http://dx.doi.org/10.1016/j.jco.2012.04.005
---------- VANCOUVER ----------
Heintz, J., Kuijpers, B., Rojas Paredes, A. Software Engineering and complexity in effective Algebraic Geometry. J. Complexity. 2013;29(1):92-138.
http://dx.doi.org/10.1016/j.jco.2012.04.005