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Abstract:

We prove the existence of an algorithm that, from a finite set of polynomials defining an algebraic projective variety, computes the Chow form of its equidimensional component of the greatest dimension. Applying this algorithm, a finite set of polynomials defining the equidimensional component of the greatest dimension of an algebraic (projective or affine) variety can be computed. The complexities of the algorithms involved are lower than the complexities of the known algorithms solving the same tasks. This is due to a special way of coding output polynomials, called straight-line programs. © 2001 Academic Press.

Registro:

Documento: Artículo
Título:Computing Chow Forms and Some Applications
Autor:Jeronimo, G.; Puddu, S.; Sabia, J.
Filiación:Departamento de Matemática, Fac. de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pab. I, (1428) Buenos Aires, Argentina
Palabras clave:Algorithmic algebraic geometry; Chow form; Complexity theory; Equidimensional decomposition; Polynomial equations
Año:2001
Volumen:41
Número:1
Página de inicio:52
Página de fin:68
DOI: http://dx.doi.org/10.1006/jagm.2001.1177
Título revista:Journal of Algorithms
Título revista abreviado:J Algorithms
ISSN:01966774
CODEN:JOALD
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01966774_v41_n1_p52_Jeronimo

Referencias:

  • Berkowitz, S.J., On computing the determinant in small parallel time using a small number of processors (1984) Inform. Process. Lett., 18, pp. 147-150
  • Caniglia, L., How to compute the Chow Form of an unmixed polynomial ideal in single exponential time (1990) AAECC, pp. 25-41. , Springer-Verlag, Berlin
  • Chistov, A.L., Grigor'ev, D.Y., (1983) Subexponential Time Solving Systems of Algebraic Equations, , LOMI preprint E-9-83, E-10-83, Steklov Institute, Leningrad
  • Fitchas, N., Galligo, A., Morgenstern, J., Precise sequential and parallel complexity bounds for quantifier elimination over algebraically closed fields (1990) J. Pure Appl. Algebra, 67, pp. 1-14
  • Giusti, M., Heintz, J., Algorithmes -disons rapides- Pour la décomposition d'une variété algébrique en composantes irréductibles et équidimensionnelles (1991) Progress in Mathematics, 94, pp. 169-193. , "Effective Methods in Algebraic Geometry" (T. Mora and C. Traverso, Eds.), Birkhauser, Basel
  • Giusti, M., Heintz, J., La détermination des points isolés et de la dimension d'une veriété algébrique peut se faire en temps polynomial (1993) Symposia Matematica, 34, pp. 216-256. , "Computational Algebraic Geometry and Commutative Algebra, Proceedings of the Cortona Conference on Computational Algebraic Geometry and Commutative Algebra,"
  • Heintz, J., On the computational complexity of polynomials and bilinear mappings, a survey (1989) Lecture Notes in Computer Science, 356, pp. 269-300. , "Proc. 5th Internat. Conf. AAECC 5, Menorca, 1987" (L. Huguet and A. Poli, Eds.), Springer-Verlag, Berlin/New York
  • Heintz, J., Schnorr, C.P., Testing polynomials which are easy to compute (1982) Monogr. de L'Enseignement Math., 30, pp. 237-254
  • Kaltofen, E., Greatest common divisors of polynomials given by straight line programs (1988) J. Assoc. Comput. Mach., 35 (1), pp. 231-264
  • Krick, T., Pardo, L.M., A computational method for diophantine approximation (1996) Progress Math., 143, pp. 193-253
  • Mulmuley, K., A fast parallel algorithm to compute the rank of a matrix over an arbitrary field (1986) Proc. 18th ACM Symp. Theory of Computing, pp. 338-339
  • Puddu, S., Sabia, J., An effective algorithm for quantifier elimination over algebraically closed fields using straight line programs (1998) J. Pure Appl. Algebra, 129, pp. 173-200
  • Shafarevich, I.R., (1974) Basic Algebraic Geometry, , Springer-Verlag, Berlin/New York
  • Strassen, V., Vermeidung von Divisionen (1973) Crelle J. Reine Angew. Math., 264, pp. 184-202

Citas:

---------- APA ----------
Jeronimo, G., Puddu, S. & Sabia, J. (2001) . Computing Chow Forms and Some Applications. Journal of Algorithms, 41(1), 52-68.
http://dx.doi.org/10.1006/jagm.2001.1177
---------- CHICAGO ----------
Jeronimo, G., Puddu, S., Sabia, J. "Computing Chow Forms and Some Applications" . Journal of Algorithms 41, no. 1 (2001) : 52-68.
http://dx.doi.org/10.1006/jagm.2001.1177
---------- MLA ----------
Jeronimo, G., Puddu, S., Sabia, J. "Computing Chow Forms and Some Applications" . Journal of Algorithms, vol. 41, no. 1, 2001, pp. 52-68.
http://dx.doi.org/10.1006/jagm.2001.1177
---------- VANCOUVER ----------
Jeronimo, G., Puddu, S., Sabia, J. Computing Chow Forms and Some Applications. J Algorithms. 2001;41(1):52-68.
http://dx.doi.org/10.1006/jagm.2001.1177