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Abstract:

Let K be an algebraically closed field, V ⊂ Kn be a smooth equidimensional algebraic variety and I (V) ⊂ K[x1,...,xn] be the ideal of all polynomials vanishing on V. We show that there exists a system of generators f1,...,fm of I (V) such that m ≤ (n - dim V) (1 + dim V) and deg(fi) ≤ deg V for i = 1,...,m. If char(K) = 0 we present a probabilistic algorithm which computes the generators f1,..., fm from a set-theoretical description of V. If V is given as the common zero locus of s polynomials of degrees bounded by d encoded by straight-line programs of length L, the algorithm obtains the generators of I (V) with error probability bounded by E within complexity s(ndn)O(1)log2 (⌈1/E⌉)L. © 2004 Elsevier Ltd. All rights reserved.

Registro:

Documento: Artículo
Título:Computing generators of the ideal of a smooth affine algebraic variety
Autor:Blanco, C.; Jeronimo, G.; Solernó, P.
Filiación:Departamento de Matemática, Fac. de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina
Palabras clave:Computation of the radical of a regular ideal; Efficient generation of polynomial ideals; Number and degree of generators of polynomial ideals; Regular signs; Straight-line programs
Año:2004
Volumen:38
Número:1
Página de inicio:843
Página de fin:872
DOI: http://dx.doi.org/10.1016/j.jsc.2004.02.002
Título revista:Journal of Symbolic Computation
Título revista abreviado:J. Symb. Comput.
ISSN:07477171
PDF:https://bibliotecadigital.exactas.uba.ar/download/paper/paper_07477171_v38_n1_p843_Blanco.pdf
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_07477171_v38_n1_p843_Blanco

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Citas:

---------- APA ----------
Blanco, C., Jeronimo, G. & Solernó, P. (2004) . Computing generators of the ideal of a smooth affine algebraic variety. Journal of Symbolic Computation, 38(1), 843-872.
http://dx.doi.org/10.1016/j.jsc.2004.02.002
---------- CHICAGO ----------
Blanco, C., Jeronimo, G., Solernó, P. "Computing generators of the ideal of a smooth affine algebraic variety" . Journal of Symbolic Computation 38, no. 1 (2004) : 843-872.
http://dx.doi.org/10.1016/j.jsc.2004.02.002
---------- MLA ----------
Blanco, C., Jeronimo, G., Solernó, P. "Computing generators of the ideal of a smooth affine algebraic variety" . Journal of Symbolic Computation, vol. 38, no. 1, 2004, pp. 843-872.
http://dx.doi.org/10.1016/j.jsc.2004.02.002
---------- VANCOUVER ----------
Blanco, C., Jeronimo, G., Solernó, P. Computing generators of the ideal of a smooth affine algebraic variety. J. Symb. Comput. 2004;38(1):843-872.
http://dx.doi.org/10.1016/j.jsc.2004.02.002