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.
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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