Abstract
The aim of this paper is to study the following problem: • Let f 1, f 2, …, f n , be n polynomials with integer coefficients such that: 1.for 1 ≤ i ≤n, f i - is a polynomial of the variables (X 1, …, X i ), monic in X i , of degree d i in X i ; 2.for 1 ≤ i ≤n, for 1 ≤ j ≤i, f i is of degree δ j ≤ d j in X j .
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References
M. Coste, M-F. Roy, Thorn’s lemma, the coding of real algebraic numbers and the topology of semi algebraic sets, Journal of Symbolic Computation 5 (1988), 121–129.
A. Dickenstein, N. Fitchas, M. Giusti, C. Sessa, The membership problem for unmixed polynomials ideals is solvable in subexponential time. Preprint
L. Gonzales, H. Lombardi, T. Recio, M-F. Roy, Sous résultants et spécialisation de la suite de Sturm, RAIRO (to appear).
J. Heintz, M-F. Roy, P. Solernâ, Sur la complexité du principe de Tarski-Seidenberg, Bulletin de la SMF (to appear).
T. Krick, A. Logar, Membership problem, representation problem and the computation of the radical for one dimensional ideals. (in these proceedings)
D. Lazard, Solving zero dimensional algebraic system, Preprint LITP june 1989.
H. Lombardi, Algébre élémentaire en temps polynomial, Thése, Université de Nice, Publications Mathématiques de Besançon (1989).
M-F. Roy, A. Szpirglas, Complexity of computation on real algebraic numbers, Journal of Symbolic Computation (to appear).
M-F. Roy, A. Szpirglas, Complexity of the computation of cylindrical decomposition and topology of real algebraic curves using Thorn’s lemma, in “Real algebraic and analytic geometry,” Trento, Springer Lecture Notes in Math, 1988.
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Roy, MF., Szpirglas, A. (1991). Sign determination on zero dimensional sets. In: Mora, T., Traverso, C. (eds) Effective Methods in Algebraic Geometry. Progress in Mathematics, vol 94. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0441-1_30
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DOI: https://doi.org/10.1007/978-1-4612-0441-1_30
Publisher Name: Birkhäuser, Boston, MA
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