À l’aide du Nullstellensatz effectif, on trouve des bornes inférieure et supérieure explicites des valeurs critiques non nulles d’un polynôme, en termes des coefficients de celui-ci.
With the help of the effective Nullstellensatz, we give explicit lower and upper bounds for the non-zero critical values of a polynomial in terms of its coefficients.
@article{AIF_1995__45_2_421_0,
author = {Ronga, Felice},
title = {Un proc\'ed\'e d'\'elimination effective et quelques applications},
journal = {Annales de l'Institut Fourier},
pages = {421--435},
publisher = {Association des Annales de l'institut Fourier},
volume = {45},
number = {2},
year = {1995},
doi = {10.5802/aif.1460},
zbl = {0819.13010},
mrnumber = {96m:14075},
language = {fr},
url = {http://archive.numdam.org/item/AIF_1995__45_2_421_0/}
}
Ronga, Felice. Un procédé d'élimination effective et quelques applications. Annales de l'Institut Fourier, Tome 45 (1995) no. 2, pp. 421-435. doi : 10.5802/aif.1460. http://archive.numdam.org/item/AIF_1995__45_2_421_0/
[1] , Bounds for the degrees in the Nullstellensatz, Ann. of Math., 126 (1987), 577-591. | MR 89b:12001 | Zbl 0641.14001
[2] , , , Sur la complexité du principe de Tarsky-Seidenberg, Bulletin de la Société Mathématique de France, 118 (1990), 101-126. | Numdam | MR 92g:03047 | Zbl 0767.03017
[3] and , Solving Systems of Polynomial Inequalities in Subexponential Time, J. Symbolic Computation, 5 (1988), 37-64. | MR 89h:13001 | Zbl 0662.12001
[4] , Polynomials with multiple zeros, Mathematika, 14 (1967), 181-196. | MR 36 #6592 | Zbl 0173.05101
[5] , Sharp effective Nullstellensatz, Journal of the American Math. Soc., 1 (1988), 963-975. | MR 89h:12008 | Zbl 0682.14001
[6] , Recherche de solutions d'inéquations polynomiales, Astérisque, 192 (1990), 11-16. | MR 92f:13032 | Zbl 0767.26011
