Nullstellensatz effectif et Conjecture de Serre (Théorème de Quillen‐Suslin) pour le Calcul Formel
Noaï Fitchas, André Galligo · Mathematische Nachrichten · 1990
Abstract Let k be an arbitrary field, X1,….,Xn indeterminates over k and F1…, F3 ε ∈ k[X1…,Xn] polynomials of maximal degree \documentclass{article}\pagestyle{empty}\begin{document}$ d: = \mathop {\max }\limits_{1 \le i \le a} \deg $\end{document} (Fi). We give an elementary proof of the following effective Nullstellensatz: Assume that F1,…,F have no common zero in the algebraic closure of k. Then there exist polynomials P1…, P3 ε ∈ k[X1…,Xn] such that \documentclass{article}\pagestyle{empty}\begin{document}$ 1: = \mathop \Sigma \limits_{1 \le i \le a} $\end{document} PiFi and This result has many applications in Computer Algebra. To exemplify this, we give an effective quantitative and algorithmic version of the Quillen‐Suslin Theorem baaed on our effective Nullstellensatz.