LIP6 1998/004
- Reports
Calcul de polynômes caractéristiques associés à certains anneaux quotients - Ph. Aubry, A. Valibouze
- 18 pages - 02/11/1998- document en - http://www.lip6.fr/lip6/reports/1998/lip6.1998.004.ps.gz - 84 Ko
- Contact : Philippe.Aubry (at) nulllip6.fr, Annick.Valibouze (at) nulllip6.fr
- Ancien Thème : CALFOR
- Keywords : computer algebra, triangular set, resolvent, Galois theory, characteristic polynomial
- Publisher : Annick.Valibouze (at) nulllip6.fr
Let $k$ be a perfect field. This paper presents an effective algorithm that computes characteristic polynomials of endomorphisms of quotient rings defined from the polynomial ring $k[x_1,ldots ,x_n]$ by an ideal generated by a triangular set of polynomials. We establish that some ideals which occur in Galois theory
satisfy the former requirement. These results are exploited to compute efficiently relative resolvents which are a fundamental tool in the effective algebraic Galois theory.
satisfy the former requirement. These results are exploited to compute efficiently relative resolvents which are a fundamental tool in the effective algebraic Galois theory.