Algorithms for the universal decomposition algebra - École polytechnique Access content directly
Preprints, Working Papers, ... Year : 2012

Algorithms for the universal decomposition algebra


Let k be a field and let f be a polynomial of degree n in k [T]. The symmetric relations are the polynomials in k [X1, ..., Xn] that vanish on all permutations of the roots of f in the algebraic closure of k. These relations form an ideal Is; the universal decomposition algebra is the quotient algebra A := k [X1, ..., Xn]/Is. We show how to obtain efficient algorithms to compute in A. We use a univariate representation of A, i.e. an explicit isomorphism of the form A=k [T]/Q (T), since in this representation, arithmetic operations in A are known to be quasi-optimal. We give details for two related algorithms, to find the isomorphism above, and to compute the characteristic polynomial of any element of A.
Fichier principal
Vignette du fichier
Algorithms_for_the_universal_decomposition_algebra.pdf (264.13 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-00669806 , version 1 (14-02-2012)


  • HAL Id : hal-00669806 , version 1


Romain Lebreton, Éric Schost. Algorithms for the universal decomposition algebra. 2012. ⟨hal-00669806⟩
253 View
238 Download


Gmail Facebook X LinkedIn More