La première méthode générale de factorisation des polynômes. Autour d'un mémoire de F. T. Schubert (2001)
Mignotte, Maurice (Author)
Stefanescu, Doru (Author)
Revue d'Histoire des Mathématiques
Volume: 7
Pages: 67--89
We analyse two little known papers of N.Bernoulli (1708) and F.T.Schubert (1794) on the factorization of integer polynomials as well as the work of L.Kronecker and B.A.Hausmann on the same topic. The factorization method of Bernoulli-Schubert uses the calculus and the interpolation of finite differences. It was rediscovered by Kronecker (1882), who used Lagrange interpolation. Both procedures allow the effective factorization of polynomials having small degrees and coefficients. An algorithm combining the results of Bernoulli-Schubert and Kronecker was obtained by B.A.Hausmann. His method is particularly useful for the factorization of stable polynomials. The three methods are briefly compared with modern factorization algorithms.
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