Decomposition of polynomials and approximate roots
Algebraic Geometry
2009-10-12 v1 Commutative Algebra
Abstract
We state a kind of Euclidian division theorem: given a polynomial P(x) and a divisor d of the degree of P, there exist polynomials h(x),Q(x),R(x) such that P(x) = h(Q(x)) +R(x), with deg h=d. Under some conditions h,Q,R are unique, and Q is the approximate d-root of P. Moreover we give an algorithm to compute such a decomposition. We apply these results to decide whether a polynomial in one or several variables is decomposable or not.
Cite
@article{arxiv.0910.1676,
title = {Decomposition of polynomials and approximate roots},
author = {Arnaud Bodin},
journal= {arXiv preprint arXiv:0910.1676},
year = {2009}
}