Decomposition of polynomials and approximate roots
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- by Arnaud Bodin PDF
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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 $P(x) = h\circ Q(x) +R(x)$, 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.References
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Additional Information
- Arnaud Bodin
- Affiliation: Laboratoire Paul Painlevé, Mathématiques, Université de Lille 1, 59655 Villeneuve d’Ascq, France
- MR Author ID: 649245
- ORCID: 0000-0001-9933-856X
- Email: Arnaud.Bodin@math.univ-lille1.fr
- Received by editor(s): March 10, 2009
- Received by editor(s) in revised form: October 6, 2009
- Published electronically: February 2, 2010
- Communicated by: Bernd Ulrich
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 138 (2010), 1989-1994
- MSC (2010): Primary 13B25
- DOI: https://doi.org/10.1090/S0002-9939-10-10245-7
- MathSciNet review: 2596034