zbMATH — the first resource for mathematics

A polynomial decomposition algorithm. (English) Zbl 0704.12003
Algebra and geometry, Proc. 2nd Span. Belg. Week, II SBWAG, Santiago de Compostela/Spain 1989, Alxebra 54, 75-90 (1990).
[For the entire collection see Zbl 0694.00008.]
The authors present an algorithm to decompose a polynomial over a field. The basic structure of the algorithm is to compute an indecomposable polynomial h(x) of lower degree than f(x) as a candidate component of the decomposition; to compute g(x), if it exists, such that \(f(x)=g(x)\circ h(x)\) and to decompose g(x) recursively. Details are given. As an application, consider a decomposable polynomial, \(f(x)=g(x)\circ h(x)\). First compute the zeros \(z_ i\) of g(x). Then the zeros of f(x) are the zeros of the polynomials \(h_ i(x)=h(x)-z_ i\).

12E05 Polynomials in general fields (irreducibility, etc.)
12Y05 Computational aspects of field theory and polynomials (MSC2010)