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An algorithm on quasi-ordinary polynomials. (English) Zbl 0692.13011
Applied algebra, algebraic algorithms and error-correcting codes, Proc. 6th Int. Conference, AAECC-6, Rome/Italy 1988, Lect. Notes Comput. Sci. 357, 59-73 (1989).
[For the entire collection see Zbl 0671.00023.]
Let K be a field of characteristic zero, and let F be a univariate polynomial over K[X] or K[[X]]. The roots can be expressed as elements of \(\bar K[[X^{1/d}]]\), where \(\bar K\) is a finite extension of K and \(d\in {\mathbb{N}}.\)
This is not true in general for multivariate polynomials. However, there is a class of polynomials over \(K[[X_ 1,...,X_ n]]\) for which the same property holds. These polynomials are called quasi-ordinary. The authors present an algorithm in case K is a computable field and \(n=2\). One can apply the algorithm in the theories of local analytic branches, rational parametrizations and distinguished pairs - algebraic numbers and algebraic series.
Reviewer: G.Molenbergh

MSC:
13F20 Polynomial rings and ideals; rings of integer-valued polynomials
13F25 Formal power series rings
68W30 Symbolic computation and algebraic computation
13-04 Software, source code, etc. for problems pertaining to commutative algebra