### Impacto

Luengo Velasco, Ignacio and Raimondo , Mario and Alonso García, María Emilia
(1989)
*An algorithm on quasi-ordinary polynomials.*
Lecture Notes in Computer Science, 356
.
pp. 59-73.
ISSN 0302-9743

Official URL: http://www.springerlink.com/content/y57m4130345633hg/

## Abstract

Let K be a field of characteristic O, and let R denote K[X] or K[[X]]. It is well known that the roots of a polynomial FisinR[Z] are fractional powers series in K[[X 1d/]], where Kmacr is a finite extension of K and disin N, and they can be obtained by applying the Newton Puiseux algorithm. Although this is not true for polynomials in more than one variable, there is an important class of polynomials FisinR[Z] (R=K[[X 1, . . ., X n]]=K[[Xlowbar]]), called quasi-ordinary (QO) polynomials, for which the same property holds (i.e. their roots are fractional power series in Kmacr[[Xlowbar 1d/]]). The goal of the paper is to give an algorithm to compute these fractional power series for K (a computable field) and n=2

Item Type: | Article |
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Uncontrolled Keywords: | Quasi-ordinary polynomials; Multivariate polynomials; Computable field; Algorithm |

Subjects: | Sciences > Mathematics > Algebra |

ID Code: | 16842 |

Deposited On: | 24 Oct 2012 08:54 |

Last Modified: | 21 Mar 2013 14:14 |

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