
01334278
j
01334278
Sasaki, Tateaki
Kako, Fujio
Solving multivariate algebraic equation by Hensel construction.
Japan J. Ind. Appl. Math. 16, No.2, 257285 (1999).
1999
Springer, Tokyo
EN
algebraic computation
roots of multivariate polynomials
formal power series
Puiseux series
Newton polygon
Hensel's construction
symbolic resolution
Zbl 0371.68019
doi:10.1007/BF03167329
The paper deals with calculating the roots of multivariate polynomials with respect to one of the variables involved. The roots are computed in terms of formal power series or Puiseux series in the remaining variables. The authors use the wellknown methods of Newton polygon and the generalized Hensel's construction (which they modify slightly in the case the polynomial has multiple roots). First, they apply their method to a polynomial in two variables, and then they adapt is to several indeterminates. The authors state that, when dealing with symbolic resolution and algebraic numbers, their method uses less algebraic numbers to represent a root than NewtonPuiseux's method or KungTraub's method [see {\it H. T. Kung} and {\it J. F. Traub}, J. Assoc. Comput. Mach. 25, 245260 (1978; Zbl 0371.68019)]. They also state that, when dealing with numerical approximations, the method used in this paper is more accurate than the NewtonPuiseux's one.
J.Sabia (Buenos Aires)