Back to Search
Start Over
Determination of the limits for multivariate rational functions
- Source :
- Science China Mathematics. 57:397-416
- Publication Year :
- 2013
- Publisher :
- Springer Science and Business Media LLC, 2013.
-
Abstract
- The purpose of this paper is to solve the problem of determining the limits of multivariate rational functions. It is essential to decide whether or not {ie1-1} for two non-zero polynomials f, g ∈ ℝ[x1, …, xn] with f(0, …, 0) = g(0, …, 0) = 0. For two such polynomials f and g, we establish two necessary and sufficient conditions for the rational function {ie1-2} to have its limit 0 at the origin. Based on these theoretic results, we present an algorithm for deciding whether or not {ie1-3}, where f, g ∈ ℝ[x1, …, xn] are two non-zero polynomials. The design of our algorithm involves two existing algorithms: one for computing the rational univariate representations of a complete chain of polynomials, another for catching strictly critical points in a real algebraic variety. The two algorithms are based on the well-known Wu’s method. With the aid of the computer algebraic system Maple, our algorithm has been made into a general program. In the final section of this paper, several examples are given to illustrate the effectiveness of our algorithm.
Details
- ISSN :
- 18691862 and 16747283
- Volume :
- 57
- Database :
- OpenAIRE
- Journal :
- Science China Mathematics
- Accession number :
- edsair.doi...........490079a6e1bdf0ea1a4398d6662e4ffb