RationalFunctionLimit - Maple Help

RegularChains[AlgebraicGeometryTools]

 RationalFunctionLimit
 compute the limit of a rational function at a pole

 Calling Sequence RationalFunctionLimit(f, p)

Parameters

 f - a multivariate rational function p - a list of assignments for the variables of f

Description

 • The command RationalFunctionLimit(f,p) returns either undefined if the rational function f does not admit a finite limit at the point given by p, or the limit of f at p otherwise.
 • If p is a pole of f, that is, if p cancels the denominator of f, then it is assumed that p is an isolated pole of f, that is, f has no poles other than p in a neighborhood of p.
 • This command is part of the RegularChains[AlgebraicGeometryTools] package, so it can be used in the form RationalFunctionLimit(..) only after executing the command with(RegularChains[AlgebraicGeometryTools]).  However, it can always be accessed through the long form of the command by using RegularChains[AlgebraicGeometryTools][RationalFunctionLimit](..).

Examples

 > $\mathrm{with}\left(\mathrm{RegularChains}\right):$$\mathrm{with}\left(\mathrm{AlgebraicGeometryTools}\right):$
 > $\mathrm{RationalFunctionLimit}\left(\frac{{x}^{2}y{z}^{2}}{{x}^{4}+{y}^{4}+{z}^{4}},\left[x=0,y=0,z=0\right]\right)$
 ${0}$ (1)
 > $\mathrm{RationalFunctionLimit}\left(\frac{wz+{x}^{2}+{y}^{2}}{{w}^{2}+{x}^{2}+{y}^{2}+{z}^{2}},\left[x=0,y=0,z=0,w=0\right]\right)$
 ${\mathrm{undefined}}$ (2)
 > $\mathrm{RationalFunctionLimit}\left(\frac{{x}^{6}}{{w}^{6}+{l}^{2}+{t}^{2}+{x}^{2}+{y}^{2}+{z}^{2}},\left[x=0,y=0,z=0,w=0,t=0,l=0\right]\right)$
 ${0}$ (3)

References

 Parisa Alvandi, Changbo Chen, Marc Moreno Maza "Computing the Limit Points of the Quasi-component of a Regular Chain in Dimension One." Computer Algebra in Scientific Computing (CASC), Lecture Notes in Computer Science - 8136, (2013): 30-45.
 Parisa Alvandi, Masoud Ataei, Mahsa Kazemi, Marc Moreno Maza "On the Extended Hensel Construction and its application to the computation of real limit points." J. Symb. Comput. 98: 120-162 (2020)

Compatibility

 • The RegularChains[AlgebraicGeometryTools][RationalFunctionLimit] command was introduced in Maple 2020.