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RegularChains[AlgebraicGeometryTools]

  

RationalFunctionLimit

  

compute the product of two matrices modulo a regular chain

 

Calling Sequence

Parameters

Description

Examples

References

Compatibility

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 neighbourhood 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

withRegularChains:withAlgebraicGeometryTools:

RationalFunctionLimitx2yz2x4+y4+z4,x=0,y=0,z=0

0

(1)

RationalFunctionLimitwz+x2+y2w2+x2+y2+z2,x=0,y=0,z=0,w=0

undefined

(2)

RationalFunctionLimitx6w6+l2+t2+x2+y2+z2,x=0,y=0,z=0,w=0,t=0,l=0

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.

• 

For more information on Maple 2020 changes, see Updates in Maple 2020.

See Also

LimitPoints

RegularChainBranches