`poles` function?? Name conflict with `ControlSystems`

[B-LIE]

I have imported (using) both Polynomials and ControlSystems, and am told there is a name conflict: both packages export a function poles.

In ControlSystems, this is a key function (roots of denominator polynomials in transfer functions).

I am trying to find out what this function does in Polynomials, but I cannot find it in the documentation??

Question: I assume it is an important function in Polynomials (since it is exported), but what does it do?

[jverzani]

It is documented, but with a bit of time can be unexported. I'd hope that doesn't disrupt too many users. Before proceeding, I'll compare exports.

[B-LIE]

It is not a big deal. It is just puzzling -- I searched for poles in the Polynomials.jl documentation, but could not find it there.

I got an error message in Julia when I tried to use the poles command, expecting it to work for the transfer function. After some restarting where I sequentially commented out the import of various packages, I found that it was related to Polynomials.jl.

Now that I am aware of the conflict, I just do import Polynomials as pln (or whatever).

[stevengj]

For reference, Polynomials.poles is defined here:

Polynomials.jl/src/rational-functions/common.jl

Lines 428 to 448 in 835a136

	## ---- zeros, poles, ...
	"""
	poles(pq::AbstractRationalFunction{T};
	method=:numerical, multroot_method=nothing, kwargs...) where {T}
	For a rational function `p/q`, first reduces to normal form, then finds the roots and multiplicities of the resulting denominator.
	* `method` is used to pass to `lowest_terms`
	* `multroot_method` is passed to the method argument of `multroot`, which can be `:direct` (the faster default) or `:iterative` (the slower, and possibly more robust alternate). The default is `:direct` save for `Big` values in which case `:iterative` is used.
	"""
	function poles(pq::AbstractRationalFunction{T};
	method=:numerical, # for lowest_terms
	multroot_method=nothing, # :direct or:iterative
	kwargs...) where {T}
	pq′ = lowest_terms(pq; method=method, kwargs...)
	den = denominator(pq′)
	mmethod = something(multroot_method, default_multroot_method(T))
	mr = Multroot.multroot(den; method=mmethod)
	(zs=mr.values, multiplicities = mr.multiplicities)
	end

and does what you might expect, computing poles of a rational function.

It has a docstring, but it should be added to the manual if it isn't there.

[stevengj]

I'm not sure why it should be unexported, if Polynomials.jl supports rational functions?

If you have a conflict, you can simply use it as ControlSystems.poles or Polynomials.poles, or explicitly import one, no?

[B-LIE]

I certainly agree that it should not be un-exported since Polynomials.jl supports rational functions/polynomials. I did not know that rational polynomials was supported, but I find a description of this in the home page of Polynomials.jl. However, I have not found a description of poles.

Related to rational polynomials...

• Is it possible to take a (Taylor) series expansion of the rational function?

I can take a Taylor series expansion using Symbolics.jl.

HOWEVER, I tried to specify a series expansion in 1/x at x=infinity, but that does not work in Symbolics.jl. So I had to do a trick of specifying f(x), and then do the Taylor series of f(1/x) at x=0. Which has two problems:

• I need to do various tricks of expand and/or simplify + other tricks with Symbolics.jl
• The result comes out as a series in x, although I know that "x" now means "1/x".

[stevengj]

It can compute derivatives of rational functions, so you can use these to get the Taylor-series coefficient around any desired point. I'm not sure if there is a more efficient way. However, that should be discussed in a separate issue.