Using rational functions

[andreasvarga]

I would like to use rational functions as elements of rational matrices. I wonder if this package is still actively developed and if it can be expected that a registered and fully tested version will be available in the near future.

[aytekinar]

Hi @andreasvarga. First of all, I would like to thank you for your interest in the package. It's not been in active development for so long.

@neveritt mentioned to me about this interest last weekend, and he was the one to create #13. I will accept that PR and check Julia's 1.X version release to see what else I can do to the package to improve its functionalities.

By the way, I would gladly accept any constructive feedback from you as well as PRs in the process.

[andreasvarga]

My interest in rational functions is related to my intent to extend the functionality of the recently released package MatrixPencils to handling of rational matrices. Presently, all functions for handling of polynomial matrices (specified as 3-D arrays containing the coefficient matrices), can also accept, as inputs, matrices with polynomial entries, as defined in the Polynomials package. Thus, for example, it is possible to easily enter polynomial matrices in a quasi-symbolic way, as below:

using Polynomials
λ = Polynomial([0,1],:λ)
P = [λ^2 λ; λ 1]

I would be very please to be able to have a similar facility to enter rational matrices, for example, in the form:

using RationalFunctions
λ = Polynomial([0,1],:λ)
P = [λ^2/(λ+1) λ/(λ^2+1); λ 1]

A nice extension would be, of course, to fully support rational matrices (apparently this is planned for polynomial matrices in the Polynomials package).

[andreasvarga]

The above code should probably be

using RationalFunctions
λ = RationalFunction([0,1],1,:λ)
P = [λ^2/(λ+1) λ/(λ^2+1); λ 1]