Rational function

[jverzani]

This adds an AbstractRationalFunction type for holding rational functions. In #308 it was suggested that this could be useful. Construction of the primaryRationalFunction type borrows the // syntax from the Rational type of Base. Other subtypes are possible.

The https://github.com/andreasvarga/DescriptorSystems.jl/blob/main/src/types/RationalFunction.jl implementation is mostly realized as a subtype of AbstractRationalFunction as an example (for now it isn't included when the package is loaded).

The https://github.com/aytekinar/RationalFunctions.jl package was a guide, but the main RationalFunction implementation does not include information about conjugated variables.

The conj method has not (yet) been defined.

The new exports are poles and residues. The "zeros" are found by roots. As well, the function lowest_terms is exported to cancel common factors. (The name cancel is used in SymPy and Mathematica, but wasn't used for this as it seemed like a useful generic elsewhere, though it is tempting.)

There is a simple implementation for fitting rational functions using least squares, fit(RationalFunction, xs, ys, m, n). (There are more accurate and robust fitting implementations elsewhere in the package ecosystem, such as BaryRational.) As for fitting, this provides a natural home for the Pade function that is still available via PolyCompat, and now re-implemented by fit(RationalFunction, p::Polynomial, m,n).

The plot recipe seems to do an okay job of plotting basic rational functions, though perhaps it could be tweaked in places.

[codecov]

Codecov Report

Merging #335 (fa950a6) into master (e9f59d7) will decrease coverage by 8.69%.
The diff coverage is 44.90%.

@@            Coverage Diff             @@
##           master     #335      +/-   ##
==========================================
- Coverage   91.54%   82.85%   -8.70%     
==========================================
  Files          16       21       +5     
  Lines        1963     2420     +457     
==========================================
+ Hits         1797     2005     +208     
- Misses        166      415     +249     

Impacted Files	Coverage Δ
src/rational-functions/plot-recipes.jl	0.00% <0.00%> (ø)
...c/rational-functions/rational-transfer-function.jl	0.00% <0.00%> (ø)
src/polynomials/multroot.jl	92.38% <50.00%> (+0.07%)	⬆️
src/rational-functions/common.jl	56.04% <56.04%> (ø)
src/rational-functions/rational-function.jl	60.00% <60.00%> (ø)
src/polynomials/ngcd.jl	95.68% <66.66%> (-0.60%)	⬇️
src/rational-functions/fit.jl	71.23% <71.23%> (ø)
src/common.jl	90.74% <100.00%> (+0.33%)	⬆️
... and 6 more

---

Continue to review full report at Codecov.

Legend - Click here to learn more
Δ = absolute <relative> (impact), ø = not affected, ? = missing data
Powered by Codecov. Last update e9f59d7...fa950a6. Read the comment docs.