work on polynomial_composition. Close #520

[jverzani]

Start on some special cases for polynomial composition that improve inferrability.

[codecov]

Codecov Report

Attention: Patch coverage is 0% with 6 lines in your changes missing coverage. Please review.

Project coverage is 75.18%. Comparing base (6f5e5bb) to head (cd1cc01).
Report is 64 commits behind head on master.

Files with missing lines	Patch %	Lines
...polynomials/standard-basis/immutable-polynomial.jl	0.00%	6 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #524      +/-   ##
==========================================
- Coverage   76.59%   75.18%   -1.42%     
==========================================
  Files          35       34       -1     
  Lines        3739     3534     -205     
==========================================
- Hits         2864     2657     -207     
- Misses        875      877       +2     

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[nsajko]

A polynomial composed with zero is the polynomial's constant term, not always zero. For example, if we have f(x) = 1 and g(x) = 0, f∘g is 1, not 0.

[nsajko]

Apart from that, I don't think the promotion is necessary, that is, I think you could just ignore S, because the value of q is always zero, independently of S.

[nsajko]

Could you also add fallback methods for polynomial_composition that would work by simply converting the ImmutablePolynomial to Polynomial?

Something like:

polynomial_composition(p::Polynomial, r::ImmutablePolynomial) = p(Polynomial(r))