[WIP] Ring type (issue #349, #234)

[jverzani]

In response to issue #329 and an earlier -- much more intrusive -- PR #234, this
relaxes T in AbstractPolynomial{T,X}to be any type, not just T <: Number.

The main operations should mostly work, but we use some assumptions on methods for T that
get exposed below.

At a minimum, it seems the following should work for this to be useful when T has +,* defined for it:

p::Polynomial{T,:x}
q::Polynomial{T,:x}
s::Number
c::T

# scalar mult (note c::S * p::Polynomial{T,X} is not defined, even if it may make sense for some T)
s*p
p*s
c*p
p*c

# poly add
p + q

# poly mult
p * q

# poly powers
p^2

# implicit promotion
p + s
p + c # possible error, but p + P([c]) should work

# evaluaion a + b*x + c*x^2 (left multiply by coefficients)
p(s)
p(c)

# ∂, ∫
derivative(p)
integrate(p)

# matrix element
[p q]
[p s] # not always

See the new tests for details.

[codecov]

Codecov Report

Merging #350 (b47325f) into master (11457cf) will decrease coverage by 0.52%.
The diff coverage is 69.23%.

@@            Coverage Diff             @@
##           master     #350      +/-   ##
==========================================
- Coverage   78.79%   78.26%   -0.53%     
==========================================
  Files          23       23              
  Lines        2650     2719      +69     
==========================================
+ Hits         2088     2128      +40     
- Misses        562      591      +29     

Impacted Files	Coverage Δ
src/polynomials/factored_polynomial.jl	0.00% <0.00%> (ø)
src/show.jl	76.99% <0.00%> (-1.39%)	⬇️
src/polynomials/standard-basis.jl	87.89% <42.22%> (-6.31%)	⬇️
src/abstract.jl	45.71% <50.00%> (ø)
src/contrib.jl	92.64% <75.00%> (ø)
src/polynomials/ChebyshevT.jl	93.95% <80.00%> (-0.49%)	⬇️
src/polynomials/LaurentPolynomial.jl	89.41% <80.00%> (-0.22%)	⬇️
src/common.jl	89.38% <81.25%> (-0.81%)	⬇️
src/polynomials/SparsePolynomial.jl	98.29% <94.44%> (+0.14%)	⬆️
src/polynomials/ImmutablePolynomial.jl	94.11% <95.00%> (+0.48%)	⬆️
... and 1 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 11457cf...b47325f. Read the comment docs.