Add adhoc arithmetics for FreeAssociativeAlgebraElem

[lgoettgens]

Resolves #1865

(tests copied from MPoly-test.jl, and added another few lines for QQ/Rational{Int} tests)

[fingolfin]

How about reducing code duplication and increasing flexibility by doing this instead:

Suggested change

	function *(a::FreeAssociativeAlgebraElem, n::Union{Integer, Rational, AbstractFloat})
	z = zero(a)
	fit!(z, length(a))
	j = 1
	for i = 1:length(a)
	c = a.coeffs[i]*n
	if !iszero(c)
	z.coeffs[j] = c
	z.exps[j] = a.exps[i]
	j += 1
	end
	end
	z.length = j - 1
	return z
	end
	function *(a::FreeAssociativeAlgebraElem{T}, n::T) where {T <: RingElem}
	z = zero(a)
	fit!(z, length(a))
	j = 1
	for i = 1:length(a)
	c = a.coeffs[i]*n
	if !iszero(c)
	z.coeffs[j] = c
	z.exps[j] = a.exps[i]
	j += 1
	end
	end
	z.length = j - 1
	return z
	end
	function mul!(z::T, a::T, n::RingElement) where {T <: FreeAssociativeAlgebraElem}
	fit!(z, length(a))
	j = 1
	for i = 1:length(a)
	c = a.coeffs[i]*n
	if !iszero(c)
	z.coeffs[j] = c
	z.exps[j] = a.exps[i]
	j += 1
	end
	end
	z.length = j - 1
	return z
	end
	*(a::FreeAssociativeAlgebraElem, n:: Union{Integer, Rational, AbstractFloat}) = mul!(z, a, n)
	*(a::FreeAssociativeAlgebraElem{T}, n::T) where {T <: RingElem} = mul!(z, a, n)

[lgoettgens]

The signature for mul! here is too wide, as this would capture mul!(::T, ::T, ::T) where T <: FreeAssociativeAlgebraElem as well. But I added something similar, with a restricted signature

[codecov]

Codecov Report

Attention: Patch coverage is 81.81818% with 6 lines in your changes missing coverage. Please review.

Project coverage is 88.15%. Comparing base (5ffdd2d) to head (df5df26).
Report is 1 commits behind head on master.

Files with missing lines	Patch %	Lines
src/generic/FreeAssociativeAlgebra.jl	81.81%	6 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #1866      +/-   ##
==========================================
- Coverage   88.17%   88.15%   -0.02%     
==========================================
  Files         120      120              
  Lines       30220    30250      +30     
==========================================
+ Hits        26645    26668      +23     
- Misses       3575     3582       +7     

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