WIP: TaylorRec

[lbenet]

TaylorRec{T,N} is an implementation of multivariate Taylor polynomials as a recursive dense representation, including tests. It is in the "TaylorRec" branch.

The idea is to generate a polynomial in N variables as a polynomial of one variable, with coefficients that are polynomials in N-1 variables. For the time being, it is incorporated along TaylorSeries, i.e., without any replacement. It seems to be much slower, probably due to the bad memory management that the recursion imposes.

@dpsanders I think this is partially what you had in mind in #11, avoiding the problem I described there. There are some nice things of this approach; yet, the performance is bad...

[lbenet]

Things that work nicely here (related to this comment):

julia> x = @taylorRec(1,6)
TaylorSeries.TaylorRec{Float64,1}([0.0,1.0,0.0,0.0,0.0,0.0,0.0])

julia> y = @taylorRec(2,6)
TaylorSeries.TaylorRec{Float64,2}([TaylorSeries.TaylorRec{Float64,1}([0.0,1.0,0.0,0.0,0.0,0.0,0.0])])

julia> (x^2-y^2) / (x+y);   # a nice `pretty-print` is not yet fully done; result is x-y

julia> TaylorSeries.pretty_print(ans)
" ( - 1.0⋅x₂ ) + ( 1.0 )⋅x₁"

So the result is indeed x-y. Other examples that can be factorized also work.