I'd like to compute explicitly symmetric Macdonald functions associated to arbitrary (possibly non-reduced) root systems, using Computer Algebra System. 


Unfortunately Sage seems to only implement the A-type Macdonald polynomials <http://www.sagemath.org/doc/reference/sage/combinat/sf/macdonald.html>


* Is there a nice paper where a combinatorial formula is provided?
* Has somebody happened to implement it in some programming language?


Of course I can perform the Gram-Schmidt orthogonalization w.r.t. the known measure, but I'll keep it as a last resort.



Explicit method to compute Macdonald/Koornwinder functions
There is a better way to compute Macdonald polynomials explicitly than through Gram-Schmidt orthogonalization: using the action of the Macdonald operators.
Details can be found here DOI <http://dx.doi.org/10.1112/S0010437X03000149> (also avaliable in a somewhat longer version at arXiv:math/0303263)


The first few Macdonald polynomials can be computed in closed form from the Pieri formula.
Details can be found here DOI <http://dx.doi.org/10.1007/s00209-010-0727-0> (also available at arXiv:1009.4482)


