Coxeter
CoxeterThe program contains an implementation of the computation of inverse Kazhdan-Lusztig polynomials. Recall that they are the unique family of polynomials Qx,y s.t. the matrix ((-1)l(y)-l(x)Qy,x) be the inverse of the matrix (Px,y); one may also define them combinatorially as the generlized Stanley polynomials for the interval $[x,y]$, for the same R-function as the ordinary ones (these being the generalized Stanley polynomials associated to the dual poset of [x,y].)
This part of the program could certainly be improved; it is in any case a lot slower than the computation of the ordinary polynomials. It has also been checked much less thoroughly, mostly for lack of comparison material! For finite groups, it is known that Qx,y = Pw0y,w0x for all x <= y in the group, where w0 is the longest element in the group. I have checked that for the groups A6, B5, F4 and H4, the inverse polynomials computed with the algorithm of the program coincide with the Pw0y,w0x computed with the algorithm for the ordinary polynomials; this should be a rather convincing verification (of both computations, actually.)