Implementation of Stanley's algorithm for projective group imbeddings (Q1015163)

\textit{R. Stanley} developed an algorithm to compute the intersection cohomology Betti numbers for toric varieties [Adv. Stud. Pure Math. 11, 187--213 (1987; Zbl 0652.52007)]. This algorithm was generalized by \textit{M. Brion} and \textit{R. Joshua} [J. Eur. Math. Soc. (JEMS) 6, No. 4, 465--481 (2004; Zbl 1129.14033)]. The algorithm has been implemented in GAP. The implementation is described in the paper. All necessary information on reductive varieties is given at the beginning. Several examples are discussed and the corresponding GAP-sessions are given.