#################################################################### # Compute products in the equivariant cohomology of Fl(2,4;5) # # and the equivariant quantum cohomology of Gr(2,5), reproducing # # Example 2.2 and Example 2.5 in the paper # # "Mutations of puzzles and equivariant cohomology of two-step # # flag varieties" by A. Buch. # #################################################################### read equivcalc: with(equivcalc): t2y := {seq(t[i] = y[i+1]-y[i], i=1..4)}: printf("H_T(Fl(2,4;5)):\n"): Fl(2,4,5): up := X[1,4,2,5,3]: # 012-string 01201 vp := X[2,4,1,3,5]: u := sp_weyl(up): v := sp_weyl(vp): prd := expand(subs(t2y, htmult(u, v))): lprint(weyl_sp(u * v = prd)): printf("\n"): printf("QH_T(Gr(2,5)):\n"): Gr(2,5): la := X[2,1]: mu := X[3,1]: u := part_weyl(la): v := part_weyl(mu): prd := expand(subs(t2y, comin_qhtmult(u, v))): lprint(weyl_part(u * v = prd)): ###