####################################################################
#  Compute the products necessary for the proof of Theorem 4.1     #
#  in the paper "K-theory of minuscule varieties"                  #
#  by A. Buch and M. Samuel.                                       #
####################################################################


read equivcalc:
with(equivcalc):


compute_products := proc(parts)
  local i, j, u, v, prd:
  for i from 1 to nops(parts) do
    for j from 1 to i do
      u := part_weyl(parts[i]):
      v := part_weyl(parts[j]):
      prd := kmult(u, v):
      lprint(weyl_part(u * v = prd)):
    od:
  od:
  printf("\n"):
  NULL:
end:


printf("Cayley plane E6/P6:\n"):
rs("E6", 6):
compute_products([X[4], X[4,4]]):

printf("Freudenthal variety E7/P7:\n"):
rs("E7", 7):
compute_products([X[5], X[5,4]]):


###
