[math-fun] Decades ago, David R. Barton wrote Macsyma's polynomial decomposer:

(c18) (ratsubst(x^2+3,x,x^3-27),%% = polydecomp(%%,x)) 6 4 2 3 2 (d18) x + 9 x + 27 x = [x - 27, x + 3] But it won't recognize the numerator of a composition of rational functions: (c20) (num(ratsubst(x+3/x,x,x^3-27)),%% = polydecomp(%%,x)) 6 4 3 2 (d20) x + 9 x - 27 x + 27 x + 27 = 6 4 3 2 [x + 9 x - 27 x + 27 x + 27] Anyone know how to do this? I can't even remember how Barton's program works, despite attending his elegant presentation at IBM Yorktown (SYMSAC 76?). --rwg