/* Normal Form */
load("power-7.lisp");
/* This is a quick hack to check if a division produces a negitive power */ 
NegativePowerP(expr):=block([lov:listofvars(expr),flag:false],
   for v in lov do (
      if lopow(expr,v) < 0 then return(flag:true)
   ),
   flag
)$
lterm1(p):=ratdisrep(lterm(p,listofvars(p)))$

NormalForm(p,f) := block([s:length(f)],
   block([r:0,a:MAKE_ARRAY('ANY, s+1),i,dividing,q],
      for i:1 thru s do a[i]:0,
      while p # 0 do (
         i : 1,
         dividing : true,
         while ((i<=s) AND (dividing)) do (
	    q:divide(lterm1(p),lterm1(f[i])),
            if q[2] = 0 and not NegativePowerP(q[1]) then (
               a[i] : a[i] + q[1],
               p : p - expand(q[1]*f[i]),
               dividing : false)
            else i : i+1),
         if (dividing) then (
            r : r + lterm1(p),
            p : p - lterm1(p))),
      r))$
/* print(NormalForm(x^2*y + x*y^2+y^2, [x*y - 1, y^2- 1])); */