>> Sorry, this is not correct. It is in FIELD (for EXPR INT)
Excuse me, I was to quick again. Here is the (hopefully correct) anaylysis:
exquo(simplify((A2^a)*(A+2^a))::UP(A,EXPR INT),(A2^a)::UP(A,EXPR INT))
calls exquo$SUP(EXPR INT). This implements exact division of polynomials p1 by p2 as usual. After each subtraction  done via fmecg$SUP  the result is again stored in p1. exquo terminates when p1 is the empty list  note that SUPs are stored as lists of pairs (degree, coefficient)  or the degree of p2 is larger than p1. In the latter case, exquo fails.
Thus, in our case, at one point p1 is 4^a2^(2*a), which is zero mathematically, but axiom does not know it. In particular, p1 is not the empty list, but rather a constant polynomial...
It would be interesting to see how MuPAD or Aldor handle this.
