Thu 30 Sep 2004 09:31:59 AM UTC, comment #3:
>> 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((A-2^a)*(A+2^a))::UP(A,EXPR INT),(A-2^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^a-2^(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.
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