Start up Axiom, and type in the following integral integrate(sqrt(1+x^(-2/3)),x)
Then type in the same integral again. Maybe try the same integral a few more times. Do you get the same answer each time? I don't. I see the same behavior from axiom-20050901-4.1 (Debian sid) and axiom-20050201-1 (Debian sarge). I get two possible answers, one is (x^(3/2)+1)*sqrt(x^(3/2)+1) and the other one is a much more complicated radical expression. Ironically, the longer expression takes less time to compute. Differentiating both answers gets me back to the original integrand. Also, their curves coincide when plotted. It seems that each time the answer is correct. However, the shorter one is obviously more attractive because it looks simpler. Clearly, Axiom takes two different paths through the integration algorithm, even when give identical input. What is the cause of the branch? Is there a non-deterministic step somewhere in the algorithm? Incidentally, is there a canonical form for radical expressions in which the two forms of the answer can be compared and directly shown to be the same? Thanks in advance. Igor _______________________________________________ Axiom-math mailing list [email protected] http://lists.nongnu.org/mailman/listinfo/axiom-math
