Dear Sumant, "Sumant S.R. Oemrawsingh" <[EMAIL PROTECTED]> writes:
> (1) -> h(k,x)==1/2 + 1/%pi * atan(k*x) > (2) -> f(k,x)==x**2 * (h(k,x)-h(k,-x)) > (4) -> g(x)==limit(f(k,x),k=%plusInfinity) > What I would think is that, since g(x) is a sum of two functions, the > integral would split up into a sum of integrals as well. Hm, why should g(x) be a sum of two functions? My axiom gives me upon issueing g x x abs(x) > (6) -> integrate(g(x),x=-1..1,"noPole") > integrate(g(x),x=-1..1,"noPole") > (6) -> > (6) "failed" > Type: Union(fail: failed,...) This just says that axiom couldn't do the integral. In particular, bugs aside, it is a "proof" that it not expressible as an elementary function. (The Risch algorithm is more or less completely implemented in axiom, and axiom will spit out an error message if you hit an unimplemented branch.) > So I've been looking a bit into how this could be done in spad. But I've not > been able to understand where and how the functionality of such special > functions is or can be implemented, or if I somehow would have to extend the > definition or workings of the integrate function itself. For a start, I'd think it is easier to split up integration boundaries semi-automatically, as I indicated in a previous email. If you are really interested in the internals, I think that intpm.spad is for you, it tells axiom some pattern matching rules. In my opinion, we should go the mupad way here, the source of axiom is a horror, while the one of mupad is extremely easy to grasp and to extend. But that's way beyond my (computer algebra) skills. All the best, Martin _______________________________________________ Axiom-developer mailing list [email protected] http://lists.nongnu.org/mailman/listinfo/axiom-developer
