C Y writes: > Re: fixing bug - Well, I can give it a shot if it's simple to find...
Well, what you need to find out is how the Risch algorithm would handle sin(x^2). Maybe it is simply handled by pattern matching, as exp(-x^2) is... In this case, fixing it would be easy. Mathematica also has a representation for sin(x^n), but I don't know whether it is "useful". (It's in terms of incomplete Gamma functions) > I've got some learning to do though. Me thinks the Risch algorithm > would be a rather ambitious way to try getting the hang of the Axiom > source code... Note that Axioms source is very nicely split into two parts: the "Algebra", implementing its mathematical capabilities, and the rest (compiler, interpreter, display, graphics, ...) > Ah, yes - the Risch algorithm. Do you happen to know if the full > algorithm is described online anywhere? Ideally both Risch's algorithm > and the extensions by Cherry et. al. for special functions would be > formally implimented (or documented since a fair part of it must > already be present.) Apparently nobody impliments the full algorithm > due to complexity?: http://mathworld.wolfram.com/RischAlgorithm.html > I wonder if it's too complex for the Axiom system, given the structure > it has in place. I've never studied it, but given how critical it is > to both systems it's high time I learned about it. If you are interested, it's certainly worth the effort. > > Unfortunately Manuel Bronstein died. I don't know anybody who would > > be able to document these routines. > > Well, when the great fall the lesser must pick up the torch. With some luck (and brains), the lesser become great that way. > I need to get ahold of some basic materials (Bronstein's books would be > useful, I'd wager :-) and get as much up to speed as my brain allows. I > need to learn Axiom's guts anyway and this sounds like a possibly useful > way. Maybe I could warm up by implimenting a physical units domain in > Axiom, although lord knows how I'd convince it to display things in the form > (numbers and variables)*units, or recognize Newtons out of a*kg*b*s^-2*c*m. > Does Axiom have provisions for non-standard display conventions and > substitution like that? Output is easy. )sh OUTFORM tells you everything you want to know about it. Pattern matching is there too. )sh PATMATCH or rather, use HyperDoc. Martin _______________________________________________ Axiom-developer mailing list Axiom-developer@nongnu.org http://lists.nongnu.org/mailman/listinfo/axiom-developer
