On Nov 16, 6:50 pm, cliclic...@freenet.de wrote: > TimDaly schrieb: > > > > > > > On Oct 19, 5:16 pm, cliclic...@freenet.de wrote: > > > Richard Fateman schrieb: > > > > > cliclic...@freenet.de wrote: > > > > >... > > > > > they claim to deliver the antiderivative of any elementary function if > > > > > it can also be written in terms of elementary functions... > > > > > At least Maxima / Macsyma makes no such claims, and in particular > > > > neither implements completely the algebraic case of the Risch algorithm. > > > > Undoubtedly simpler examples will stump these programs. > > > > Errh. Ok. Alright. Maxima users are excused for the time being - they > > > may hand in their answers after the next integrator overhaul. On the > > > other hand, Derive also makes do with less than 1000 general > > > integration rules like > > > INT(F((a+b*x)^(1/n),x),x) -> > > > n/b*SUBST(INT(x^(n-1)*F(x,(x^n-a)/b),x),x,(a+b*x)^(1/n)), > > > or > > > INT(x^m*LN((a*x^n)^q),x) -> > > > x^(m+1)*LN((a*x^n)^q)/(m+1)-n*q*x^(m+1)/(m+1)^2. > > > What counts in the end is the ability to handle real-life integrals like > > > the problem posed. Maybe Risch's is not the best way? > > > > And now pssss. They are all crouched over their screens. No sound but > > > the occasional keyboard click and slurp of coffee. Papa Wolfram looks > > > particularly grave. Will he and his crew flunk again? > > > > Martin ;) > > > Interesting. Where do you find such patterns? > > Do you have a catalog of them I can try? > > Could you be more specific? Does your "catalog of patterns" refer to my > integration problems, or perhaps to my associative memory connecting > attempts to solve them with concepts like "coffee" and "Wolfram" (which > is further linked to "Papa") and "trance"? > > Martin.
Do you have a catalog of patterns (in source code) of the form: INT(F((a+b*x)^(1/n),x),x) -> n/b*SUBST(INT(x^(n-1)*F(x,(x^n-a)/b),x),x,(a+b*x)^(1/n)), I would like to see what patterns you have and compare them against the integration test suite that Axiom uses. Tim _______________________________________________ Axiom-developer mailing list Axiom-developer@nongnu.org http://lists.nongnu.org/mailman/listinfo/axiom-developer