[Axiom-developer] Re: Is your CAS no a weakling anymore?

[TimDaly]

On Nov 16, 6:50 pm, address@hidden wrote:
> TimDaly schrieb:
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> > On Oct 19, 5:16 pm, address@hidden wrote:
> > > Richard Fateman schrieb:
>
> > > > address@hidden 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