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

From: TimDaly
Subject: [Axiom-developer] Re: Is your CAS no a weakling anymore?
Date: Mon, 16 Nov 2009 09:29:20 -0800 (PST)
User-agent: G2/1.0

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?

Tim Daly
Axiom Lead Developer
Elder of the Internet

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