Re: [Axiom-developer] Re: About Schaums.

[Waldek Hebisch]

Martin Rubey wrote:
> root <address@hidden> writes:
> >   Axiom has a closed form for 2 integrals where Schaums has series.
> 
> But at least one of them seems to be wrong. Since it seems that my message was
> overlooked, I repeat it here:
> 
> address@hidden writes:
> 
> >   14:668 SCHAUMS AND AXIOM DIFFER (Axiom has closed form)
> 
> But I'm not so sure that it is correct, at least not for a=1 and x in 0..1.
> 
> draw(D(integrate(asech(x)/x,x),x)-asech(x)/x, x=0..1)
> 

Integral of 'asech(x)/x' is definitely wrong.  I belive that the
error is in 'lfextendedint':

    lfextendedint(f, x, g) ==
      empty?(l := varselect(kernels f, x)) => [x::F * f, 0]
      symbolIfCan(k := kmax(l))
        case SE =>
          map(multivariate(#1, k), extendedint(univariate(f, k),
                                               univariate(g, k)))
      ...

AFAICS we need stronger condition than 'case SE' (and extra code
to handle remaining cases).
 
-- 
                              Waldek Hebisch
address@hidden