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Topic: An independent integration test suite
Replies: 42   Last Post: Jul 25, 2013 6:09 PM

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 clicliclic@freenet.de Posts: 1,245 Registered: 4/26/08
Re: An independent integration test suite
Posted: Jul 19, 2013 3:22 PM

clicliclic@freenet.de schrieb:
>
> daly@axiom-developer.org schrieb:

> >
> > Albert,
> >
> > I'm getting different answers than you for some of the problems.
> > In Axiom, if I do
> >
> > t0:=1/((1-x)^(9/2)*(1+x)^(5/2))
> > t1:=integrate(t0,x)
> > t2:=D(t1,x)
> > t3:=t0-t2
> >
> > I get 0 as a result. However, when I take the derivative of your
> > result and difference it from your initial equation I get a
> > non-constant result dependent on x.
> >
> > Perhaps you could check your answer in other systems and let me
> > know if you agree.
> >
> > I will be posting the first set of results shortly.
> >

>
> This integrand appears on page 1102 of rich1b.input.pdf. Its
> antiderivative
>
> - (8*x^5 - 16*x^4 - 4*x^3 + 24*x^2 - 9*x - 6)
> /(21*(1 - x)^(7/2)*(x + 1)^(3/2))
>
> is simply an algebraic function, so should be behave the same on all
> systems. Indeed your expression d000 at the bottom of page 1103
> simplifies to zero for arbitrary complex x.
>
> You are having more serious problems with the integrands on pages 994,
> 996, 998, 1000, 1004, 1008, 1017, 1019, 1020, 1021, 1022, 1107, 1109,
> and maybe elsewhere. Can FriCAS handle these (correctly) already?
>

The problem with the last two integrands is merely one of simplification
as for the integrand on page 1102 - I mistook these for cases of
branch-cut memory loss.

Martin.