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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 11:34 AM

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?

Martin.