Date: Jul 21, 2013 1:30 AM
Author: daly@axiom-developer.org
Subject: Re: An independent integration test suite

On Friday, July 19, 2013 11:34:11 AM UTC-4, clicl...@freenet.de wrote:
> 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.


I have completed the Rich's test set (a+b x)^m (A+B x) (d+e x)^p for Axiom.
The results are at http://axiom-developer.org/axiom-website/CATS

Just a side note, the "source" format is a pamphlet file which is pure latex.
Axiom uses these literate programming documents. The executable code lives
in a "chunk" environment (similar to a "verbatim" environment). This file
format is used so the expected results are cached in readable form.

To run these files (e.g for rich2.input.pamphlet), start Axiom and type
)tangle rich2
)read rich2
The first command reads rich2.input.pamphlet and creates rich2.input
The second command reads and executes rich2.input

You can also check the results for regression failures with the command
)regress rich2
This command reads a file "rich2.output" (which is the spool file output
requested by the )spool command in the rich2.input file).

Failing stanzas (not marked "ok to fail") will generate a "FAILED" line.
A summary of FAILED lines is given at the end.

Some of the tests do not compare with the stored results (the --R comments)
because Axiom uses a random number generator and may get different constants.
Only explicitly "FAILED" lines are interesting.

I'll post again as I generate more results.

Tim