Date: Jul 15, 2013 11:09 PM
Author: Albert D. Rich
Subject: Re: An independent integration test suite

On Monday, July 15, 2013 10:16:42 AM UTC-10, da...@axiom-developer.org wrote:

> For some of the integration problems Axiom finds more than one result.
> For instance,
>
> t1:=sqrt(a+b*x)/x
>
>
> +-------+
> \|b x + a
> (1) ----------
> x
>
> Type: Expression(Integer)
>
> (2) -> integrate(t1,x)
>
>
> (2)
>
> +-+ +-------+
> +-+ - 2\|a \|b x + a + b x + 2a +-------+
> [\|a log(----------------------------) + 2\|b x + a ,
> x
>
> +-------+
> +---+ \|b x + a +-------+
> - 2\|- a atan(----------) + 2\|b x + a ]
> +---+
> \|- a
>
> Type: Union(List(Expression(Integer)),...)
>
> The posted suite only shows one answer.
> How should a test suite handle this?


Providing users a choice is always good, so I would compare both results with the optimal antiderivative in the test-suite and take the highest grade. However, if either result is invalid (i.e. fails to differentiate to the original integrand), give a negative grade.

Albert