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