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Topic: The integration test suites for Sage.
Replies: 14   Last Post: Sep 14, 2013 1:53 PM

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 Peter Luschny Posts: 23 Registered: 11/18/06
Re: The integration test suites for Sage.
Posted: Sep 6, 2013 2:51 PM
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>> Albert used Maxima 5.28 whereas I used Sage 5.10. I do not know which
>> Maxima version Sage 5.10 uses. They might be different.

> The Maxima integrator would be undergoing noticeable development then. A
> pleasant surprise.

Well, I don't know. I just switched from Sage 5.10 to 5.11 and
there are differences with regard to the Charlwood problems!
Problem 8 for example now has a monster solution; so long that
I did not care to check if it is right or wrong.

> Charlwood_problem(43)
> integrand : tan(x)/sqrt(tan(x)^4 + 1)
> antideriv : -1/4*sqrt(2)*arctanh(-1/2*(tan(x)^2-1)*sqrt(2)/sqrt(tan(x)^4+1))
> maxima : -1/4*sqrt(2)*arcsinh(2*sin(x)^2 - 1)

> After sign inversion the Maxima result appears to be correct on
> the real axis.

Yes. And what about

diff(-1/4*sqrt(2)*arctanh(-1/2*(tan(x)^2-1)*sqrt(2)/sqrt(tan(x)^4+1)),x)
= tan(x)/sqrt((tan(x))^4+1)
versus
diff(-1/4*sqrt(2)*arcsinh(cos(2*x)),x)
= sin(2*x)/sqrt(cos(4*x)+3)

tan(x)/sqrt((tan(x))^4+1) = sin(2*x)/sqrt(cos(4*x)+3) on the real axis?

> But then Maxima doesn't claim to deliver antiderivatives for the
> entire complex plane, or does it?

What are rules of the game anyway: Does the 'Charlwood test'
require antiderivatives for the entire complex plane or
only for the real line? Charlwood writes: "We consider integrals of
real elementary functions of a single real variable in the examples
that follow."

>> Charlwood_problem(49)
>> integrand : arcsin(x/sqrt(-x^2 + 1))
>> antideriv : x*arcsin(x/sqrt(-x^2 + 1)) + arctan(sqrt(-2*x^2 + 1))
>> maxima : x*arcsin(x/sqrt(-x^2 + 1)) - 1/2*(-2*I*x^2 + I)/

sqrt(2*x^2 - 1) - 1/2*I*sqrt(2*x^2 - 1) - 1/2*I*log(sqrt(2*x^2 - 1) - 1)
+ 1/2*I*log(sqrt(2*x^2 - 1) + 1)

> The Sage/Maxima result is more than just deficient: it is incorrect for
> -1/SQRT(2) < x < 1/SQRT(2) on the real axis.

Ok.

Peter

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