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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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Posts: 959
Registered: 4/26/08
Re: The integration test suites for Sage.
Posted: Sep 7, 2013 4:35 PM
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peter.luschny@gmail.com schrieb:
> [...] 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.

You may label any solution of more than ten times the size of the model
solution a "useless monster" and categorically refuse to analyze it any

> > 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?

Looks alright to me on the real axis. Is this what Sage/Maxima 5.11
returns for Charlwood's problem 43?

> > 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."

In order to compare systems whose default domain can be either the
real numbers or the complex numbers, Albert needs model antiderivatives
that hold on the entire complex plane, but for the former systems he
accepts as valid any evaluation that holds on the real axis. In the
Timofeev suite I took care to supply complex model antiderivatives for
the same reason. On the other hand, I expect real-only answers to be
fully adequate in professor Charlwood's calculus teaching context.


PS: How about contributing a chapter of the Timofeev suite yourself?
Axel Vogt has already promised chapter 6 (26 sundry integrands) in
addition to chapters 3 and 7, and Albert Rich didn't sound altogether
uninterested. I have already started on chapter 4 (132 algebraic
integrands). The remaining chapters are:

Chapter 2: 90 rational integrands
Chapter 5: 120 trigonometric integrands
Chapter 8: 109 exponential and hyperbolic integrands
Chapter 9: 59 inverse trigonometric integrands

It might make sense first to contact Albert in order to avoid a
duplication of work. Timofeev's book can be found at:


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