```Date: Sep 6, 2013 2:51 PM
Author: Peter Luschny
Subject: Re: The integration test suites for Sage.

>> 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 andthere are differences with regard to the Charlwood problems!Problem 8 for example now has a monster solution; so long thatI 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 oronly for the real line? Charlwood writes: "We consider integrals of real elementary functions of a single real variable in the examplesthat 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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