On 03/13/2018 12:53 PM, Waldek Hebisch wrote:
When trying to integrate:
integrate(1/(x^4+2*a*x^2+a^2-1),x)
I get a list containing "all possible solutions"; that's okay, but how
do I determine what conditions the alternatives hold for?  Is there an
automated way; or do I have to evaluate each solution separately
Well, each solution is supposed to be correct solution.  Which
one is more appropriate depends on conditions unknown to the
integrator.

?Dealing with the same problem I tried:
complexIntergrate()
and got one solution.
Should I just go with complexIntegrate() all the time?
_You_ decide what you need.  But in general result of 'complexIntegrate'
is likely to be futher from user input than result of 'integrate'.

I am evaluating the Rubi test suite in Maxima and trying fricas as a
fall back when Maxima fails; and trying to keep the interface simple.
Depends what you want to check.  In some tests I checked all solutions
returned by FriCAS, in other cases just the first result.

I am just differentiating the integral produced and matching that to the integrand. Then doing a "leaf count" of the resulting integral and comparing that to the Rubi form. Actually falling back on Fricas is probably cheating, and won't fly with the Rubi author.
i.e. if Maxima returns an unevaluated value I call Fricas :)
I can't resist showing that there is a free program that does solve the integral. I suppose that one could weld the two together (say like Sage does) and communicate by real "pipes" rather than through the disk :) ; and just call them different "modes".  Since they have different Goals (typed vs. nontyed (more or less)) that seems better than rewriting or merging both; or some such.

RayR

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