> Hmm, what your 'deepunivariate' should do when kernel is
> 'sqrt(x^3 - x)'?

Well, in "deepunivariate(exp, first kernels sqrt(x^3-x))", normally
(x^3-x)|exp, that's the case when the function is constructed by
composition. If that's not the case, then ilog2atan can't simplify
this case.  So I think INTG0 is not needed.

> OTOH transformations done by INTG0 may introduce
> artifacts and one of task done in 'irexpand.spad' is
> the eliminate (or minimize) artifacts due to earlier
> steps.  So you need to look at impact on all integrals.

I think current patch minimizes artifacts for some input
and doesn't increase artifacts for others. So it's a step
forward.

But your example makes me realized that in general this
simplification is not an algorithm (impossible to solve all input):
for example "g x == sqrt(x+1)+sqrt(x-1)",
then the kernels are [x,sqrt(x+1),sqrt(x-1)] and you can't
figure out the "real variable" should be "sqrt(x+1)+sqrt(x-1)".

So for a trival class of integrands, there can't be an algorithm
that can compute their continuous integral. Is that a theorem?
Or common knowledge?

or

-- 
You received this message because you are subscribed to the Google Groups 
"FriCAS - computer algebra system" group.
To unsubscribe from this group and stop receiving emails from it, send an email 
to [email protected].
To post to this group, send email to [email protected].
Visit this group at https://groups.google.com/group/fricas-devel.
For more options, visit https://groups.google.com/d/optout.

Reply via email to