On Fri, Aug 27, 2021 at 2:21 AM Dima Pasechnik <dimp...@gmail.com> wrote:
> How are these integrals above computed by Sage? Via Maxima, or in some
> other way?

When I implemented this, they were all computed in Maxima by default,
unless otherwise requested.  Thus symbolic integration may be
orthogonal to the pynac vs symengine discussion.  You can browse  some
of the beautiful decades(!) old Maxima lisp code for integration
starting here:
https://github.com/andrejv/maxima/blob/master/src/defint.lisp
I'm cc'ing RJF in case he has some perspective to add.

Pynac has a lot of I think nontrivial efficient hooks back into Sage
for working with various data types, and doing things like equality
testing, fast evaluation of expression (fast_float, etc.), so it'll be
quite a lot of work to switch away from.   I created pynac as a fork
of ginac only because there was a very talented student trying for a
year to do something similar more from scratch in Cython, and I got
impatient.   It's too bad pynac is unmaintained now; I think the basic
idea wasn't so bad, and the performance was pretty good.

-- William

> > and sympy.integrate(*map(sympify, (dgamma(x, a, b), (x, 0, 
> > 1)))).simplify()._sage_() never returns. Res ipsa loquitur…
> >
> > BTW : many Sympy integrations result in Sympy’s Piecewise expressions 
> > (correctly transcripted as Sage’s cases) involving logical expressions 
> > using Sympy’s symbolic logical functions/operators And, Or and Not, which 
> > have currently no equivalent in Sage (but see Trac#31911…)
> >
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-- 
William (http://wstein.org)

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