On Fri, 27 Aug 2021, 20:45 William Stein, <wst...@gmail.com> wrote:

> 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.
>

ginac, in fact, continues to be maintained, and even developed, after a
long hiatus. But the pynac fork diverged from it long time ago, and
naturally backporting new code/fixes from ginac appears to be very hard.



> -- 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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