Add giac interface to integrate

[mforets]

Provide a giac_integrator function, which relies on the external (but standard) Giac package.

A test could be:

sage: integrate(abs(cos(x)), x, 0, 2*pi, algorithm='giac')
4

This test is chosen because (at the time or writing) Maxima gives a wrong result (0), SymPy gives i don't know (unevaluated), and Fricas (optional package) gives 'failed'.

Component: calculus

Keywords: giac, integrate, symbolics

Author: Marcelo Forets

Branch/Commit: 8e1af6d

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/22891

[mforets]

comment:1

(minor, documentation): in symbolic/integration/integral.py, the word EXAMPLES appears two times, first in the usual place, then just after the ALIASES. this is a bit strange. shall we remove the second one?

[mforets]

Branch: u/mforets/t/mforets/giac_integrator

[mforets]

comment:3

setting to review; i've added the new optional keyword algorithm='giac', and for the moment i wouldn't know if there is something else that needs to be done with respect to this ticket! feedback welcome

---

New commits:

8e1af6d

add giac external integrator

[mforets]

Commit: 8e1af6d

[kcrisman]

comment:4

Love this. Don't see any obvious problems with the commit (I haven't tested it, though, just reading through).

On a related note, can you test out the various tickets at https://trac.sagemath.org/wiki/symbolics#Integrationtickets with this? In particular the abs_integrate ones, see e.g. #12731. If the integrator here is powerful enough, it might be time to replace the Maxima integrator with this one; the Maxima one has many errors (though in my opinion is still way better than not having one, as most of those are on relatively "interesting" functions like your example, abs and other stuff with branch issues).

[mforets]

comment:5

we may want to ensure a symbolic integral wrapper, for instance with (cf. #22138):

sage: n = var('n')
sage: integral(x^n*sin(x), x, algorithm='giac')
...
NotImplementedError: Unable to parse Giac output: integrate(x^n*sin(x),x)

but in other cases it already returns unevaluted:

sage: integrate(log(1+x)/x, x, 0, 1, algorithm='giac')
integrate(ln(x + 1)/x, x, 0, 1)

[mforets]

comment:6

Replying to @kcrisman:

Love this. Don't see any obvious problems with the commit (I haven't tested it, though, just reading through).

On a related note, can you test out the various tickets at https://trac.sagemath.org/wiki/symbolics#Integrationtickets with this? In particular the abs_integrate ones, see e.g. #12731. If the integrator here is powerful enough, it might be time to replace the Maxima integrator with this one; the Maxima one has many errors (though in my opinion is still way better than not having one, as most of those are on relatively "interesting" functions like your example, abs and other stuff with branch issues).

:) here are some gist of hard integrals

[tscrim]

Reviewer: Travis Scrimshaw

[tscrim]

comment:7

I think this is something that we should get into the next Sage, but we should discuss on another ticket, and possibly sage-devel, switching the default integrator.

[mforets]

comment:8

Replying to @tscrim:

I think this is something that we should get into the next Sage, but we should discuss on another ticket, and possibly sage-devel, switching the default integrator.

thanks for the review!

yes, IMO some action should be taken (for example to double check with numerical integrator and show a warning if nonsense is detected / dispatch another integrator for known issues eg. abs-trig or some special functions). i am not a big fan of 'blatantly wrong' answers, because from the user's point of view, it makes you loose a lot of confidence on the software.

[kcrisman]

comment:9

Oh yeah, we would want some super testing if we switched the default. But the problem is that currently Maxima's integration for anything involving branches or abs is weak, at least the way we interface with it.

As a first approximation, perhaps we could have a system where we removed the abs_integrate option from Maxima and then had Sage use either Sympy or giac as a backup if "integral" was in the returned Maxima output... anyway, that's for sage-devel, for sure.

[vbraun]

Changed branch from u/mforets/t/mforets/giac_integrator to 8e1af6d