Opened 7 months ago
Last modified 4 weeks ago
#16643 needs_review defect
integrate() problem
Reported by: | rws | Owned by: | |
---|---|---|---|
Priority: | major | Milestone: | sage-duplicate/invalid/wontfix |
Component: | symbolics | Keywords: | integration, maxima |
Cc: | Merged in: | ||
Authors: | Reviewers: | Peter Bruin | |
Report Upstream: | Fixed upstream, but not in a stable release. | Work issues: | |
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description (last modified by nbruin)
I interrupted Sage after 5min of churning without result:
sage: f=diff((tan(x)+x)*e^tan(x),x) (tan(x)^2 + 1)*(x + tan(x))*e^tan(x) + (tan(x)^2 + 2)*e^tan(x) sage: integrate(f,x)
On a faster computer:
sage: %time integrate(f,x) CPU times: user 3min 58s, sys: 50 ms, total: 3min 58s Wall time: 3min 58s integrate((tan(x)^2 + 1)*(x + tan(x))*e^tan(x) + (tan(x)^2 + 2)*e^tan(x), x)
On the other hand, for the equivalent expression
sage: g=e^tan(x)*sec(x)^2*(tan(x)+x)+e^tan(x)*(sec(x)^2+1) sage: %time integrate(g,x) RuntimeError: ECL says: In function CAR, the value of the first argument is 0 which is not of the expected type LIST
which happens in maxima/ECL with abs_integrate loaded, but not in maxima/SBCL. Upstream: https://sourceforge.net/p/maxima/bugs/2781/
Change History (12)
comment:1 Changed 7 months ago by nbruin
comment:2 Changed 7 months ago by nbruin
The following helps perhaps to locate the problematic code. The following fragment does complete (but after considerable time):
from sage.interfaces.maxima_lib import * args=((tan(x)^2 + 1)*(x + tan(x))*e^tan(x) + (tan(x)^2 + 2)*e^tan(x), x) expr=EclObject(([max_integrate],[sr_to_max(SR(a)) for a in args])) result=maxima_eval(expr) max_to_sr(result)
this is the code the integrator would execute, and it does return the integral unevaluated. So somehow we're avoiding the error above.
Indeed, the difference seems to be how you feed the expression. Sage actually DOES return this integral (unevaluated), it just takes longer. The difference is in how you give the integral. The expression for the derivative that maxima computes gives the result above. However, the form computed by sage still works. If you do in maxima
... (%i6) f: (tan(x)^2 + 1)*(x + tan(x))*exp(tan(x)) + (tan(x)^2 + 2)*exp(tan(x)); (%o6) %e^tan(x)*(tan(x)^2+2)+%e^tan(x)*(tan(x)+x)*(tan(x)^2+1) (%i7) integrate(f,x); (%o7) 'integrate(%e^tan(x)*(tan(x)^2+2)+%e^tan(x)*(tan(x)+x)*(tan(x)^2+1),x)
everything is fine.
So the only report for Maxima is the above question why ECL runs into an error for the particular integral given there. This integral is not the one encountered with the original sage script and the sage code does finish correctly (albeit after a rather long time).
comment:3 Changed 7 months ago by nbruin
- Description modified (diff)
- Summary changed from integrate() infinite loop to integrate() problem
I changed the title and description, because I found evidence there is no infinite loop involved. Please change back if you're unhappy with the change.
comment:4 Changed 7 months ago by nbruin
- Description modified (diff)
comment:5 Changed 7 months ago by nbruin
- Description modified (diff)
comment:6 Changed 7 months ago by kcrisman
- Report Upstream changed from N/A to Reported upstream. No feedback yet.
comment:7 Changed 6 months ago by vbraun_spam
- Milestone changed from sage-6.3 to sage-6.4
comment:8 Changed 7 weeks ago by kcrisman
See also #12731.
comment:9 Changed 6 weeks ago by kcrisman
- Report Upstream changed from Reported upstream. No feedback yet. to Fixed upstream, but not in a stable release.
It's claimed that upstream has this 'fixed' in some sense now.
comment:10 Changed 6 weeks ago by pbruin
- Milestone changed from sage-6.4 to sage-duplicate/invalid/wontfix
- Reviewers set to Peter Bruin
- Status changed from new to needs_review
With Maxima 5.34.1 and also with 5.35.1 (see #17514), both integrals are returned unevaluated:
sage: f = diff((tan(x) + x) * e^tan(x), x) sage: %time integrate(f, x) CPU times: user 5min 32s, sys: 12 ms, total: 5min 32s Wall time: 5min 33s integrate((tan(x)^2 + 1)*(x + tan(x))*e^tan(x) + (tan(x)^2 + 2)*e^tan(x), x) sage: g = e^tan(x) * sec(x)^2 * (tan(x) + x) + e^tan(x) * (sec(x)^2 + 1) sage: %time integrate(g,x) CPU times: user 4min 43s, sys: 128 ms, total: 4min 44s Wall time: 4min 44s integrate((x + tan(x))*e^tan(x)*sec(x)^2 + (sec(x)^2 + 1)*e^tan(x), x)
I propose to close this since the ECL error appears to have been fixed upstream and the example takes too long to be a sensible doctest.
comment:11 Changed 6 weeks ago by kcrisman
some terrifyingly huge trig expression
says upstream... though I am agnostic on whether to close this, one could repurpose it as "make this integral faster" and ask upstream for that (or see if Sympy can do it faster, or whatever).
comment:12 Changed 4 weeks ago by rws
SymPy? is much faster to concede defeat.
sage: f=(tan(x)^2 + 1)*(x + tan(x))*e^tan(x) + (tan(x)^2 + 2)*e^tan(x) sage: %time integrate(f,x) CPU times: user 5min 45s, sys: 219 ms, total: 5min 45s Wall time: 5min 45s integrate((tan(x)^2 + 1)*(x + tan(x))*e^tan(x) + (tan(x)^2 + 2)*e^tan(x), x) sage: import sympy sage: x = sympy.Symbol('x') sage: %time sympy.integrate(f,x) CPU times: user 9.51 s, sys: 36 ms, total: 9.54 s Wall time: 9.52 s Integral((x + tan(x))*(tan(x)**2 + 1)*exp(tan(x)) + (tan(x)**2 + 2)*exp(tan(x)), x)
This may be a reportable issue upstream:
Without the load(abs_integrate) the code seems to execute fine (by returning the integral unevaluated). This does not fully explain why sage seems to get stuck on it, though. Perhaps a try/except that is a little too agressive in suppressing problems?
Also, the problem does not arise in Maxima 5.30.0 on SBCL 1.1.8-2, so it may be a problem with maxima-ecl interaction (so it depends a little on how well the maxima-devs want to support ECL)
Also executing domain: complex;load(to_poly_solve);load(simplify_sum); (as we do in sage) doesn't affect the outcome.