Opened 5 years ago
Last modified 2 months ago
#17511 needs_info defect
Get integral of abs(sin(x)) and abs(cos(x)) right
Reported by: | kcrisman | Owned by: | |
---|---|---|---|
Priority: | major | Milestone: | sage-8.9 |
Component: | calculus | Keywords: | abs_integrate |
Cc: | slelievre | Merged in: | |
Authors: | Frédéric Chapoton | Reviewers: | Vincent Delecroix |
Report Upstream: | Reported upstream. Developers acknowledge bug. | Work issues: | |
Branch: | Commit: | ||
Dependencies: | Stopgaps: | #12731 |
Description (last modified by )
See this comment, discussion in #13364, the supposed fix at https://sourceforge.net/p/maxima/bugs/2520/, this ask.sagemath question, and so forth.
E.g. this is annoying (but apparently right)
(%i1) load(abs_integrate); (%i3) display2d:false; (%o3) false (%i4) integrate(abs(sin(x)),x); (%o4) 4*(abs(sin(x))*(atan(sin(x)/(cos(x)+1))/2 +sin(x)/((cos(x)+1)*(2*sin(x)^2/(cos(x)+1)^2+2))) /abs(cos(x)+1) -(signum(1/(cos(x)+1))*signum(sin(x))*log(2*sin(x)^2/(cos(x)+1)^2+2) -signum(1/(cos(x)+1))*signum(sin(x))*log(sin(x)^2/(cos(x)+1)^2+1) +signum(1/(cos(x)+1))*signum(sin(x)) *(2*sin(x)*atan(sin(x)/(cos(x)+1))/(cos(x)+1) -log(2))) /4)
but it doesn't do the definite integral at all, even the easy ones where abs does nothing on the interval!
Change History (17)
comment:1 Changed 5 years ago by
comment:2 Changed 5 years ago by
- Report Upstream changed from Not yet reported upstream; Will do shortly. to Reported upstream. Developers acknowledge bug.
comment:3 Changed 5 years ago by
- Description modified (diff)
comment:4 Changed 5 years ago by
- Stopgaps set to #12731
comment:5 Changed 4 years ago by
Reported again at https://groups.google.com/forum/#!topic/sage-support/1Hcv29UyqVo
comment:6 Changed 7 months ago by
- Keywords abs_integrate added
comment:7 Changed 4 months ago by
Everything works in 8.9.b7 after #27958. Some doctests were added there.
Maybe one could add one doctest for
sage: integrate(abs(sin(x)),x) -cos(x)*sgn(sin(x)) + sgn(sin(x))
comment:8 Changed 3 months ago by
- Branch set to u/chapoton/17511
- Commit set to 4a8dff966bffe1f792c9d2acbfa9d9c03b15a5e4
- Milestone changed from sage-6.5 to sage-8.9
- Status changed from new to needs_review
comment:9 Changed 3 months ago by
- Reviewers set to Vincent Delecroix
This answer
sage: integrate(abs(sin(x)),x) -cos(x)*sgn(sin(x)) + sgn(sin(x))
is *very* wrong (outside of [-pi, pi])! It takes negative values
sage: f = integrate(abs(sin(x)), x) sage: (f(5) - f(0)).n() -0.716337814536774
and the integral is supposed to go to +oo
as x -> +oo/-oo
...
comment:10 Changed 3 months ago by
But this is correct
sage: integrate(abs(sin(x)), x, 0, 10) cos(10) + 7
comment:11 Changed 3 months ago by
And I like very much
sage: %time integrate(abs(sin(x)), x, algorithm='sympy') CPU times: user 8.09 s, sys: 99 µs, total: 8.09 s Wall time: 8.1 s integrate(abs(sin(x)), x)
comment:12 Changed 3 months ago by
Indeed. Giac is responsible for the wrong answer. This should be reported upstream.
sage: integrate(abs(sin(x)),x,algorithm='maxima') integrate(abs(sin(x)), x) sage: integrate(abs(sin(x)),x,algorithm='sympy') integrate(abs(sin(x)), x) sage: integrate(abs(sin(x)),x,algorithm='giac') -cos(x)*sgn(sin(x)) + sgn(sin(x)) sage: integrate(abs(sin(x)),x,algorithm='fricas') integral(abs(sin(x)), x) sage: integrate(abs(sin(x)),x,algorithm='mathematica_free') -cos(x)*sgn(sin(x))
comment:13 follow-up: ↓ 14 Changed 3 months ago by
But giac is also providing the correct answer for the definite integral, where sympy fails to deliver:
sage: integrate(abs(cos(x)),x,0,44,algorithm='maxima') integrate(abs(cos(x)), x, 0, 44) sage: integrate(abs(cos(x)),x,0,44,algorithm='sympy') -sin(44) + 4 sage: integrate(abs(cos(x)),x,0,44,algorithm='giac') sin(44) + 28 sage: integrate(abs(cos(x)),x,0,44,algorithm='fricas') integrate(abs(cos(x)), x, 0, 44) sage: integrate(abs(cos(x)),x,0,44,algorithm='mathematica_free') sin(44) + 28
comment:14 in reply to: ↑ 13 Changed 3 months ago by
Replying to chapoton:
But giac is also providing the correct answer for the definite integral, where sympy fails to deliver:
[...]
which should also be reported upstream I guess...
comment:15 Changed 3 months ago by
- Branch u/chapoton/17511 deleted
- Commit 4a8dff966bffe1f792c9d2acbfa9d9c03b15a5e4 deleted
- Status changed from needs_review to needs_info
comment:16 Changed 2 months ago by
- Cc slelievre added
Samuel, would you please report to giac the failure of comment:12 ?
comment:17 Changed 2 months ago by
I emailed Bernard Parisse, here is his reply:
Ce n'est pas une erreur, au sens ou un avertissement est renvoyé 0>> integrate(abs(sin(x)) Warning adding 1 ) at end of input Attention, l'intégration de abs() ou sign() suppose un signe constant par intervalles (vérifié si l'argument est réel): Verifiez [abs(sin(x))] Discontinuités aux zeros de sin(x) were not checked sign(sin(x))-cos(x)*sign(sin(x)) // Time 0.04 C'est à l'utilisateur de prendre garde aux discontinuites de la primitive pour calculer une intégrale définie s'il utilise la primitive renvoyée. Lorsqu'on demande à giac une intégrale définie, il essaie de tenir compte des discontinuités, et il fait le calcul numérique en parallèle pour verifier. En cas de non concordance, les 2 valeurs sont renvoyées (la plupart du temps c'est la valeur numérique qui est la bonne).
which roughly translates as
This is not an error, in the sense that a warning is issued: 0>> integrate(abs(sin(x)) Warning adding 1 ) at end of input Caution, integrating abs() or sign() assumes piecewise constant sign (check if the argument is real): Check [abs(sin(x))] Discontinuities at zeros of sin(x) were not checked sign(sin(x))-cos(x)*sign(sin(x)) // Time 0.04 It is up to the user to check for discontinuities of the antiderivative to compute an integral using the antiderivative returned by giac. When asking giac for an integral on an interval, it tries to take discontinuities into account, and does the numerical integration in parallel to check. In case of mismatch, both values are returned (most of the time the numerical value is the one that is correct).
Worse,