Opened 23 months ago
Last modified 3 months ago
#24117 new defect
integrate(sqrt(1-4*sin(x)^2),x) is wrong
Reported by: | slabbe | Owned by: | |
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Priority: | major | Milestone: | sage-8.1 |
Component: | calculus | Keywords: | maxima, abs_integrate |
Cc: | Merged in: | ||
Authors: | Reviewers: | ||
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description
I received an email from Pierre Arnoux saying that this is wrong:
sage: integrate (sqrt(1-4*sin(x)^2),x, algorithm='maxima') -1/12*sin(3*x) + 1/4*sin(x)
Quoting what Pierre says: "Ce qui est visiblement faux: il y a un point d'inflexion horizontal en 0 alors que la fonction à intégrer vaut 1 en 0, ça ne peut pas être une primitive. Est-ce que vous avez une idée de ce qui ne marche pas?"
Other programs in Sage just can't solve this integral:
sage: integrate (sqrt(1-4*sin(x)^2),x, algorithm='fricas') # installed with "sage -i fricas" integral(sqrt(4*cos(x)^2 - 3), x) sage: integrate (sqrt(1-4*sin(x)^2),x, algorithm='giac') integrate(sqrt(-4*sin(x)^2 + 1), x) sage: integrate (sqrt(1-4*sin(x)^2),x, algorithm='sympy') ....does not halt...
Change History (5)
comment:1 Changed 23 months ago by
comment:2 Changed 22 months ago by
Here is how I would describe this bug in the integrate function. (This can be turned into a doctest when this bug is resolved.)
sage: f(x) = sqrt(1-4*sin(x)^2) sage: F(x) = integrate(f(x), x) sage: F(x) -1/12*sin(3*x) + 1/4*sin(x)
Comparing the derivative of F with f shows this is wrong.
sage: g(x) = diff(F(x), x) sage: g(x) -1/4*cos(3*x) + 1/4*cos(x) sage: f(0), g(0) (1, 0)
Looking at the plots of f and F also reveals an error:
sage: xr = (-0.4, 0.4) sage: plot(f, xr, color='blue') + plot(F, xr, color='red')
Here, f (blue curve) is 1 at 0, so its primitive F (red curve) should have slope 1 at 0, instead of 0.
comment:3 Changed 22 months ago by
There are half a dozen similar tickets to this. The reason is that Sage uses a (now) unmaintained package of Maxima, see #12731 for an overview.
comment:4 Changed 4 months ago by
- Keywords abs_integrate added
comment:5 Changed 3 months ago by
this one is fixed by #27958, that needs review
See also #18821.