#11590: Integrating the sgn() function can produce incorrect results
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Reporter: mjo | Owner: burcin
Type: PLEASE CHANGE | Status: new
Priority: major | Milestone:
Component: calculus | Keywords:
Work_issues: | Upstream: N/A
Reviewer: | Author:
Merged: | Dependencies:
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Actual result:
{{{
sage: integrate(x * sgn(x^2 - 1/4), x, -1, 0)
1/2
}}}
Since the argument to sgn() has only one root, -1/2, on (-1, 0), there are
only two subintervals on which sgn() can have different values. In
particular,
{{{
sage: sgn(x^2 - 1/4)(x = -0.75)
1
sage: sgn(x^2 - 1/4)(x = -0.25)
-1
}}}
Now, the original, actual result should be equivalent to the sum of the
following:
{{{
sage: integrate(x, x, -1, -0.5)
-0.375
sage: integrate(-x, x, -0.5, 0)
0.125
}}}
So, something went wrong during the initial integration.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11590>
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