#10550: integration not working
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Reporter: mariah | Owner: burcin
Type: defect | Status: new
Priority: minor | Milestone: sage-4.6.2
Component: calculus | Keywords:
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Comment(by mhampton):
Seems like there might be two issues here. One is that the default for
integrate_numerical (which is what I think gets called here after symbolic
integration fails) only uses a maximum of 87 sample points. This
parameter can be set by using integrate_numerical directly but I don't
think it can be through integrate.
The second possible issue is that it seems that integrate_numerical tries
to create a fast version of the function, but this is not done in an
accurate way. I believe this code was written prior to fast_callable,
which seems to help:
{{{
g = abs(x^2-1)^(-2/3)
gc = fast_callable(g,vars=[x],domain=RDF)
for i in range(3,15):
print i, RR(g.integrate(x, -10^i, 10^i)), integral_numerical(gc,
-10^i, 10^i, max_points=150)
3 12.0193735393553 (12.019608153321734, 9.1957321661164813e-05)
4 12.3400570107857 (12.341098980932561, 9.1150919425152691e-05)
5 12.4880961536322 (12.49028406429874, 6.9889256990153531e-05)
6 12.5548875258538 (12.55959625938481, 7.1073622858611871e-05)
7 12.6007931754768 (12.591761943525762, 0.00010294503436049848)
8 12.5769884999380 (12.60668258943978, 0.00010062716727896715)
9 12.6035401600491 (12.613617891834338, 0.00014081135169109776)
10 12.4014006867096 (12.616777202843952, 9.2533059420607869e-05)
11 11.1318879504315 (12.618201503159618, 0.0025695049437327948)
12 7.82165950876205 (12.618006422456004, 0.00021237998608546343)
13 6.48361691536824 (12.618918276607321, 0.0032425594623566767)
14 6.32209292067043 (12.619569344159935, 0.0097174091356236336)
}}}
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10550#comment:1>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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