#10550: integration not working
------------------------+---------------------------------------------------
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: |
------------------------+---------------------------------------------------
Comment(by dsm):
Just for the record, if given enough precision and the singularity
locations, mpmath does okay in tanh-sinh on the infinite range:
{{{
sage: import mpmath
sage: dpss = [int(10*1.25**i) for i in [0..15]]
sage: qq = []
sage: for dps in dpss:
....: mpmath.mp.dps = dps
....: q = mpmath.quad(lambda x: abs(x^2 - 1)^(-2/3), (-infinity, -1,
1, infinity))
....: delta = float(abs((q-qq[-1])/qq[-1])) if qq else 0.0
....: print dps, RealField(250)(q), delta
....: qq.append(q)
....:
10
12.619415730000000000000000000000000000000000000000000000000000000000000000
0.000000000000000
12
12.619588240700000000000000000000000000000000000000000000000000000000000000
1.36705461222e-05
15
12.619632936725900000000000000000000000000000000000000000000000000000000000
3.54179740682e-06
19
12.619638678800019440000000000000000000000000000000000000000000000000000000
4.55011184915e-07
24
12.619638942183136436066100000000000000000000000000000000000000000000000000
2.08708920835e-08
30
12.619638947875526360028104307100000000000000000000000000000000000000000000
4.51073913449e-10
38
12.619638947928984872554788554326908474000000000000000000000000000000000000
4.2361364495e-12
47
12.619638947929088225923816071123105700944331096000000000000000000000000000
8.18988320141e-15
59
12.619638947929088350562971317084699893895128992807003256090000000000000000
9.87660231487e-18
74
12.619638947929088350575171596623717955924858573775002931329627429009895074
9.66769302146e-22
93
12.619638947929088350575171711452592280507575074285006026048789429945225951
9.0992202549e-27
116
12.619638947929088350575171711452647219166086056903447254987222698078233522
4.35342554075e-33
145
12.619638947929088350575171711452647219167199848815619049997783218559507282
8.82586195031e-41
181
12.619638947929088350575171711452647219167199848815874865637945653424795957
2.02712328949e-50
227
12.619638947929088350575171711452647219167199848815874865637945883686562894
1.82463038671e-62
284
12.619638947929088350575171711452647219167199848815874865637945883686562894
9.97427124086e-78
}}}
and plotting it shows a very plausible logarithmic decrease in the size of
the change (can't really call it an error..) You have to give it way more
digits of precision than it actually gets right, but it's possible that it
converged in the end.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10550#comment:13>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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