#8321: numerical integration with arbitrary precision
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Reporter: burcin | Owner: burcin
Type: defect | Status: needs_work
Priority: major | Milestone: sage-4.5.3
Component: symbolics | Keywords: numerics,integration
Author: Stefan Reiterer | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Comment(by burcin):
Replying to [comment:13 maldun]:
> Replying to [comment:12 burcin]:
> > > Replying to [comment:8 kcrisman]:
> > > > Also, you might as well leave the GSL stuff in as comments, as in
the patch you posted above, or even as an optional argument, though that
may not be compatible with `_evalf_` elsewhere...
> >
> > Unfortunately, ATM, the numerical evaluation framework for symbolic
expressions doesn't support specifying different methods. This could
(probably, I didn't check the code) be done by changing the interpretation
of the python object we pass around to keep the algorithm parameter and
the parent, instead of just the parent. Is this a desirable change? Shall
we open a ticket for this?
> >
> I personally would highly recommand this. Consider for example highly
oscillating integrals like
> \int_0^pi f(x) sin(n*x) dx for large n's or the example from Runge:
> http://en.wikipedia.org/wiki/Runge%27s_phenomenon.
> I would also suggest to take scipy into consideration to provide
indiviual data points.
> On friday, I and a colleague of mine had a simple example of a piecewise
function, that only scipy could do properly while mpmath failed, (even
matlab had problems) because I handled individual data points.(mpath also
provides different quadrature rules)
> If you would like I could work on this
That would be great. I suggest making that a new enhancement ticket
though. Let's fix this bug first and use mpmath for numerical evaluation.
We should also open a new ticket for numerical integration of double
integrals as Mike was asking in comment:9.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8321#comment:15>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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