#8321: numerical integration with arbitrary precision
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Reporter: burcin | Owner: burcin
Type: defect | Status: needs_work
Priority: major | Milestone: sage-4.7.2
Component: symbolics | Keywords: numerics,integration
Work_issues: | Upstream: N/A
Reviewer: | Author: Stefan Reiterer
Merged: | Dependencies:
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Comment(by zimmerma):
Replying to [comment:28 kcrisman]:
> This should really be finished and fixed. Does anyone have any
objection to something that does what Stefan implements (using mpmath) but
then has lots of examples in numerical integration and `integrate` warning
people not to trust floating-point, even with high precision,
calculations? Otherwise this ticket could get doomed by the "must be
perfect" problem.
we are still waiting for comparison figures for errors and timings (see
comment [comment:12]).
In those comparisons, I'd like to have arbitrary precision examples (say
20, 50, 100, 200, 500
and 1000 digits).
> Are there specific places where this patch is causing incorrect or worse
behavior? Burcin's example seems to be equally bad for both, and I
disagree with maldun that we shouldn't return symbolic answers. At some
point you have to make a decision, and the definite integral should
naturally be symbolic if at all possible.
of course {{{integrate(...)}}} will first give a symbolic result if any,
then {{{integrate(...).n()}}} will evaluate numerically this symbolic
value.
We should explain in the documentation of {{{integrate}}} how to avoid the
symbolic evaluation
(for example adding the {{{hold}}} option). Anyway this is a different
issue than this ticket.
Paul
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8321#comment:29>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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