#8321: numerical integration with arbitrary precision
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Reporter: burcin | Owner:
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 fredrik.johansson):
The singleton trick definitely needs to be implemented; it can save a
factor 4x or more.
Then there is the question of whether to use !GaussLegendreRel or
!TanhSinhRel by default. Gauss-Legendre is somewhat faster for smooth
integrands; Tanh-Sinh is much better for something like {{{sqrt(-x^2 +
1)}}} on {{{[0,1]}}} (note that the values with mpmath_rel above are
wrong!) or almost anything on an infinite interval (this should be tested
as well!). I would favor !TanhSinhRel.
Anyway, I agree that it would be sensible to use GSL by default.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8321#comment:38>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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