#8321: numerical integration with arbitrary precision
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Reporter: burcin | Owner:
Type: defect | Status: needs_work
Priority: major | Milestone: sage-5.0
Component: symbolics | Resolution:
Keywords: numerics,integration, sd32 | Work issues: add more
arbitrary precision tests
Report Upstream: N/A | Reviewers: Paul Zimmermann
Authors: Stefan Reiterer | Merged in:
Dependencies: | Stopgaps:
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Comment (by nbruin):
Replying to [comment:51 zimmerma]:
> Sage 4.8 can now integrate the formula in this ticket
You are right that for this ticket, the original example doesn't test
generic numerical integration. The numerical approximation of the
resulting expressions in gamma functions seems suspect, though:
{{{
sage: h = integral(sin(x)/x^2, (x, 1, pi/2));
sage: H1=h.n(digits=20)
sage: H2=h.n(digits=100)
sage: delta=parent(H2)(H1)-H2
sage: delta
0
sage: parent(delta)
Complex Field with 336 bits of precision
sage: H2.imag_part()
5.421010862427522170037264004349708557128906250000000000000000000000000000000000000000000000000000000e-20
}}}
Also note that the equality tests as stated in the examples are not direct
evidence that something is going wrong:
{{{
sage: a=RealField(10)(1)
sage: b=RealField(20)(1)+RealField(20)(2)^(-14)
sage: a,b
(1.0, 1.0001)
sage: a == b
True
}}}
I guess the numbers are coerced into the parent with least precision
before being compared ...
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8321#comment:53>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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