On Sat, Feb 20, 2010 at 9:40 PM, John H Palmieri <jhpalmier...@gmail.com>wrote:
> On Feb 19, 9:11 am, John Cremona <john.crem...@gmail.com> wrote:
> > On 19 February 2010 06:32, Minh Nguyen <nguyenmi...@gmail.com> wrote:
> >
> > > Hi folks,
> >
> > > This is the final alpha release of Sage 4.3.3. The next release would
> > > be an rc0. The development version of Sage is now in feature freeze.
> >
> > On 32-bit Suse I get this fuzz:
> >
> > File "/local/jec/sage-4.3.3.alpha1/devel/sage/sage/misc/functional.py",
> > line 705:
> > sage: h.n()
> > Expected:
> > 0.33944794097891573
> > Got:
> > 0.33944794097891567
>
> I was curious about this, so I tried specifying the number of digits:
>
> sage: h = integral(sin(x)/x^2, (x, 1, pi/2)); h
> integrate(sin(x)/x^2, x, 1, 1/2*pi)
> sage: h.n()
> 0.33944794097891573
> sage: h.n(digits=14)
> 0.33944794097891573
> sage: h.n(digits=600)
> 0.33944794097891573
> sage: h.n(digits=600) == h.n(digits=14)
> True
> sage: h.n(prec=50) == h.n(prec=1000)
> True
>
> Is there an inherit limit in Sage on the accuracy of numerical
> integrals?
>
You can use mpmath for arbitrary precision integration:
sage: import mpmath
sage: mpmath.mp.dps = 50
sage: mpmath.quad(lambda x: mpmath.sin(x)/x**2, [1, mpmath.pi/2])
mpf('0.33944794097891567969192717186521861799447698826917531')
Fredrik
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