On Tue, Oct 28, 2014 at 8:19 AM, Christophe Bal <[email protected]> wrote:
> Hello.
>
> I'm writing a french book about SageMathCloud and I'm looking for known
> wrong results given by Sage due to floats calculations, or due to the method
> used. Do you know such things ? My idea is to show to new user that a CAS or
> a numerical tool is not Math God.
>
> For my part, I really like the following one. Try it, it is funny even if I
> know what is is the reason of the unexpected result.
>
> --------------------------
> u = 1.0/3
>
> for i in range(100):
> u = 4*u - 1
>
> print u
> --------------------------
This is a good motivation for RIF (real interval field), which tracks
errors, e.g.,
u = RIF(1/3)
for i in range(100):
u = 4*u - 1
print u
The output is 0.?e44, which means no digits are known to be right.
See [1].
[1]
https://cloud.sagemath.com/projects/4a5f0542-5873-4eed-a85c-a18c706e8bcd/files/support/2014-10-28-083459-funny-and-wrong.sagews
--
William Stein
Professor of Mathematics
University of Washington
http://wstein.org
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