On Sunday, February 21, 2016 at 10:10:10 AM UTC-8, tdumont wrote:
>
> I have students who want to compute decimals of pi...so, what can we do
> with RealField(n) ?
> I make the following script (pi.sage):
>
> ------------------------
> for p in [2..10]:
> R=RealField(10^p)
> pii=4*atan(R(1))
> print p,R,pii
> ------------------------
>
Note that a single element of RealField(10^10) needs more than a Gigabyte
to be represented. I don't think it's reasonable to expect that on a normal
machine, with general purpose code (that will not try to minimize
allocating intermediate results in separate memory!), a call like "atan"
will work in reasonable time.
Normally, evaluating
R=RealField(5^10)
4*atan(R(1))
still finishes in reasonable time. It seems that your interruption left a
corruption somewhere. It would be useful if you can get a fairly reliable
way of producing the state in which you get NaNs. Then debugging might be
an option.
In the mean time, I don't think there's an issue for teaching: Just stick
to a few less bits precision. 10^10 bits of precision is a little insane.
That's the domain where you'd expect to need special-purpose code that
takes care to not waste memory.
> Then, using sage 7.0 or 7.1.beta4:
>
> attach("pi.sage")
>
> This produces a lot of seemingly correct output, but, as it takes a too
> long time to finish :-), I interrupt the computation (Ctrl-c).
>
> So, lets try again; replace 10 by 5 in the for statement (I do not leave
> sage). I get NaNs:
>
>
> 2 Real Field with 100 bits of precision NaN
> 3 Real Field with 1000 bits of precision NaN
> 4 Real Field with 10000 bits of precision NaN
> 5 Real Field with 100000 bits of precision NaN
> .....
>
> Strange.
>
> Yours
> t.d.
>
>
>
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