On Thu, Apr 24, 2008 at 7:35 AM, bill.p <[EMAIL PROTECTED]> wrote:
>
> I needed to derive some continued fractions and a quick search of the
> index suggests that the Pari-GP function 'contfrac' might be what I
> needed.
> A simple test in the notebook:
>
> gp('contfrac(sqrt(6))')
>
> produced
>
> [2, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4,
> 2, 4, 2, 4, 2,
> 4, 2, 4, 2, 4, 2]
>
> which is not exactly what I expected. I'd expect either:
>
> [2;2,4]
> or
> [2,2,4,2,4,2,4,2,4,....]
>
> the latter implying that the expansion continues. Does the result
> given mean that
> Pari is using a limited precision evaluation of sqrt(6)?
Yes.
> I'd prefer
> the first of my expected
> results, giving a simple infinite continued fraction.
There is no such functionality in pari or as far as I know in Sage.
By the way, Sage also has a continued_fraction command.
sage: a = continued_fraction(sqrt(6),200); a
[2, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4,
2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2,
4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4]
[2, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 2, 1]
William
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