2008/4/24 William Stein <[EMAIL PROTECTED]>:
>
> 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]
In fact there is a whole "continued fraction field" implemented in
sage.rings.contfrac.py, with a lot of clever looking code in it, but
it does not (as far as I could see) implement the construction which
bill.p wanted from a quadratic surd. That file seems to have no
Author listed, so I don't know who wrote it!
John
>
> William
>
>
>
> >
>
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