Re: precision issue

[John Cremona <john.cremona@gmail.com>]

Thanks, Karim (and also Charles Greathouse who replied off-list for
some reason).  OK, so I did not recognise 2^63-1 and read the wrong
version of the manual, sorry.

On the main point -- it would be very good to have this done well.  I
am using it to compute some Hilbert class polynomials (and yes, I know
there are many other methods).

John

On 19 July 2010 14:01, Karim Belabas <Karim.Belabas@math.u-bordeaux1.fr> wrote:
> * John Cremona [2010-07-19 14:35]:
>> Consider the following (using a recent svn on a 64-bit machine):
>>
>> ? D = -37*4
>> %1 = -148
>> ? tau = (2+sqrt(D))/4
>> %2 = 1/2 + 3.0413812651491098444998421226010335310*I
>> ? ellj(tau)
>> %3 = -199147904.00096667436353951991474362130 + 4.733165431326070833 E-30*I
>> ? real(ellj(tau))
>> %4 = -199147904.00096667436353951991474362130
>> ? precision(real(ellj(tau)))
>> %5 = 38
>> ? precision(imag(ellj(tau)))
>> %6 = 19
>> ? real(tau)
>> %7 = 1/2
>> ? precision(real(tau))
>> %8 = 9223372036854775807
>> ? precision(imag(tau))
>> %9 = 38
>>
>> I don't like the way that j(tau)'s imaginary part only has half the
>> precision of the real part.  Since tau is known to have real part
>> *exactly* 1/2 we know that j(tau) is real, so could we not set the
>> imaginary par of the returned value to exact 0?  (similarly when
>> Re(tau)=0).  This must be quite a common special case.
>
> 1) Trying to answer your question, I just had a look at the code, and it
> must be rewritten anyway. (Correct algorithm in terms of \eta(tau),
> implemented in a highly inefficient way.)
>
> 2) This is analogous to
>
>  (14:44) precision((1.+1e-30) - 1.)
>  %2 = 19
>
>
> I'll see what I can do.
>
> Cheers,
>
>    K.B.
>
> P.S:
>> And secondly, why that bizarre value for precision(real(tau))?  I even get
>>
>> ? precision(0)
>> %12 = 9223372036854775807
>>
>> while looks like a bug since I thought that exact objects had precision 0.
>
> The documented behaviour is :
>
> (14:38) gp > ??precision
> precision(x,{n}):
>
>   gives the precision in decimal digits of the PARI object x. If x is an exact
> object, the largest single precision integer is returned.
>
>
> --
> Karim Belabas, IMB (UMR 5251)  Tel: (+33) (0)5 40 00 26 17
> Universite Bordeaux 1          Fax: (+33) (0)5 40 00 69 50
> 351, cours de la Liberation    http://www.math.u-bordeaux1.fr/~belabas/
> F-33405 Talence (France)       http://pari.math.u-bordeaux1.fr/  [PARI/GP]
> `
>