Re: sqrtint for rationals

[James Wanless <james@grok.ltd.uk>]

Hi Karim (Belabas),
Thanks very much for your response.
Actually Andreas (Enge) has already set me straight (off-list) very  
nicely wrt this:
The problem (I understand) is one of speed/accuracy trade-off. Andreas  
mentioned that number theory software (eg pari/gp !!! :)))) already  
does this as much as it can with simple fractions, but, that this is  
just too totally infeasible from a speed point-of-view w/ more complex  
fractions/operations [as you mention too!]
Thanks to all on the list for indulging me w/ my original query -  
hopefully it wasn't _too_ off-topic or trivial - I (for one at any  
rate) certainly learnt something...
Thanks again, and Happy Pi Day!
J

On 14 Mar 2012, at 09:52, Karim Belabas wrote:

> * James Wanless [2012-03-14 10:18]:
> > Speaking of which, I _think_ I might have a solution for the Table- 
> > maker's
> > dilemma:
> > Specifically, if one has available integers of any length already ie
> > thru' GMP, then why can't one just use _perfectly correct_ rationals
> > (described as two integers, top and bottom of a fraction) [a little
> > bit akin to two-coordinate complex numbers].
> > I don't see why then one couldn't carry through rationals w/ perfect
> > accuracy thru all operations...
>
> Try to make it work with "operation" = exp(), for instance.
> You'll see the problem. :-)
>
> Cheers,
>
>    K.B.
> --
> 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]
> `