Re: Changing PARI types

["Karim.Belabas" <Karim.Belabas@math.u-psud.fr>]

On Fri, 11 May 2001, Gerhard Niklasch wrote:
> In response to:
> > Message-ID: <Pine.SOL.3.96.1010511082001.8135A-100000@elios>
> > Date: Fri, 11 May 2001 08:28:52 +0100 (BST)
> > From: Mark Chimley <M.Chimley@bristol.ac.uk>
> > 
> > I have used "ground" to round the coefficients of a polynomial to the
> > nearest integers, however the type of the coefficients remains at 6
> > (probably real or complex). This means that rootsmod (GEN) cannot handle
> > the polynomial (the error actually comes from factormod, which is used
> > by rootsmod). Is it possible to change the type of the coefficients so
> > that they can be handled by rootsmod?
> > 
> > For example, can I do something like:
> > 
> > settyp (H [i], 1);
> > 
> > for each coefficient, or would this be horribly dangerous?
> 
> That would change the type marker of the object whilst leaving
> the bit pattern as it is, and is very unlikely to result in a
> recognizable PARI integer!

As a matter of fact, it will. A "random" 31 bit integer presumably
(corresponding to the adress of the real part).

> (Look up "type" in the manual or
> online help.)  But you can get an integer directly:
> 
> ===8<---
> (17:23) gp > ??round
[...]
> So, grndtoi() is what you're looking for.

Well, the difference between ground and grndtoi is that the latter cannot
fail with an error message:

(13:16) gp > round (1.5e30)  \\ ground behaviour
  ***   precision loss in truncation

(13:16) gp > round(1.5e30, &e) \\ rndtoi behaviour
%1 = 1500000000000000000000000000000
(13:16) gp > e
%2 = 5
(so the last 5 bits are subject to caution)


I think the real problem is

(13:18) gp > type(round(0*I))
%3 = "t_COMPLEX"

Whereas:

(13:16) gp > round(0*I)
%4 = 0
(13:18) gp > type (%)
%5 = "t_INT"

In that case, the answer is simplify().

[ or ground(greal()) if you don't want to check accuracy  ]

    Karim.

-- 
Karim Belabas                    email: Karim.Belabas@math.u-psud.fr
Dep. de Mathematiques, Bat. 425
Universite Paris-Sud             Tel: (00 33) 1 69 15 57 48
F-91405 Orsay (France)           Fax: (00 33) 1 69 15 60 19
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