Re: Gaussian Integer factorisation at right angles

[Bill Allombert <allomber@math.u-bordeaux.fr>]

On Sun, Jan 09, 2005 at 02:13:10PM +0100, Karim Belabas wrote:

> * Phil Carmody [2005-01-06 17:31]:
> > Is there any reason why things should get rotated by 90 degrees?
> > 
> > (18:16) gp > factorback(factor(17+0*I))
> 
> The same one as for
> 
> (14:16) gp > factorback(factor(-x))
> %1 = x
> 
> (or worse, factor(x*y) ... ).
> 
> factor() is a little inconsistent in that it factors up to units in the
> chosen UFD, _except_ if the latter hapens to be Z, in which case
> annoying factors (-1)^1 crop up.

That is not entirely true:
? factor(17+0*I)
%1 =
[-I 1]

[4 - I 1]

[4 + I 1]

factoring Gaussian integers report a unit. 

In this case, the unit is wrong.

Cheers,
Bill.