Re: bnfissunit

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

On Thu, Jun 25, 2015 at 10:36:48AM +0100, John Cremona wrote:
> The function bnfissunit() returns the coordinate vector if given an
> S-unit and the empty vector if the element given is not as S-unit.  If
> all I want is to check for being an S-unit, without needing the
> exponent vector, is it possible that this could be done faster?  The
> situation I have is that I have a lot of elements to test, and most of
> them will not be S-units, and I want it to be fast (of course).  If S
> is empty, one can check for being a unit just by looking at the norm.
> Here one could first check that the norm is only divisible by the
> correct rational primes, but that is not sufficient of course (would
> it be faster to do that?  the elements will be large and computing
> their norms not so trivial).

I would suggest you check if the element and its inverse is an S-integer.

Cheers,
Bill