Bill Allombert on Thu, 20 Apr 2017 00:30:04 +0200

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Re: Class groups and S-units of relative extension

On Wed, Apr 19, 2017 at 12:58:46PM -0700, Watson Ladd wrote:
> Dear all,
> I have a number field L obtained as a tower over a number field K that I
> would like to obtain the S-units of. Currently I treat L as global which is
> infeasible (It has huge degree). 

Degree by itself is not a limitation. The real limitation is the

> If I use bnfinit (rnfinit (K, pol)) will
> this use the relative algorithms or will it attempt the absolute one?

I do not think the relative algorithm have ever been fully implemented

> Furthermore, if L is a compositum of simpler fields can I use that
> information as well?

No. However automorphisms, if any, will be computed and used.

But actually, the real limitation is elsewhere: without modification,
to compute the S-units, bnfinit needs to compute the algebraic form
of the fundamental units which can easily overflow the memory.