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 discriminant. > 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 anywhere. > 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. Cheers, Bill.