Karim Belabas on Sat, 03 May 2008 18:40:10 +0200


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Re: Special Hilbert Class Field computation 

* Kurt Foster [2008-05-03 17:51]:
> I've got a bnf structure, field = bnfinit(poly) with field,clgp,no = 2.  
> I want the Hilbert Class Field.  A classical solution (due to Hilbert 
> himself) is to find an integral element which is not a square, but is a 
> square mod 4, i.e. mod 4zk.

A simple generic solution is to use idealstar / ideallog :
 if bid = idealstar(nf,id), x square mod id <=> ideallog(nf,x,bid) is 0 mod 2.

Btw: rnfkummer is probably very fast in this case.

Cheers,

    K.B.
--
Karim Belabas, IMB (UMR 5251)  Tel: (+33) (0)5 40 00 26 17
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