Jay on Wed, 7 May 2003 19:10:44 -0400

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Re: Ray Class Fields

On Wednesday, May 7, 2003, at 05:49  PM, A. Lozano-Robledo wrote:

 = [18,[18],[[2]~]]

What am I doing wrong? Am I defining correctly the field of rational


You are correctly defining everything above, and PARI is comuting it correctly. The problem is that ray class field for Q with conductor 37 is the _maximal real subfield_, of index 2, of Q(37th roots). You need to tell bnrclass to produce ramification at infinity.

Note that your input is equivalent to

gp > Q=bnfinit(x);
gp > bnrclass(Q,[37,[0]])
 = [18, [18], [[2]~]]

as here I have explicitly told PARI not to produce any ramification at the one infinite place, and this was implicitly assumed in your computation. The following input forces ramification:

gp > bnrclass(Q,[37,[1]])
 = [36, [36], [[2]~]]

and gives the field you desire as well.

I should also note that using bnrclass was tremendously faster for producing Q(37th roots) than bnfinit was.

I hope this helps,


Jonathan Pottharst
333 Western Ave. #2  Cambridge, MA  02139
email: jayp@mit.edu  aim: sharlaon  icq: 4374738
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