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Factor base of class group computation

asked 2015-05-01 03:39:15 +0200

JM gravatar image

updated 2015-07-31 17:52:51 +0200

FrédéricC gravatar image

After calculating the class group using SAGE's .class_group() functionality, is there any way to find out the internal details of the calculation such as the factor base of prime ideals that was used, similar to the output given by PARI's bnfinit command? Or is the only way to just do the class group calculation by calling PARI's bnfinit command directly?

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answered 2015-05-02 18:47:09 +0200

Francis Clarke gravatar image

The following does involve calling PARI's bnfinit. But for a number field K, K.class_group() calls bnfinit, the output of which is cached. The factor base used can be recovered as follows:

sage: K.<a> = NumberField(x^3 - 11)
sage: map(K.ideal, K.pari_bnf()[4])
[Fractional ideal (2, a + 1),
Fractional ideal (5, a - 1),
Fractional ideal (-a + 2),
Fractional ideal (2, a^2 + a + 1),
Fractional ideal (a)]
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Thank you! I didn't know about .pari_bnf(). When I ran gp.bnfinit() on my number field, I got an error (with a warning about the field not being weakly super solvable). But K.pari_bnf() worked like a charm. Thanks!

JM gravatar imageJM ( 2015-05-03 04:24:45 +0200 )edit

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Asked: 2015-05-01 03:39:15 +0200

Seen: 307 times

Last updated: May 02 '15