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?
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)]
Asked: 2015-05-01 03:39:15 +0100
Seen: 333 times
Last updated: May 02 '15
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