Hello:
I am working at my Number Theory lectures and I have found a bug (?). This is
the output:
/////////////////// SAGE 2.9.1 ///////////////////
sage: K.<a>=CyclotomicField(23)
sage: O=K.maximal_order()
sage: (2*O).factor()
*** Warning: large Minkowski bound: certification will be VERY long.
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "/home/notebook/sage_notebook/worksheets/admin/3/code/13.py",
line 4, in <module>
exec compile(ur'(Integer(2)*O).factor()' + '\n', '', 'single')
File
"/usr/local/sage/local/lib/python2.5/site-packages/sympy/plotting/",
line 1, in <module>
File "sage_object.pyx", line 92, in
sage.structure.sage_object.SageObject.__repr__
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/structure/factor\
ization.py", line 187, in _repr_
t = str(self[i][0])
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/rings/number_fie\
ld/number_field_ideal.py", line 218, in __repr__
return "Fractional ideal %s"%self._repr_short()
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/rings/number_fie\
ld/number_field_ideal.py", line 235, in _repr_short
return '(%s)'%(', '.join([str(x) for x in self.gens_reduced()]))
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/rings/number_fie\
ld/number_field_ideal.py", line 553, in gens_reduced
dummy = self.is_principal(proof)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/rings/number_fie\
ld/number_field_ideal.py", line 714, in is_principal
bnf = self.number_field().pari_bnf(proof)
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/rings/number_fie\
ld/number_field.py", line 1464, in pari_bnf
self.pari_bnf_certify()
File
"/usr/local/sage/local/lib/python2.5/site-packages/sage/rings/number_fie\
ld/number_field.py", line 1497, in pari_bnf_certify
if self.pari_bnf(certify=False, units=True).bnfcertify() != 1:
File "gen.pyx", line 6474, in sage.libs.pari.gen._pari_trap
sage.libs.pari.gen.PariError: not enough precomputed primes, need
primelimit ~ (35)
But if you type the following lines using gp interface, it works:
sage: K=gp.bnfinit(cyclotomic_polynomial(23))
sage: gp.idealfactor(K,2)
[[2, [1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0]~, 1, 11, [1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0]~], 1; [2, [1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0]~, 1, 11, [1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0]~], 1]
All the best,
Enrique
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