Probably to output nice reps for the answer ideal... A "feature" that
obviously has to be removed.
By the way I will likely be completely offline until dec 31 evening,
since i am going to the middle of nowhere...
- William
(Sent from my iPhone.)
On Dec 29, 2007, at 2:18 PM, "John Cremona" <[EMAIL PROTECTED]>
wrote:
>
> But why would Sage be computing the class group in order to factor 2
> in K?
>
> John
>
> On 29/12/2007, [EMAIL PROTECTED]
> <[EMAIL PROTECTED]> wrote:
>>
>> 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
>>
>>
>> ---
>> ---
>> --------------------------------------------------------------------
>> Mensaje enviado mediante una herramienta Webmail integrada en *El
>> Rincon*:
>> ------------->>>>>>>> https://rincon.uam.es
>> <<<<<<<<--------------
>>
>>
>>
>>>
>>
>
>
> --
> John Cremona
>
> >
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