thanks, all clear now!
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On Jun 16, 2009, at 11:18 PM, Craig Citro wrote:
>
>> How about
>>
>> sage: p = 7
>> sage: K. = QQ[p^(1/p)]
>> sage: q^p
>> 7
>> sage: F. = K.residue_field(q)
>> sage: F
>> Residue field of Fractional ideal (a)
>>
>> Of course as p splits completely the residue field is always
>> isomorphic to Z/
> How about
>
> sage: p = 7
> sage: K. = QQ[p^(1/p)]
> sage: q^p
> 7
> sage: F. = K.residue_field(q)
> sage: F
> Residue field of Fractional ideal (a)
>
> Of course as p splits completely the residue field is always
> isomorphic to Z/pZ (with the obvious reduction map, as q * q^(p-1) ==
> p).
>
A
On Jun 16, 2009, at 6:16 PM, bonzerpotato wrote:
> Does anyone know how to deal with non-integer modulo arithmetic on
> sage? What about using mathematica?
>
> I'm referring to a situation such as, for p prime, q a p-th root of p,
> then dealing with an element a of K = Q(q) using
>
> a = n mod q
