On Wed, 15 May 2019 at 17:03, Kwankyu <ekwan...@gmail.com> wrote:
> Hi Chandra,
>
> What is Place (x^2 + x + 1, x*y + 1)? Is it ideal generated by
>>
>> (x^2 + x + 1, x*y + 1).
>>
>>
> No. Place (x^2 + x + 1, x*y + 1) is the unique place of the function field
>
> at which both functions x^2 + x +1, x*y + 1 vanish.
>
> Thank you for your response. We know that a place is the unique maximal
ideal of a local (valuation) ring obtained from the valuation map, which is
well known to be a principle ideal.
So, there will be a single generator for a place. But here it is
represented by two polynomials. We didn't get what it means. Can we find
the corresponding valuation ring, valuation map
ant the generator for the place?
>
>
>> What is the value of $\frac{xy}{(x^2 + x + 1) } +
>>
>> \frac{1}{x^2 + x + 1}+$ Place $(x^2 + x + 1, x y + 1)$?
>>
>>
> You cannot add an element of the function field with a place.
>
Actually by this we meant the element modulo the place ( a maximum ideal).
>
>
>> It is an element of residue field which is isomorphic to
>>
>> $\mathbb{F}_{2^2}$. Since $\mathbb{F}_{2^2}$ is isomorphic
>> to $\mathbb{F}^2_{2}$ as a vector space,
>>
>> I want value in $\mathbb{F}^2_{2}$.
>>
>>
> vector(a)
>
> or you can use the maps returned by
>
> k.vector_space(map=True)
>
> if k is the residue field.
>
>
>
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