Dear all,
I have written the following code:
K.<x> = FunctionField(GF(2));
R.<y> = K[]
L.<y> = K.extension(y^2 +y+x+1/x)
print L.places(2)
p = L.places(2)[1]
print p
G=p.divisor()
LG=G.basis_function_space()
print LG
Output is as follows:
[Place (x^2 + x + 1, x*y + 1), Place (x^2 + x + 1, x*y + x + 1)]
Place (x^2 + x + 1, x*y + x + 1)
[1, (x/(x^2 + x + 1))*y + 1/(x^2 + x + 1)]
What is Place (x^2 + x + 1, x*y + 1)? Is it ideal generated by
(x^2 + x + 1, x*y + 1).
What is the value of $\frac{xy}{(x^2 + x + 1) } +
\frac{1}{x^2 + x + 1}+$ Place $(x^2 + x + 1, x y + 1)$?
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 $\mathbb{F}^2_{2}$.
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