I am trying to calculate a place of the degree 8 extension field of a
rational function field over GF(2^16) in SageMath. However, when I do this,
it is taking a very long time and doesn't produce a result even after hours
of computation.
The commands I am running:
sage: F.<x> = FunctionField(GF(2^16))
sage: R.<y> = F[]
sage: f = y^8 + x*y^6 + x^2*y^4 + y^3 + x
sage: K.<z> = F.extension(f)
sage: K.places(8)[:1]
The goal of doing this is to evaluate a basis of the Riemann-Roch space of
a divisor of F at a degree 8 place of K, in order to embed a length 8
vector of elements in F_{2^16} into a single element in F_{2^128}. I am
running this in SageMath 10.5 on a Ubuntu 22.04 virtual machine using
VirtualBox 7.0.14.
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