On Tuesday, 10 December 2024 at 18:29:14 UTC-8 skchandh...@gmail.com wrote:

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]


This line produces a list of all places of F of degree 8. So that's a huge 
list! It wouldn't fit in memory. If you want to get some places to 
experiment with, you probably want to create them without creating all 
degree 8 places. Perhaps something like

K(x-1).divisor().support()

gives some usable places.

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