Function Field

[Santanu Sarkar]

Hi,

  This code works well. 

K.<x> = FunctionField(GF(2)) 

R.<y> = K[]

f=y^2 + y + 1/x

L.<y> = K.extension(f)

print L.places(1)

But if I take f=y^2 + y + 1/x, it is giving error. 

[Vincent Delecroix]

Hello,

It works for me and I obtain

[Place (1/x, y), Place (1/x, y + 1), Place (x, x*y)]

Could you describe the SageMath version you are using?

Vincent

[Santanu Sarkar]

Hi,

  Sorry. This is not working:

K.<x> = FunctionField(GF(2)) 

R.<y> = K[]

f=y^2 + 1 + 1/x

L.<y> = K.extension(f)

print L.places(1)

I am using https://sagecell.sagemath.org/

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[Dima Pasechnik]

this is also not working in 8.8.beta4:

Does one need beta5? Or some ticket which is not yet in?

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[Kwankyu]

Hi,

It is because f is not separable. If you see the documentation, places() method is supported only for global function fields, and global function fields in sage are separable extensions of rational function fields (over finite fields). You may use a separable model of L instead.

sage: Ls, from_Ls, to_Ls = L.separable_model()

sage: Ls.places()

[Place (1/x_, 1/x_*y_ + 1), Place (x_, y_), Place (x_, y_ + 1)]

Kwankyu