Ask Your Question
1

Taking the span in a polynomial ring

asked 2023-06-07 10:55:29 +0200

czioj gravatar image

I was trying to make a vector subspace of linear polynomials on the finite field of size 2 by taking

R.<X>=PolynomialRing(GF(2))
span([X^(2^j) for j in range(3)], GF(2))

But I get an error ending by :

ValueError: The elements of gens (= [X, X^2, X^4]) must be defined over base_ring (= Finite Field of size 2) or its field of fractions.

How do I fix this ?

edit retag flag offensive close merge delete

1 Answer

Sort by ยป oldest newest most voted
0

answered 2023-06-08 22:23:09 +0200

Max Alekseyev gravatar image

updated 2023-06-08 22:23:53 +0200

Perhaps, you want a free module rather than span:

R.<X>=PolynomialRing(GF(2))
FreeModule(GF(2), [X^(2^j) for j in range(3)])

which gives

Free module generated by {X, X^2, X^4} over Finite Field of size 2

edit flag offensive delete link more

Your Answer

Please start posting anonymously - your entry will be published after you log in or create a new account.

Add Answer

Question Tools

Stats

Asked: 2023-06-07 10:55:29 +0200

Seen: 132 times

Last updated: Jun 08 '23