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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

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 ?

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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:

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

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

Seen: 132 times

Last updated: Jun 08 '23