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Taking the span in a polynomial ring

asked 1 year ago

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 ?

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answered 1 year ago

Max Alekseyev gravatar image

updated 1 year ago

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

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Asked: 1 year ago

Seen: 224 times

Last updated: Jun 08 '23