span of vectors over an extension field but with coefficients from the base field [closed]

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Hi all,

Assume I have a vector space with coefficients from a finite extension field. How can I make the sub space spanned by vectors over that extension field but with coefficients from the base field? When I do something like this:

F = GF(2) FF.= F.extension(4) VS = VectorSpace(FF, 6)

span([VS.random_element() for i in range(3)], F) I get an error that "is not compatble with base_ring". But if I would replace VS with VS = FreeModule(ZZ, 6) it works. But that is not what I want. Are there any solutions?