[GAP Forum] subspace spanned by random subset (of finite field over subfield)

[fvanhove at cage.ugent.be]

Dear members of the GAP forum,

I would like to consider a big Galois field as a vector space over its  
prime subfield.
Hence I started with:

gf:=GF(3^6);
w:=PrimitiveElement(gf);
W:=AsVectorSpace(PrimeField(gf),gf);

Now I would for instance like to compute the dimension of the subspace  
(over GF(3)) spanned by {w,w^5,w^6}.
(Note that I am actually not expecting that that subset is linearly  
independent)

But if I understand
http://www.gap-system.org/Manuals/doc/htm/ref/CHAP059.htm#SECT001
correctly, then the only way to construct subspaces is by expressing  
vectors in terms of coordinates using some basis.

Is this correct?

Thanks in advance,
Kind regards,
Frédéric





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