Dear GAP forum, I would like to ask some questions relating to the construction of the bijection from k^n to the extension of k of degree n. I have used the following codes
*gap> k:=GF(2^2);;gap> x:=X(k,"x");; g:=x^3+x+1;; gap> Kg:=AlgebraicExtension(k,g);;* Then, an element in Kg has a form: a+bt+bt^2 (a, b, c in *k*, g(t)=0). I want to construct the bijection T: *k*^3->Kg is define by (a,b,c)->a+bt+bt^2. As we know that *k*^3 and Kg are 3-dimesional vector space over over *k*. To consider Kg as a *k*-vector space, I use *gap> Kg:=AsVectorSpace(k,Kg);<algebra-with-one of dimension 6 over GF(2^2)>* So, we can build an isomorphism from *k*^3 to K. But *gap> Size(Basis(Kg));* *6 //not 3gap> Size(Basis(k^3));3* >From that, I can not construct an isomorphism from to *k*^3 ->Kg. *gap>f:=LeftModuleGeneralMappingByImages(k^3,Kg,Basis(k^3),Basis(Kg));Error, <gens> and <imgs> must have the same length* Could you help me how to construct the the bijection T: *k*^3->Kg? Thank you very much. Best regards, Huta _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
