### Normal base of a finite extersion field

Hi all,

any finite extension (say degree *n*) of a field *K* may be considered as vector space over *K*. In particular, the roots of any irreducible polynomial *f* of degree *n* over a finite field *K* constitute a basis of this vector space.

Does SageMath provide a routine to construct the vector space for given *K* and *f*?

Such a vector space seems to be used internally when constructing *Kn=GF(K.order()^n,'a',modulus=f)*. If so then the question becomes: Is this vector space open to the public? And how can I use it?

Thanks in advance
Wolfgang Jansen