# Revision history [back]

### 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?

 2 retagged FrédéricC 3497 ●3 ●34 ●68

### 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?