# Thread: Basisrepresentation of elements in fields

1. ## Basisrepresentation of elements in fields

HI!
Consider the system
$
b = q_0 + q_1 \beta+ \cdots + q_{n-1} \beta^{n-1}
$

with
$
b \in L \textrm{, where } L = \mathbb Q(\beta) \textrm{ is a finite, algebraic extension of } \mathbb Q \textrm{ and } \{1,\beta,\cdots,\beta^{n-1} \}$

is a $\mathbb Q$-Base of L. How to find $q_i \in \mathbb Q$?

I'm really clueless and would be very grateful for any ideas.
Thanks

2. hey, I really need some information about this. What's the problem? Too trivial, too difficult, impossible?? no ansatz at all?