HI!

Consider the system

$\displaystyle

b = q_0 + q_1 \beta+ \cdots + q_{n-1} \beta^{n-1}

$

with

$\displaystyle

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

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

Thanks