Originally Posted by

**Bernhard** Thanks SlipEternal, that is pretty clear, but just one issue ...

You write:

" ... ... if we consider $\displaystyle F(u)$ as a vector space over $\displaystyle F$ with basis $\displaystyle \{u^0,u^1,\ldots, u^{\deg(u)-1}\}$, then $\displaystyle \{v^0, v^1, \ldots, v^{\deg(u)-1}\}$ must span a linear subspace ... ..."

How do we know for sure that $\displaystyle \{v^0, v^1, \ldots, v^{\deg(u)-1}\}$ is a subspace ... why is it not possible that $\displaystyle \{u^0,u^1,\ldots, u^{\deg(u)-1}\} \subseteq \{v^0, v^1, \ldots, v^{\deg(u)-1}\}$ - that is $\displaystyle \{v^0, v^1, \ldots, v^{\deg(u)-1}\} $ is a superspace of F(u) - that is $\displaystyle F(u) \subseteq F(v) $

Can you clarify?

Peter