# Extended Euclid with polynomials

Suppose given polynomials $e,q,h,r$ in $R[x]$, $p \in R$ (R a ring), how can I use Sage to find $f$ in $R[x]$ so $f e = q h + r (\text{mod } p)$?

Similarly, given $f,g$ in $R[x]$ with $\text{gcd}(f,g)=1$, what function can I use to compute $s,t$ in $R[x]$ so $s f + g h = 1 (\text{mod } p)$ ?