Let $ {\mathbb{K}}$ be a field. Let $ a,b,c \in {\mbox{${\mathbb{K}}$}}[x]$ be three non-zero univariate polynomials in $ x$ with coefficients in $ {\mathbb{K}}$ . We are interested in computing the polynomials $ u, v \in {\mbox{${\mathbb{K}}$}}[x]$ such that

$\displaystyle a u + b v = c$ (2)

holds. Let $ g \in {\mbox{${\mathbb{K}}$}}[x]$ be the gcd of $ a, b$ and let $ s, t \in {\mbox{${\mathbb{K}}$}}[x]$ be such that

$\displaystyle a s + b t = g$ (3)

holds. Remember that $ g,s,t$ can be computed by the Extended Euclidean Algorithm.

Marc Moreno Maza