Statement

Let $f$ and $g$ in ${\mbox{${\mathbb{Z}}$}}[x]$ be two polynomials with respective degrees $m \geq n > 0$ . We assume that $g$ is monic, that is, its leading coefficient is $1$ . Let $B_f$ and $B_g$ be upper bounds for the absolute value of a coefficient in $f$ and $g$ respectively. We aim at computing the quotient $q$ and the remainder $r$ in the division of $f$ by $g$ by means of a modular method.