Definition 1

With the above notation the determinant of the matrix $M(f, g, p, q)$ is called the resultant of the pair $(f, g)$ for the degrees $p$ and $q$, or simply the resultant of $f$ and $g$ if $p = \deg f$ and $q = \deg g$.

The resultant is denoted by $\operatorname{res}_{p,q}(f, g)$ or simply $\operatorname{res}(f, g)$ when $p = \deg f$, $q = \deg g$.