Common-factor reduction of a rational map
= Common-factor reduction of a rational map
{title2=$\deg R=\max(\deg p,\deg q)-\deg\gcd(p,q)$}
Cancel the common polynomial factors of $p$ and $q$ before computing the <degree of a rational map of the Riemann sphere>. Removable common zeros do not contribute sheets. The reduced maximum polynomial degree is the number of inverse images of a generic target value, counted with positive holomorphic local degrees.