= Wronskian of a rational map
{c}
{title2=$W=p'q-pq'$}
For a reduced <rational map> $R=p/q$, its derivative is $W/q^2$ with $W=p'q-pq'$. Away from target-coordinate poles, the zeros of this <Wronskian> identify its <ramification points of a holomorphic map>; at a pole use the reciprocal coordinate $q/p$. A pole of order $m$ contributes ramification order $m-1$, and infinity must also be checked in local coordinates. For degree $N$ the <Riemann-Hurwitz formula> gives total ramification $2N-2$. The affine polynomial $W$ can have fewer finite zeros because some ramification lies at infinity. In the <rational map approximation for Skyrmions>, these directions have zero angular baryon density.
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