Show that the factor (left(z_{i}-z_{j} ight)^{m}) in the Moore-Read wave function (also present in the phenomenological Laughlin

Show that the factor \(\left(z_{i}-z_{j}\right)^{m}\) in the Moore-Read wave function (also present in the phenomenological "Laughlin wave function" for a theoretical description of the FQHE) implies there are \(m\) "vortices" at each position. A vortex ansatz is \(f(r) e^{i \alpha}\), where \(r, \alpha\) are the radius and the polar angle in the plane, respectively, and one can impose a consistency condition on the ansatz (and so find it).