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Computation and visualization of general Riemann surfaces
              $w[z]$ of arbitrary algebraic functions

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M. Trott

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Date:  July 20th (Saturday)\\
Time: 11:00-11:30\\

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Abstract
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A polynomial $p(w,z)$ in two variables $w$ and $z$ with numeric coefficients represents an
analytic function $w(z)$. As such it represents a Riemann surface. Here we are interested in the
visualization of this Riemann surface (not only in the topological sense of determining the genus).
$\Re(w(z))$ and $\Im(w(z))$ are proper representations of the surface. Two methods, one based on
implicitization and one based on the numerical solution of differential equations on the various
sheets for the construction of proper representations of the Riemann surface are discussed. 3D
graphics of examples of various total degree are shown. 

