May 26, 2018

Visualize some real algebraic geometry

surf is a tool to visualize some real algebraic geometry plane algebraic curves, algebraic surfaces and hyperplane sections of surfaces. surf is script driven and has optionally a nifty GUI using the Gtk widget set.

The algorithms should be stable enough not to be confused by curve/surface singularities in codimension greater than one and the degree of the surface or curve. This has been achieved quite a bit. We have drawn curves of degree up to 30 and surfaces of degree up to 20 successfully. However, there are examples of curves/surfaces of lower degree where surf fails to produce perfect images. This happens especially if the equation of the curve/surface is not reduced. Best results are achieved using reduced equations. On the other hand, surf displays the Fermat-curves accurately for degree up to 98.

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