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surf version 1.0.1

Stephan Endrass <>

May 28, 2000

The aim was to have a tool to visualize some real algebraic geometry: plane algebraic curves given as zero locus of a polynomial in two variables, algebraic surfaces given as zero locus of a polynomial in three variables, hyperplane sections of surfaces: algebraic space curves given as zero locus of two polynomials in three variables: a polynomial of arbitrary degree (the surface) and a linear polynomial (the hyperplane), and lines on surfaces given by two points on a surface. 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.

1. Overview

2. Introduction to surf's command language

3. Features

4. List of all reserved words

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