Automatic Determination of Algebraic Surfaces as Loci of Points
3D-Loci Discovery (3D-LD), a web-based system for automatic discovery of geometric loci in the space, is described. Its basic engine is based on the Groebner basis method. 3D-LD can be used to easily (re)discover many loci-related geometric surfaces, and it has allowed us to generalize a recent extension of Simson-Steiner’s theorems due to Guzmán.
Being accessible through the web, 3D-LD is platform independent, and can be linked with other graphical tools. It uses the symbolic capabilities of Mathematica and CoCoA, by means of the recently distributed application webMathematica, a Java servlet technology allowing the generation of dynamic web content. A simple description of 3D-LD and some examples of use are available at http://rosalia.uvigo.es/sdge/web/3D/.
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