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Automatic Determination of Algebraic Surfaces as Loci of Points

Francisco Botana
Organization: University of Vigo, Spain
Department: Dept. of Applied Mathematics
Journal / Anthology

Lecture Notes in Computer Science
Year: 2003
Volume: 2657
Issue: (ICCS '03)
Page range: 879–886

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 Guzm´an. 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/.

*Applied Mathematics > Visualization
*Mathematics > Geometry > Solid Geometry
*Wolfram Technology > Special Versions > webMathematica