Software using the Gröbner cover for geometrical loci computation and classification. (English) Zbl 1437.13001

Abánades, Miguel A.; Botana, Francisco; Montes, Antonio; Recio, Tomás

Hong, Hoon (ed.) et al., Mathematical software – ICMS 2014. 4th international congress, Seoul, South Korea, August 5–9, 2014. Proceedings. Berlin: Springer. Lect. Notes Comput. Sci. 8592, 492-499 (2014).

Summary: We describe here a properly recent application of the Gröbner cover algorithm (GC) providing an algebraic support to dynamic geometry computations of geometrical loci. It provides a complete algebraic solution of locus computation as well as a suitable taxonomy allowing to distinguish the nature of the different components. We included a new algorithm Locus into the Singular grobcov.lib library for this purpose. A web prototype has been implemented using it in GeoGebra.
For the entire collection see [Zbl 1293.65003].

MSC:

13-04	Software, source code, etc. for problems pertaining to commutative algebra
13P25	Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.)
13P10	Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
65D18	Numerical aspects of computer graphics, image analysis, and computational geometry

Keywords:

locus; taxonomy; dynamical geometry; Gröbner cover

Software:

GeoGebra; grobcov.lib; SINGULAR