论文信息 - Some applications of Grobner bases

Some applications of Grobner bases

Previously (see ibid., vol.6, no.2, 2004), we discussed the geometry of linear and algebraic systems. We also defined ideals and bases so that we could introduce the concept of Grobner bases for algebraic system solving. In this article, we give more details about Grobner bases and describe their main application (algebraic system solving) along with some surprising derived ones: inclusion of varieties, automatic theorem-proving in geometry, expert systems, and railway interlocking systems.

Luis M. Laita | Eugenio Roanes-Lozano | Eugenio Roanes-Macías

[1] L. M. Laita,et al. A polynomial model for multi-valued logics with a touch of algebraic geometry and computer algebra , 1998 .

[2] David A. Cox,et al. Ideals, Varieties, and Algorithms , 1997 .

[3] Bruno Buchberger,et al. Applications of Gröbner Bases in Non-linear Computational Geometry , 1987, Trends in Computer Algebra.

[4] L. M. Laita,et al. Railway interlocking systems and Gröbner bases , 2000 .

[5] Laureano González Vega,et al. Algebraic-Geometric Methods for the Manipulation of Curves and Surfaces , 2001 .

[6] Erich Kaltofen,et al. Computer algebra handbook , 2002 .