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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… (More)

A natural 3D extension of the Steiner chains problem, original to the authors of this article, where circles are substituted by spheres, is presented. Given three spheres such that either two of them are contained in (or intersect) the third one, chains of spheres, each one externally tangent to its two neighbors in the chain and to the first and second… (More)

Although exact methods for solving general polynomial systems are incorporated into well-known computer algebra systems such as Derive, Maple, Mathematica, MuPad, and Reduce, only a small portion of the scientific community knows about them. This article introduces one such method - Grobner bases - for non-mathematicians in an intuitive way. Specifically,… (More)