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- Eugenio Roanes-Macías, Eugenio Roanes-Lozano
- Automated Deduction in Geometry
- 2006

- Eugenio Roanes-Lozano, Luis M. Laita, Eugenio Roanes-Macías, Michael J. Wester, José Luis Ruiz-Lozano, Carlos Roncero
- Mathematics and Computers in Simulation
- 2009

- Eugenio Roanes-Lozano, Eugenio Roanes-Macías, Luis M. Laita
- Computing in Science & Engineering
- 2004

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)

- Eugenio Roanes-Macías, Eugenio Roanes-Lozano
- Mathematical and Computer Modelling
- 2007

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)

- Eugenio Roanes-Lozano, Eugenio Roanes-Macías, Luis M. Laita
- Computing in Science & Engineering
- 2004

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)

- Eugenio Roanes-Lozano, Luis M. Laita, Eugenio Roanes-Macías
- Mathematics and Computers in Simulation
- 2004

- Eugenio Roanes-Lozano, Alfonso González-Bermejo, Eugenio Roanes-Macías, Justo Cabezas
- SIAM Review
- 2006

We first briefly describe an algebraic model of classical and modal many-valued logics due to the authors and introduced in previous works. A similar approach, also using Computer Algebra techniques (Gröbner bases) and oriented to perform effective calculus in a continuous logic: Minimal Polynomial Logic (MPL) is presented. The implementation has been… (More)