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The Geometry of Algebraic Systems and Their Exact Solving Using Gröbner Bases
March/April 2004 (vol. 6 no. 2)
pp. 76-79
Eugenio Roanes-Lozano, Universidad Complutense de Madrid
Eugenio Roanes-Mac?as, Universidad Complutense de Madrid
Luis M. Laita, Universidad Politecnica de Madrid

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 aims to introduce one such method-Gr?bner bases-for non-mathematicians in an intuitive way. Specifically, the authors show the analogies and differences between linear and algebraic system solving, with an emphasis on the underlying geometric aspects. In the next issue, the authors will provide more details about Gr?bner bases along with some surprising applications.

Index Terms:
Grobner bases, polynomials, algebraic systems
Eugenio Roanes-Lozano, Eugenio Roanes-Mac?as, Luis M. Laita, "The Geometry of Algebraic Systems and Their Exact Solving Using Gröbner Bases," Computing in Science and Engineering, vol. 6, no. 2, pp. 76-79, March-April 2004, doi:10.1109/MCISE.2004.1267612
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