Abstract
Many problems of computational geometry involve non linear polynomials. Many of these problems can be solved with easy algorithms after transforming the polynomial set involved in their specification into Gröbner bases form. Gröbner bases of a system of polynomials are canonical finite sets of multivariate polynomials which define the same algebraic structure as the initial polynomial system. But the computation of Gröbner bases requires a large amount of time and space. However some strategies can be introduced to improve the computation. In this paper, we shortly introduce basic notions of Gröbner bases. Then we propose an algorithm for their computation which is based on a completion procedure for rewrite systems. This algorithm is extended with an orthogonal set of selection strategies which improve each sub-algorithms (reduction, inter reduction, critical pair choice). At last we discuss the use of the strategies applied to some examples (as a restriction of the well known piano mover's problem).
Partially supported by the CHIC ESPRIT Project 5291
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Monfroy, E. (1993). Gröbner bases: Strategies and applications. In: Calmet, J., Campbell, J.A. (eds) Artificial Intelligence and Symbolic Mathematical Computing. AISMC 1992. Lecture Notes in Computer Science, vol 737. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57322-4_9
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DOI: https://doi.org/10.1007/3-540-57322-4_9
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