Details:
Title  A new class of term orders for elimination  Author(s)  QuocNam Tran  Type  Article in Journal  Abstract  Elimination is a classical subject. The problem is algorithmically solvable by using resultants or by one calculation of Groebner basis with respect to an elimination term order. However, there is no existing method that is both efficient and reliable enough for applicable size problems, say implicitization of bicubic Bezier surfaces with degree six in five variables. This basic and useful operation in computer aided geometric design and geometric modeling defies a solution even when approximation using floatingpoint or modular coefficients is used for Groebner basis computation. An elimination term order can be used to eliminate U for any ideal in K[X][U]. However, for most practical problems we are given a fixed ideal, which means that an elimination term order may be too much for our calculation. In this paper, the author proposes a new approach for elimination. Instead of using a classical elimination term order for all problems or ideals as usual, the author proposes to use algebraic structures of the given system of equations for finding more suitable term orders for elimination of the given problem only. Experimental results showed that these idealspecific term orders are much more efficient for elimination. In particular, when ideal specific term orders for elimination are used with Groebner walk conversion, one can completely avoid all perturbations. This is a significant result because researchers have been struggling with how to perturb basis conversions for a long time.  Keywords  Elimination, Groebner basis, Basis conversion  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717107000314 
Language  English  Journal  Journal of Symbolic Computation  Volume  42  Number  5  Pages  533  548  Year  2007  Note  Special issue on Applications of Computer Algebra Special issue on Applications of Computer Algebra  Edition  0  Translation 
No  Refereed 
No 
