Journal of Symbolic Computation
The structure of polynomial ideals and Grobner bases
SIAM Journal on Computing
Equations for the projective closure and effective Nullstellensatz
Discrete Applied Mathematics - Special volume on applied algebra, algebraic algorithms, and error-correcting codes
Algorithm for implicitizing rational parametric surfaces
Computer Aided Geometric Design
Implicitization using moving curves and surfaces
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Hilbert functions and the Buchberger algorithm
Journal of Symbolic Computation
Converting bases with the Gröbner walk
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
A fast algorithm for Gröbner basis conversion and its applications
Journal of Symbolic Computation - Special issue on applications of the Gröbner basis method
Term Orderings on the Polynominal Ring
EUROCAL '85 Research Contributions from the European Conference on Computer Algebra-Volume 2
Implicitization of Rational Parametric Curves and Surfaces
AAECC-8 Proceedings of the 8th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Revisiting the µ-basis of a rational ruled surface
Journal of Symbolic Computation
IEEE Computer Graphics and Applications
Groebner bases computation in Boolean rings for symbolic model checking
MOAS'07 Proceedings of the 18th conference on Proceedings of the 18th IASTED International Conference: modelling and simulation
Computational D-module theory with singular, comparison with other systems and two new algorithms
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
Groebner bases computation in Boolean rings for symbolic model checking
MS '07 The 18th IASTED International Conference on Modelling and Simulation
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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 bi-cubic 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 floating-point 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 ideal-specific 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.