On the efficiency and optimality of Dixon-based resultant methods

Authors:
Arthur D. Chtcherba;Deepak Kapur
Affiliations:
University of New Mexico, Albuquerque, NM;University of New Mexico, Albuquerque, NM
Venue:
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Year:
2002

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Abstract

Structural conditions on polynomial systems are developed for which the Dixon-based resultant methods often compute exact resultants. For cases when this cannot be done, the degree of the extraneous factor in the projection operator computed using the Dixon-based methods is typically minimal. A method for constructing a resultant matrix based on a combination of Sylvester-dialytic and Dixon methods is proposed. A heuristic for variable ordering for this construction often leading to exact resultants is developed.