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Elimination and complexity
ELSEVIER
Mathematics
and Computers
in Simulation
IN SIMULATION
42 ( 1996) 427
Introduction Elimination and complexity
The following papers are dealing with the algorithmic improvements in polynomial reduction techniques. The first two papers deals with the elimination theory as initiated by Ritt and Seidenberg. P. Solerno studies this algorithm from a complexity point of view, and he gives a survey on lower and upper bounds problems, obtaining some improvements by using duality theory and arithmetic intersection theory. The paper of F. Boulier gives an optimization, based on rewriting techniques, of the Seidenberg elimination algorithm involving differential polynomials. The third paper, by C.A. Berenstein and A. Yger uses multidimensional residues for getting explicit polynomial division formulas, and for computing the complete sum of residues of rational functions. A link is done with numerical computation of multidimensional integrals. M. Giusti
Mathematics
and Computers
in Simulation
IN SIMULATION
42 ( 1996) 427
Introduction Elimination and complexity
The following papers are dealing with the algorithmic improvements in polynomial reduction techniques. The first two papers deals with the elimination theory as initiated by Ritt and Seidenberg. P. Solerno studies this algorithm from a complexity point of view, and he gives a survey on lower and upper bounds problems, obtaining some improvements by using duality theory and arithmetic intersection theory. The paper of F. Boulier gives an optimization, based on rewriting techniques, of the Seidenberg elimination algorithm involving differential polynomials. The third paper, by C.A. Berenstein and A. Yger uses multidimensional residues for getting explicit polynomial division formulas, and for computing the complete sum of residues of rational functions. A link is done with numerical computation of multidimensional integrals. M. Giusti