A homotopy for solving general polynomial systems that respects m-homogenous structures
Applied Mathematics and Computation
Algebraic and geometric reasoning using Dixon resultants
ISSAC '94 Proceedings of the international symposium on Symbolic and algebraic computation
Comparison of various multivariate resultant formulations
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
Sparsity considerations in Dixon resultants
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Extraneous factors in the Dixon resultant formulation
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Efficient variable elimination using resultants
Efficient variable elimination using resultants
Matrices in elimination theory
Journal of Symbolic Computation - Special issue on polynomial elimination—algorithms and applications
A subdivision-based algorithm for the sparse resultant
Journal of the ACM (JACM)
Conditions for exact resultants using the Dixon formulation
ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
Rectangular corner cutting and Sylvester A-resultants
ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
Rectangular corner cutting and Dixon A -resultants
Journal of Symbolic Computation
On the efficiency and optimality of Dixon-based resultant methods
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
A new sylvester-type resultant method based on the dixon-bezout formulation
A new sylvester-type resultant method based on the dixon-bezout formulation
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Cayley-Dixon projection operator for multi-univariate composed polynomials
Journal of Symbolic Computation
Multivariate resultants in Bernstein basis
ADG'08 Proceedings of the 7th international conference on Automated deduction in geometry
Formal power series and loose entry formulas for the dixon matrix
IWMM'04/GIAE'04 Proceedings of the 6th international conference on Computer Algebra and Geometric Algebra with Applications
Hi-index | 0.00 |
Structural conditions on the support of a multivariate polynomial system are developed for which the Dixon-based resultant methods compute exact resultants. The concepts of a corner-cut support and almost corner-cut support of an unmixed polynomial system are introduced. For generic unmixed polynomial systems with corner-cut and almost corner-cut supports, the Dixon based methods can be used to compute their resultants exactly. These structural conditions on supports are based on analyzing how such supports differ from box supports of d-degree systems for which the Dixon formulation is known to compute resultants exactly. Such an analysis also gives a sharper bound on the complexity of resultant computation using the Dixon formulation in terms of the support and the mixed volume of the Newton polytope of the support.These results are a direct generalization of the authors' results on bivariate systems including the results of Zhang and Goldman as well as of Chionh for generic unmixed bivariate polynomial systems with corner-cut supports.