Generalised characteristic polynomials
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Methods for mechanical geometry formula deriving
ISSAC '90 Proceedings of the international symposium on Symbolic and algebraic computation
Base points, resultants, and the implicit representation of rational surfaces
Base points, resultants, and the implicit representation of rational surfaces
MultiPolynomial Resultant Algorithms
MultiPolynomial Resultant Algorithms
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
Conditions for exact resultants using the Dixon formulation
ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
Conic tangency equations and Apollonius problems in biochemistry and pharmacology
Mathematics and Computers in Simulation
Automated Geometry Diagram Construction and Engineering Geometry
ADG '98 Proceedings of the Second International Workshop on Automated Deduction in Geometry
On the efficiency and optimality of Dixon-based resultant methods
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Exact resultants for corner-cut unmixed multivariate polynomial systems using the Dixon formulation
Journal of Symbolic Computation - Special issue: International symposium on symbolic and algebraic computation (ISSAC 2002)
Corner edge cutting and Dixon A-resultant quotients
Journal of Symbolic Computation
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Conditions for determinantal formula for resultant of a polynomial system
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
ACM Communications in Computer Algebra
Hardware-accelerated collision detection for 3D virtual reality gaming
Simulation and Gaming - Symposium: virtual reality simulation
Comparing acceleration techniques for the dixon and macaulay resultants (abstract only)
ACM Communications in Computer Algebra
Algebraic Attacks on the Courtois Toy Cipher
Cryptologia
Cayley-Dixon projection operator for multi-univariate composed polynomials
Journal of Symbolic Computation
A method for finding zeros of polynomial equations using a contour integral based eigensolver
Proceedings of the 2009 conference on Symbolic numeric computation
Decomposition of algebraic sets and applications to weak centers of cubic systems
Journal of Computational and Applied Mathematics
Bezoutian and quotient ring structure
Journal of Symbolic Computation
Comparing acceleration techniques for the Dixon and Macaulay resultants
Mathematics and Computers in Simulation
Algorithmic search for flexibility using resultants of polynomial systems
ADG'06 Proceedings of the 6th international conference on Automated deduction in geometry
The multivariate resultant is NP-hard in any characteristic
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Multivariate resultants in Bernstein basis
ADG'08 Proceedings of the 7th international conference on Automated deduction in geometry
On the computation of matrices of traces and radicals of ideals
Journal of Symbolic Computation
Cayley-Dixon resultant matrices of multi-univariate composed polynomials
CASC'05 Proceedings of the 8th international conference on Computer Algebra in Scientific Computing
On the mixed cayley-sylvester resultant matrix
AISC'06 Proceedings of the 8th international conference on Artificial Intelligence and Symbolic Computation
Parameterized variety based view synthesis scheme for multi-view 3DTV
ACCV'12 Proceedings of the 11th Asian conference on Computer Vision - Volume Part IV
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Dixon's method for computing multivariate resultants by simultaneously eliminating many variables is reviewed. The method is found to be quite restrictive because often the Dixon matrix is singular, and the Dixon resultant vanished identically yielding no information about solutions for many algebraic and geometry problems. We extend Dixon's method for the case when the Dixon matrix is singular, but satisfies a condition. An efficient algorithm is developed based on the proposed extension for extracting conditions for the existence of affine solutions of a finite set of polynomials. Using this algorithm, numerous geometric and algebraic identities are derived for examples which appear intractable with other techniques of triangulation such as the successive resultant method, the Gro¨bner basis method, Macaulay resultants and Characteristic set method. Experimental results suggest that the resultant of a set of polynomials which are symmetric in the variables is relatively easier to compute using the extended Dixon's method.