Algebraic geometry for computer-aided geometric design
IEEE Computer Graphics and Applications
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
Subresultants under composition
Journal of Symbolic Computation
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
Solving degenerate sparse polynomial systems faster
Journal of Symbolic Computation - Special issue on polynomial elimination—algorithms and applications
Generalized resultants over unirational algebraic varieties
Journal of Symbolic Computation - Special issue on symbolic computation in algebra, analysis and geometry
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
Sparse resultant of composed polynomials I* mixed-unmixed case
Journal of Symbolic Computation
Sparse resultant of composed polynomials II unmixed--mixed case
Journal of Symbolic Computation
Factoring sparse resultants of linearly combined polynomials
ISSAC '03 Proceedings of the 2003 international symposium on Symbolic and algebraic computation
Sparse Resultant under Vanishing Coefficients
Journal of Algebraic Combinatorics: An International Journal
Base points, resultants, and the implicit representation of rational surfaces
Base points, resultants, and the implicit representation of rational surfaces
Topics in resultants and implicitization
Topics in resultants and implicitization
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)
Dense resultant of composed polynomials mixed-mixed case
Journal of Symbolic Computation
Corner edge cutting and Dixon A-resultant quotients
Journal of Symbolic Computation
Exact computation of the medial axis of a polyhedron
Computer Aided Geometric Design
A new sylvester-type resultant method based on the dixon-bezout formulation
A new sylvester-type resultant method based on the dixon-bezout formulation
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The Cayley-Dixon formulation for multivariate projection operators (multiples of resultants of multivariate polynomials) has been shown to be efficient (both experimentally and theoretically) for simultaneously eliminating many variables from a polynomial system. In this paper, the behavior of the Cayley-Dixon projection operator and the structure of Dixon matrices are analyzed for composed polynomial systems constructed from a multivariate system in which each variable is substituted by a univariate polynomial in a distinct variable. Under some conditions, it is shown that a Dixon projection operator of the composed system can be expressed as a power of the resultant of the outer polynomial system multiplied by powers of the leading coefficients of the univariate polynomials substituted for variables in the outer system. A new resultant formula is derived for systems where it is known that the Cayley-Dixon construction does not contain any extraneous factor. The complexity of constructing Dixon matrices and roots at toric infinity of composed polynomials is analyzed.