Algebraic geometry for computer-aided geometric design
IEEE Computer Graphics and Applications
Geometric and solid modeling: an introduction
Geometric and solid modeling: an introduction
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
Generalized resultants over unirational algebraic varieties
Journal of Symbolic Computation - Special issue on symbolic computation in algebra, analysis and geometry
Rectangular corner cutting and Sylvester A-resultants
ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
Sparse resultant of composed polynomials I* mixed-unmixed 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
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
A new sylvester-type resultant method based on the dixon-bezout formulation
A new sylvester-type resultant method based on the dixon-bezout formulation
Resultants of skewly composed polynomials
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
A method for finding zeros of polynomial equations using a contour integral based eigensolver
Proceedings of the 2009 conference on Symbolic numeric computation
Multivariate resultants in Bernstein basis
ADG'08 Proceedings of the 7th international conference on Automated deduction in geometry
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The behavior of the Cayley-Dixon resultant construction 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. It is shown that a Dixon projection operator (a multiple of the resultant) 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. The derivation of the resultant formula for the composed system unifies all the known related results in the literature. A new resultant formula is derived for systems where it is known that the Cayley-Dixon construction does not contain any extraneous factors. The approach demonstrates that the resultant of a composed system can be effectively calculated by considering only the resultant of the outer system.