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Cayley-Dixon Projection Operator for Multi-Univariate Composed Polynomials
Journal of Symbolic Computation (2009)
  • Arthur Chtcherba
  • Deepak Kapur, University of New Mexico - Main Campus
  • Manfred Minimair, Seton Hall University

The Cayley-Dixon formulation for multivariate projection operators (multiples of resultants of multivariate polynomials) has been shown to be efficient (both exper- imentally and theoretically) for simultaneously eliminating many variables from a polynomial system. In this paper, the behavior of the Cayley-Dixon projection op- erator and the structure of Dixon matrices are analyzed for composed polynomial systems constructed from a multivariate system in which each variable is substi- tuted 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 are analyzed.

  • projection operator,
  • Dixon resultant,
  • composed polynomials
Publication Date
August, 2009
Publisher Statement
This link provides a preprint version of the published paper.
Citation Information
Arthur Chtcherba, Deepak Kapur and Manfred Minimair. "Cayley-Dixon Projection Operator for Multi-Univariate Composed Polynomials" Journal of Symbolic Computation Vol. 44 Iss. 8 (2009)
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