Cayley-Dixon projection operator for multi-univariate composed polynomials
Journal of Symbolic Computation(2009)
摘要
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.
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关键词
univariate polynomial,Cayley–Dixon,outer polynomial system,Cayley-Dixon formulation,outer system,Polynomial composition,Resultant,Dixon matrix,Cayley-Dixon projection operator,multivariate polynomial,Cayley-Dixon construction,multivariate system,polynomial system
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