Resultants for unmixed bivariate polynomial systems produced using the Dixon formulation
نویسندگان
چکیده
منابع مشابه
Resultants for Unmixed Bivariate Polynomial Systems using the Dixon formulation
A necessary and sufficient condition on the support of a generic unmixed bivariate polynomial system is identified such that for polynomial systems with such support, the Dixon resultant formulation produces their resultants. It is shown that Sylvester-type matrices can also be obtained for such polynomial systems. These results are shown to be a generalization of related results recently repor...
متن کاملResultants for unmixed bivariate polynomial systems produced using the Dixon formulation
A necessary and sufficient condition on the support of a generic unmixed bivariate polynomial system is identified such that for polynomial systems with such support, the Dixon resultant formulation produces their resultants. It is shown that Sylvester-type matrices, called Dixon dialytic matrices, can also be obtained for such polynomial systems. These results are shown to be a generalization ...
متن کاملExact resultants for corner-cut unmixed multivariate polynomial systems using the Dixon formulation
Structural conditions on the support of a multivariate polynomial system are developed for which the Dixon-based resultant methods compute exact resultants. For cases when this cannot be done, an upper bound on the degree of the extraneous factor in the projection operator can be determined a priori, thus resulting in quick identification of the extraneous factor in the projection operator. (Fo...
متن کاملA Complete Analysis of Resultants and Extraneous Factors for Unmixed Bivariate Polynomial Systems using the Dixon formulation
A necessary and sufficient condition on the support of a generic unmixed bivariate polynomial system is identified such that for polynomial systems with such support, the Dixon resultant formulation produces their resultants. It is shown that Sylvester-type matrices can also be obtained for such polynomial systems. These results are shown to be a generalization of related results recently repor...
متن کاملHybrid Dixon Resultants
Dixon 1908] describes three distinct homogeneous determinant representations for the resultant of three bivariate polynomials of bidegree (m; n). These Dixon resultants are the determinants of matrices of orders 6mn, 3mn and 2mn, and the entries of these matrices are respectively homogeneous of degrees 1, 2, and 3 in the coeecients of the original three polynomial equations. Here we mix and mat...
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ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 2004
ISSN: 0747-7171
DOI: 10.1016/j.jsc.2003.12.001