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Hybrid Dixon resultants. (English) Zbl 0960.65056
Cripps, Robert (ed.), The mathematics of surfaces. VIII. Proceedings of the 8th IMA conference held in Birmingham, GB, August and September 1998. Winchester: Information Geometers. 193-212 (1998).
Summary: A. L. Dixon [Proc. Lond. Math. Soc. 6, 49-69 (1908; JFM 40.0207.01)] 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 coefficients of the original three polynomial equations.
Here we mix and match columns from these three Dixon matrices to construct a large assortment of new hybrid determinant representations of orders ranging from \(2mn\) to \(6mn\) for the resultant of three bivariate polynomials of bidegree \((m,n)\).
For the entire collection see [Zbl 0938.00014].

MSC:
65F40 Numerical computation of determinants
15A15 Determinants, permanents, traces, other special matrix functions
65D17 Computer-aided design (modeling of curves and surfaces)
12Y05 Computational aspects of field theory and polynomials (MSC2010)
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