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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)