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Hybrid Dixon Resultants
| Content Provider | Semantic Scholar |
|---|---|
| Author | Chionh, Eng-Wee Dixon, Abstract |
| Copyright Year | 1998 |
| Abstract | 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 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). 1 Homogeneous and hybrid resultants Resultants are a powerful mathematical tool for analyzing polynomial equations Abhyankar 1976]. Since free-form curves and surfaces in computer graphics and computer aided design are represented predominantly either by polynomials or by rational functions, it is not surprising that resultants have wide ranging applications in the study of computer generated curves and surfaces. Well-known practical applications include algorithms for intersection Kajiya 1982], implicitization Sederberg et al 1984, Manocha and Canny 1992], and inversion Chionh and Goldman 1992] of free-form curves and surfaces. Theoretical applications also abound Gold-man et al 1984; Sederberg et al 1997; Cox et al 1998]. Resultants are generally expressed as determinants. For two univariate polynomials of degree n, there are two standard determinant representations for the resultant: Sylvester's resultant Van Der Waerden 1950] and Bezout's resultant Goldman et al 1984; De Montaudouin and Tiller 1984]. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.cs.rice.edu/~mzhang/research/hybrid.ps |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
