Hybrid sparse resultant matrices for bivariate systems
Our main contribution is an explicit construction of square resultant matrices, which are submatrices of those introduced by Cattani, Dickenstein and Sturmfels [4]. The determinant is a nontrivial multiple of the sparse (or toric) resultant. The matrix is hybrid in that it contains a submatrix of Sy...
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | CONF |
| Materias: | |
| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_NIS02119_v_n_p24_DAndrea |
| Aporte de: |
| Sumario: | Our main contribution is an explicit construction of square resultant matrices, which are submatrices of those introduced by Cattani, Dickenstein and Sturmfels [4]. The determinant is a nontrivial multiple of the sparse (or toric) resultant. The matrix is hybrid in that it contains a submatrix of Sylvester type and an additional row expressing the toric Jacobian. If we restrict attention to such matrices, the algorithm yields the smallest possible matrix in general. This is achieved by strongly exploiting the combinatorics of sparse elimination. The algorithm uses a new piecewise-linear lifting, defined for bivariate systems of 3 polynomials with Newton polygons being scaled copies of a single polygon. The major motivation comes from systems encountered in CAD. Our Maple implementation, applied to certain examples, illustrates our construction and compares with alternative matrices. |
|---|