Solving Degenerate Sparse Polynomial Systems Faster
| dc.creator | Rojas, J. Maurice | |
| dc.date | 1998-09-14 | |
| dc.date | 1998-09-15 | |
| dc.date.accessioned | 2026-07-07T05:26:00Z | |
| dc.date.available | 2026-07-07T05:26:00Z | |
| dc.description | Consider a system F of n polynomial equations in n unknowns, over an algebraically closed field of arbitrary characteristic. We present a fast method to find a point in every irreducible component of the zero set Z of F. Our techniques allow us to sharpen and lower prior complexity bounds for this problem by fully taking into account the monomial term structure. As a corollary of our development we also obtain new explicit formulae for the exact number of isolated roots of F and the intersection multiplicity of the positive-dimensional part of Z. Finally, we present a combinatorial construction of non-degenerate polynomial systems, with specified monomial term structure and maximally many isolated roots, which may be of independent interest. | |
| dc.description | This is the final journal version of math.AG/9702222 (``Toric Generalized Characteristic Polynomials''). This final version is a major revision with several new theorems, examples, and references. The prior results are also significantly improved | |
| dc.identifier | https://arxiv.org/abs/math/9809071 | |
| dc.identifier | http://arxiv.org/abs/math/9809071 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/77393 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Computational Complexity | |
| dc.subject | Numerical Analysis | |
| dc.title | Solving Degenerate Sparse Polynomial Systems Faster | |
| dc.type | text |