We consider the bit complexity of computing Chow forms and their generalization to multiprojective spaces. We develop a deterministic algorithm using resultants and obtain a single exponential complexity upper bound. Earlier computational results for Chow forms were in the arithmetic complexity model, and our result represents the first bit complexity bound. We also extend our algorithm to Hurwitz forms in projective space, and explore connections between multiprojective Hurwitz forms and matroid theory. The motivation for our work comes from incidence geometry where intriguing computational algebra problems remain open.
翻译:我们考虑了计算周会表格的比重复杂性以及将其概括到多预测空间。我们利用结果人开发了一种确定性算法,并获得了单一指数复杂性的上限。周会表格的早期计算结果在算术复杂性模型中,我们的结果代表了第一点复杂性。我们还把我们的算法扩大到投影空间的Hurwitz形式,并探索多预测Hurwitz形式与机器人理论之间的联系。我们工作的动力来自一些几何学,在这些几何学中,令人感兴趣的计算代数问题仍然存在。