标题： 延拓和计算代数 显示英文标题

标题： Prolongations and computational algebra

摘要： 我们探讨计算代数设置中的延拓几何概念，扩展了Landsberg和Manivel的结果，这些结果将延拓与割线流形的方程联系起来。 我们还开发了用于计算延拓的方法，这些方法具有组合性质。 作为应用，我们使用延拓推导出系统发生学中二元对称模型的新一类割线方程。 显示英文摘要

摘要： We explore the geometric notion of prolongations in the setting of computational algebra, extending results of Landsberg and Manivel which relate prolongations to equations for secant varieties. We also develop methods for computing prolongations which are combinatorial in nature. As an application, we use prolongations to derive a new family of secant equations for the binary symmetric model in phylogenetics.