用霍万斯基解方程

Pub Date : 2024-05-27 DOI:10.1016/j.jsc.2024.102340

Barbara Betti , Marta Panizzut , Simon Telen

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引用次数: 0

摘要

我们开发了一种新的特征值方法，用于求解任意域上的结构多项式方程。这些方程定义在投影代数簇上，该代数簇可以通过 Khovanskii 基（例如普吕克嵌入中的格拉斯曼）进行有理参数化。这就概括了针对环状变体的既定算法，并在计算机代数中引入了霍万斯基的有效使用。我们研究了正则性问题，并讨论了几个应用。

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Solving equations using Khovanskii bases

We develop a new eigenvalue method for solving structured polynomial equations over any field. The equations are defined on a projective algebraic variety which admits a rational parameterization by a Khovanskii basis, e.g., a Grassmannian in its Plücker embedding. This generalizes established algorithms for toric varieties, and introduces the effective use of Khovanskii bases in computer algebra. We investigate regularity questions and discuss several applications.

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