论文标题
在计算基质加权同质系统的Gröbner基础上
On the computation of Gröbner bases for matrix-weighted homogeneous systems
论文作者
论文摘要
在本文中，我们研究了几种重量系统加权的系统的结构，以及它如何影响Gröbner基础的计算。我们提出了几种用于计算具有该结构的系统的线性代数算法，无论是直接还是通过还原为现有结构。我们还提出了合适的优化技术。 作为对复杂性研究的开放，我们讨论了规律性的潜在定义，并证明它们是非空的。最后，我们介绍了来自SageMath算法的原型实现的实验数据。
In this paper, we examine the structure of systems that are weighted homogeneous for several systems of weights, and how it impacts the computation of Gröbner bases. We present several linear algebra algorithms for computing Gröbner bases for systems with this structure, either directly or by reducing to existing structures. We also present suitable optimization techniques. As an opening towards complexity studies, we discuss potential definitions of regularity and prove that they are generic if non-empty. Finally, we present experimental data from a prototype implementation of the algorithms in SageMath.
