论文标题
来自Khovanskii基地的数值同义
Numerical homotopies from Khovanskii bases
论文作者
论文摘要
我们提出了用于在有限的khovanskii的存在下求解各种方程系统的数值同质续算法。这些利用了安德森（Anderson）的平坦变性为复曲面的变化。当安德森（Anderson）的退化嵌入了投射空间时，我们的算法是一般折叠两步同型算法的特殊情况。当安德森的变性嵌入了加权的投影空间中时，我们解释了如何提升投影空间并构建对复曲面同拷贝的适当修改。使用MacAulay2在几个示例中说明了我们的算法。
We present numerical homotopy continuation algorithms for solving systems of equations on a variety in the presence of a finite Khovanskii basis. These take advantage of Anderson's flat degeneration to a toric variety. When Anderson's degeneration embeds into projective space, our algorithm is a special case of a general toric two-step homotopy algorithm. When Anderson's degeneration is embedded in a weighted projective space, we explain how to lift to a projective space and construct an appropriate modification of the toric homotopy. Our algorithms are illustrated on several examples using Macaulay2.
