论文标题
混合细分适合Canny-Emiris公式
Mixed subdivisions suitable for the Canny-Emiris formula
论文作者
论文摘要
Canny-Emiris公式给出了稀疏的结果，因为Sylvester型基质的决定因素比少数矩阵的比率是通过混合细分算法获得的。同一位作者为贪婪的方法提供了一类明确的混合细分，以使公式保持，并且在Canny和Pedersen的方法之后，构造的矩阵的尺寸小于细分算法的尺寸。当牛顿多型是分区，系统是多种合并时，我们的方法会改善矩阵的尺寸。在本文中，我们提供了更多这样的情况，我们猜想可能是升降机提供最小的矩阵尺寸。我们还描述了此公式的两个应用，即在计算机视觉和表面的隐式中，同时提供相应的朱莉娅代码。我们最终引入了一种新型的热带方法，该方法导致了其中一个结果的另一种证明。
The Canny-Emiris formula gives the sparse resultant as the ratio of the determinant of a Sylvester-type matrix over a minor of it, both obtained via a mixed subdivision algorithm. The same authors gave an explicit class of mixed subdivisions for the greedy approach so that the formula holds, and the dimension of the constructed matrices is smaller than that of the subdivision algorithm, following the approach of Canny and Pedersen. Our method improves upon the dimensions of the matrices when the Newton polytopes are zonotopes and the systems are multihomogeneous. In this text, we provide more such cases, and we conjecture which might be the liftings providing minimal size of the resultant matrices. We also describe two applications of this formula, namely in computer vision and in the implicitization of surfaces, while offering the corresponding JULIA code. We finally introduce a novel tropical approach that leads to an alternative proof of one of the results.
