Computing Tropical Points and Tropical Links

We present an algorithm for computing zero-dimensional tropical varieties based on triangular decomposition and Newton polygon methods. From it, we derive algorithms for computing points on and links of higher-dimensional tropical varieties, using intersections with affine hyperplanes to reduce the dimension to zero. We use the algorithms to show that the tropical Grassmannians \({\mathcal {G}}_{3,8}\) and \({\mathcal {G}}_{4,8}\) are not simplicial.