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We present an algorithm for computing zero-dimensional tropical varietiesbased on triangular decomposition and Newton polygon methods. From it, wederive algorithms for computing points on and links of higher-dimensionaltropical varieties, using intersections with affine hyperplanes to reduce thedimension to zero. We use the algorithms to show that the tropicalGrassmannians $\mathcal G_{3,8}$ and $\mathcal G_{4,8}$ are not simplicial.

Computing tropical points and tropical links