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Outputs (19)

On intersections and stable intersections of tropical hypersurfaces (2024)
Journal Article
Ren, Y. (2024). On intersections and stable intersections of tropical hypersurfaces. Algebraic combinatorics, 7(1), 9-15. https://doi.org/10.5802/alco.327

We prove that every connected component of an intersection of tropical hypersurfaces contains a point of their stable intersection unless that stable intersection is empty. This is done by studying algebraic hypersurfaces that tropicalize to them and... Read More about On intersections and stable intersections of tropical hypersurfaces.

Massively parallel computation of tropical varieties, their positive part, and tropical Grassmannians (2023)
Journal Article
Bendle, D., Böhm, J., Ren, Y., & Schröter, B. (2023). Massively parallel computation of tropical varieties, their positive part, and tropical Grassmannians. Journal of Symbolic Computation, 120, https://doi.org/10.1016/j.jsc.2023.102224

We present a massively parallel framework for computing tropicalizations of algebraic varieties which can make use of symmetries using the workflow management system GPI-Space and the computer algebra system Singular. We determine the tropical Grassm... Read More about Massively parallel computation of tropical varieties, their positive part, and tropical Grassmannians.

Computing zero-dimensional tropical varieties via projections (2022)
Journal Article
Görlach, P., Ren, Y., & Zhang, L. (2022). Computing zero-dimensional tropical varieties via projections. Computational Complexity, 31(1), Article 5. https://doi.org/10.1007/s00037-022-00222-9

We present an algorithm for computing zero-dimensional tropical varieties using projections. Our main tools are fast monomial transforms of triangular sets. Given a Gröbner basis, we prove that our algorithm requires only a polynomial number of arith... Read More about Computing zero-dimensional tropical varieties via projections.

Detecting tropical defects of polynomial equations (2019)
Journal Article
Görlach, P., Ren, Y., & Sommars, J. (2021). Detecting tropical defects of polynomial equations. Journal of Algebraic Combinatorics, 53(1), 31-47. https://doi.org/10.1007/s10801-019-00916-4

We introduce the notion of tropical defects, certificates that a system of polynomial equations is not a tropical basis, and provide two algorithms for finding them in affine spaces of complementary dimension to the zero set. We use these techniques... Read More about Detecting tropical defects of polynomial equations.