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cs.SC2026
Engineered Complete Intersections: Algorithmic Aspects
Alexander Esterov, Rafael Mohr, Yulia Mukhina
Engineered Complete Intersections (ECI's) are a class of sparse polynomial systems frequently arising in a number of contexts, both in pure mathematics (e.g. enumerative geometry)…
cs.SC2025
On the Computation of Newton Polytopes of Eliminants
Rafael Mohr, Yulia Mukhina
For systems of polynomial equations, we study the problem of computing the Newton polytope of their eliminants. As was shown by Esterov and Khovanskii, such Newton polytopes are mi…
cs.SC2024
A Syzygial Method for Equidimensional Decomposition
Rafael Mohr
Based on a theorem by Vasconcelos, we give an algorithm for equidimensional decomposition of algebraic sets using syzygy computations via Gröbner bases. This algorithm avoids the…