5 papers
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)…
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…
Wronski Pairs of Honeycomb Curves
Laura Casabella, Michael Joswig, Rafael Mohr
We study certain generic systems of real polynomial equations associated with triangulations of convex polytopes and investigate their number of real solutions. Our main focus is s…
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 u…
Faster computation of Whitney stratifications and their minimization
Martin Helmer, Rafael Mohr
We describe two new algorithms for the computation of Whitney stratifications of real and complex algebraic varieties. The first algorithm is a modification of the algorithm of Hel…