3 citations · 13 across the 8 of their papers we have counts for
9 papers
Detecting tropical defects of polynomial equations
Paul Görlach, Yue Ren, Jeff Sommars
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 space…
Monodromy Solver: Sequential and Parallel
Nathan Bliss, Timothy Duff, Anton Leykin +1
We describe, study, and experiment with an algorithm for finding all solutions of systems of polynomial equations using homotopy continuation and monodromy. This algorithm follows…
Computing Tropical Varieties in Macaulay2
Carlos Améndola, Kathlén Kohn, Sara Lamboglia +5
We introduce a package for doing tropical computations in Macaulay2. The package draws on the functionality of Gfan and Polymake while making the process as simple as possible for…
Computing Tropical Prevarieties in Parallel
Anders Jensen, Jeff Sommars, Jan Verschelde
The computation of the tropical prevariety is the first step in the application of polyhedral methods to compute positive dimensional solution sets of polynomial systems. In partic…
A computer algebra system for R: Macaulay2 and the m2r package
David Kahle, Christopher O'Neill, Jeff Sommars
Algebraic methods have a long history in statistics. The most prominent manifestation of modern algebra in statistics can be seen in the field of algebraic statistics, which brings…
Solving polynomial systems via homotopy continuation and monodromy
Timothy Duff, Cvetelina Hill, Anders Jensen +3
We study methods for finding the solution set of a generic system in a family of polynomial systems with parametric coefficients. We present a framework for describing monodromy ba…