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Homotopy techniques for analytic combinatorics in several variables
Kisun Lee, Stephen Melczer, Josip Smolčić
We combine tools from homotopy continuation solvers with the methods of analytic combinatorics in several variables to give the first practical algorithm and implementation for the…
The NumericalCertification package in Macaulay2
Kisun Lee
The package \texttt{NumericalCertification} implements methods for certifying numerical approximations of solutions for a given system of polynomial equations. For certifying regul…
On the polyhedral homotopy method for solving generalized Nash equilibrium problems of polynomials
Kisun Lee, Xindong Tang
The generalized Nash equilibrium problem (GNEP) is a kind of game to find strategies for a group of players such that each player's objective function is optimized. Solutions for G…
Implementing real polyhedral homotopy
Kisun Lee, Julia Lindberg, Jose Israel Rodriguez
We implement a real polyhedral homotopy method using three functions. The first function provides a certificate that our real polyhedral homotopy is applicable to a given system; t…