Bilkent University Algebra Seminars

Polyhedral Omega: Solving linear Diophantine systems
Zafeirakis Zafeirakopoulos
Gebze Technical University, Turkey
Özet : Polyhedral Omega is a new algorithm for solving linear Diophantine systems (LDS), i.e., for computing a multivariate rational function representation of the set of all non-negative integer solutions to a system of linear equations and inequalities. Polyhedral Omega combines methods from partition analysis with methods from polyhedral geometry. In particular, we combine MacMahon's iterative approach based on the Omega operator and explicit formulas for its evaluation with geometric tools such as Brion decomposition and Barvinok's short rational function representations. This synthesis of ideas makes Polyhedral Omega by far the simplest algorithm for solving linear Diophantine systems available to date.
  Tarih : 24.11.2016
  Saat : 11:00
  Yer : Mathematics Department Seminar Room SA-141
  Dil : English