15 citations · 29 across the 6 of their papers we have counts for
6 papers · 1 filter
Computing generating sets of lattice ideals
Raymond Hemmecke, Peter Malkin
In this article, we present a new algorithm for computing a generating set of a lattice ideal. This algorithm is based on a project-and-lift approach and is implemented in 4ti2. We…
Exploiting Symmetries in the Computation of Graver Bases
Raymond Hemmecke
Many challenging Graver bases computations, like for multi-way tables in statistics, have a highly symmetric problem structure that is not exploited so far computationally. In this…
Test Sets for Integer Programs with Z-Convex Objective
Raymond Hemmecke
In this paper we extend test set based augmentation methods for integer linear programs to programs with more general convex objective functions. We show existence and computabilit…
Short Rational Functions for Toric Algebra and Applications
Jesus De Loera, David Haws, Raymond Hemmecke +3
We encode the binomials belonging to the toric ideal associated with an integral matrix using a short sum of rational functions as introduced by Barvinok \ci…
On the Computation of Hilbert Bases and Extreme Rays of Cones
Raymond Hemmecke
In this paper we present a novel project-and-lift approach to compute the set of minimal generators of the semigroup for lattices . This problem c…
Polyhedral Cones of Magic Cubes and Squares
M. Ahmed, J. De Loera, R. Hemmecke
Using computational algebraic geometry techniques and Hilbert bases of polyhedral cones we derive explicit formulas and generating functions for the number of magic squares and mag…