A fast method for finding the basis of nonnegative solutions to a linear Diophantine equation
Journal of Symbolic Computation
Avoiding slack variables in the solving of linear diophantine equations and inequations
Theoretical Computer Science - Special issue: principles and practice of constraint programming
Some complexity results for polynomial ideals
Journal of Complexity
An oracle-polynomial time augmentation algorithm for integer programming
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
A Unification Algorithm for Associative-Commutative Functions
Journal of the ACM (JACM)
On the complexity of integer programming
Journal of the ACM (JACM)
A linear space algorithm for computing the hermite normal form
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
On computing Hilbert bases via the Elliot-MacMahon algorithm
Theoretical Computer Science
On the Complexity of Counting the Hilbert Basis of a Linear Diophnatine System
LPAR '99 Proceedings of the 6th International Conference on Logic Programming and Automated Reasoning
On the Complexity of Recognizing the Hilbert Basis of a Linear Diophantine System
MFCS '99 Proceedings of the 24th International Symposium on Mathematical Foundations of Computer Science
Minimal Solutions of Linear Diophantine Systems: Bounds and Algorithms
RTA '91 Proceedings of the 4th International Conference on Rewriting Techniques and Applications
Solving Linear Diophantine Equations Using the Geometric Structure of the Solution Space
RTA '97 Proceedings of the 8th International Conference on Rewriting Techniques and Applications
Using Canonical Representations of Solutions to Speed Up Infinite-State Model Checking
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
Delay Analysis in Synchronous Programs
CAV '93 Proceedings of the 5th International Conference on Computer Aided Verification
Hilbert Bases, Caratheodory's Theorem and Combinatorial Optimization
Proceedings of the 1st Integer Programming and Combinatorial Optimization Conference
HYTECH: A Model Checker for Hybrid Systems
CAV '97 Proceedings of the 9th International Conference on Computer Aided Verification
Non-standard approaches to integer programming
Discrete Applied Mathematics
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We define a basis of solutions of a system of linear inequalities and present a general algorithm for finding such a basis. Our algorithm relies on an algorithm for finding a Hilbert basis for the set of nonnegative solutions of a system of linear inequalities and can be used in conjunction with any such algorithm.