nilde-package: Nonnegative Integer Solutions of Linear Diophantine Equations...

Description Author(s) References


nilde provides functions for enumerating all existing nonnegative integer solutions of a linear Diophantine equation. The package also includes functions for solving 0-1, bounded and unbounded knapsack problems; 0-1, bounded and unbounded subset sum problems; and a problem of additive partitioning of natural numbers. The algorithm is based on a generating function of Hardy and Littlewood used by Voinov and Nikulin (1997).


Natalya Pya Arnqvist[aut, cre], Vassilly Voinov [aut], Rashid Makarov [aut], Yevgeniy Voinov [aut]

Maintainer: Natalya Pya Arnqvist <>


Voinov, V. and Nikulin, M. (1995) Generating functions, problems of additive number theory, and some statistical applications. Revue Roumaine de Mathématiques Pures et Appliquées, 40(2), 107-147

Voinov, V. and Nikulin, M. (1997) On a subset sum algorithm and its probabilistic and other applications. In: Advances in combinatorial methods and applications to probability and statistics, Ed. N. Balakrishnan, Birkhäuser, Boston, 153-163

Voinov, V. and Pya, N. (2006) A Remark on the Non-Uniqueness of a Non-Negative Integer Solution of a System of Linear Diophantine Equations with Applications to Integer Programming, Genetics, Reliability. Central Asian Journal of Management, Economics and Social Research (ISSN 1815-3356) 5(1-2), 42-47.

Voinov, V. and Pya, N. (2017) R-software for additive partitioning of positive integers. Mathematical Journal (ISSN 1682-0525), 17(1), 69-76

nilde documentation built on Dec. 17, 2021, 9:07 a.m.