DOI
10.34229/KCA2522-9664.24.5.1
UDC 5.681.3
ALGORITHMS FOR SOLVING LINEAR CONSTRAINTS IN THE RING
OF INTEGER NUMBERS
Abstract. The author proposes algorithms for constructing a pre-basis and the basis of the set of solutions for systems of linear constraints of the type of equalities and inequalities in the domains of integers, which are based on combined coefficients of constraints. The article considers the algorithm for constructing the pre-basis and basis of systems of linear equations and algorithms for constructing the fundamental system of solutions for systems of linear homogeneous and linear inhomogeneous inequalities.
Keywords: ring of integer numbers, systems of linear constraints, algorithms.
full text
REFERENCES
- 1. Kryvyi S.L. Algorithms for constructing a basis for the set of solutions of systems of linear Diophantine equations in the ring of integers. Kibernetika i sistemnyj analiz. 2009. N 6. P. 36–41.
- 2. Kryvyi S.L. Linear Diophantine constraints and their applications. K.: Interservice, 2021. 257 p.
- 3. Menezes A., van Oorschot P., Vanstons S. Handbook of applied cryptography. CRC Press, 1996. 661 p.
- 4. Schrijver A. Theory of linear and integer programming. Reprinted. Amsterdam: John Willey & Sons, 1999. 484 p.
- 5. Bockmair A., Weispfenning V. Solving numerical constraints. In: Handbook of Automated Reasoning. Elsevier Science Publishers B.V., 2001. P. 753–842.
- 6. Papadimitriou Ch.H. Zlozonosc obliczeniowa. Warszawa: Wydawnictwo Naukowo Techniczne, 2002. 539 s.
- 7. Clausen M., Fortenbacher A. Efficient solution of linear diophantine equations. Journ. Symbolic Computation. 1989. Vol. 8, N 1, 2. P. 201–216.
