Algorithms for searching the basis solution of systems of linear homogenous diophantine equations

• Autorzy: Grzywacz W. , Kryvyy S.
• Języki publikacji: EN

Abstrakty

EN

Algorithms of solving systems of linear constraints over the set of natural numbers are applied in various sciences and spheres. Among them we should highlight Petri Nets [2], logic deduction in the first order predicate calculus with use of associative-commutative unification, computer algebra [6] etc. The special case of system of linear Diophantine constraints is system of homogenous linear Diorhantine equations (SHLDE), where solutions are searched over the set of naturals or the set {0,1}. In this work the algorithms for solving SHLDE over the set of naturals will be presented.

Słowa kluczowe

EN

system of homogenous linear Diophantine equations (SHLDE)

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Computing, Multimedia and Intelligent Techniques
• Rocznik: 2007
• Tom: Vol. 3, nr 1
• Strony: 20--32
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Grzywacz W.

autor

Kryvyy S.

• Czestochowa University of Technology, Institute of Computer and Information Sciences, ul. Dąbrowskiego 73, 42-200 Częstochowa, Poland,

Bibliografia

• [1] Contenjean E., Devie H., Solving system of linear Diophantine equations. In Proc. 3rd Workshop on Unification, Lambrecht, Germany, University of Kaiserslautern, Jule, 1989.
• [2] Murata T., Petri Nets: Properties, Analysis and Applications, Proceeding of the IEEE 1989, 77, 4, 541-580.
• [3] Hilbert D., Ueber die Theorie der algebraischen Formen, Mathematische Annalen 1890, 36, 473-534.
• [4] Clausen M., Fortenbacher A., Efficient solution of linear Diophantine equations, Journ. Symbolic Computation 1989, 8, 1, 2, 201-216.
• [5] Krivoi S., A Compatible Criteria of Systems of Linear Diophantine Equations over Set of Natural Numbers, Reports of National Academy of Science of Ukraine, 1999, 5, 107-112.
• [6] Buchberger Ed.B., Collins J., Loos R., Computer Algebra (Symbolic and algebraic computations), 1986, 386.
• [7] Krivoi S., On the Algorithms for Solution of Systems of Linear Diophantine Constraints over set (0,1}, Cybernetics and System Analysis 2003, 5, 58-69.
• [8] Kryvyy S., Grzywacz W., Lopatina M., O rozwiązaniach i niektórych zastosowaniach liniowych ograniczeń w zbiorze {0,1}, Zeszyty Naukowe Politechniki Rzeszowskiej, 2003, Informatyka z. 2, 6, 43-55.