On the existence of solutions in systems of linear Diophantine equations

• Autores: Antonio Hernando, Luis de Ledesma Otamendi
• Localización: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas ( RACSAM ), ISSN-e 1578-7303, Vol. 105, Nº. 2, 2011, págs. 223-245
• Idioma: inglés
• DOI: 10.1007/s13398-011-0044-4
• Texto completo no disponible (Saber más ...)
• Resumen

  • The question about the existence of solutions in a family of systems of Diophantine linear equations can be always answered by means of a set of functions called 'Testers'. In this paper, we will propose a procedure to obtain this set of 'Testers' (named complete set of testers) which characterizes each family of systems of Diophantine equations. © 2011 Springer-Verlag.

• Referencias bibliográficas
  • Borosh, I., Treybig, L.B., Bounds on positive integral solutions of linear diophantine equations (1976) Proceedings of the American Mathematical...
  • Boudet, A., Contejean, E., Devie, H., A new AC Unification algorithm with an algorithm for solving systems of Diophantine equations (1990)...
  • Chou, T.-W.J., Collins, G.E., Algorithms for the solution of systems of linear Diophantine equations (1982) SIAM J. Comput., 11, pp. 687-708
  • Clausen, M., Fortenbacher, A., Efficient solution of linear Diophantine equations (1989) J. Symbol. Comput., 8, pp. 201-216
  • Contejean, E., Devie, H., An efficient incremental algorithm for solving systems of linear Diophantine equations (1994) Inf. Comput, 113...
  • Fang, X.G., Havas, G., On the worst-case complexity of integer gausian elimination (1997) Proceedings of the 1997 International Symposium...
  • Filgueiras, M., Tomás, A.P., A fast method for finding the basis of non-negative solutions to a linear Diophantine equation (1995) J Symbol....
  • Giesbrecht, M., Fast Computation of the Smith Normal Form of an Integer Matrix (1995) Proceedings of the 1995 International Symposium On...
  • Hernando, A., de Ledesma, L., Laita, L.M., Showing the non-existence of solutions in systems of linear Diophantine equations (2009) Math....
  • Hernando, A., New methods for proving the impossibility to solve problems through reduction of problem spaces (2009) Ann. Math. Artif. Intell
  • Huet, G., An algorithm to generate the basis of solutions to homogeneous linear Diophantine equations (1978) Inf. Process. Lett., 7 (3),...
  • Jäger, G., Wagner, C., Efficient parallelizations of Hermite and Smith normal form algorithms (2009) J. Parallel Comput., 35 (6), pp. 345-357
  • Lazebnik, F., On Systems of linear Diophantine equations (1996) Math. Mag., 69, pp. 261-266
  • Pottier, L., Minimal solutions of linear diophantine solutions: bounds and algorithms (1986) Lect. Notes Comput. Sci., 488, pp. 162-173
  • Smith, H.J.S., On systems of linear indeterminate equations and congruences (1861) Philos. Trans. R. Soc. Lond., 151, pp. 293-326
  • Storjohan, A., Near optimal algorithms for computing Smith normal forms of integer matrices (1996) Proceedings of the 1996 International...
  • Tomás, A.P., Filgueiras, M., An algorithm for solving systems of linear Diophantine equations in naturals (1997) Lect. Notes Comput. Sci.,...