{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,4]],"date-time":"2024-09-04T13:12:29Z","timestamp":1725455549543},"publisher-location":"Berlin, Heidelberg","reference-count":16,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540635864"},{"type":"electronic","value":"9783540696056"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[1997]]},"DOI":"10.1007\/bfb0023912","type":"book-chapter","created":{"date-parts":[[2005,11,19]],"date-time":"2005-11-19T02:20:36Z","timestamp":1132366836000},"page":"73-84","source":"Crossref","is-referenced-by-count":4,"title":["An algorithm for solving systems of linear diophantine equations in naturals"],"prefix":"10.1007","author":[{"given":"Ana Paula","family":"Tom\u00e1s","sequence":"first","affiliation":[]},{"given":"Miguel","family":"Filgueiras","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2005,6,10]]},"reference":[{"key":"7_CR1","doi-asserted-by":"crossref","unstructured":"Boudet, A., Contejean E., and Devie, H.: A new AC Unification algorithm with an algorithm for solving systems of Diophantine equations. In Proceedings of the 5th Conference on Logic and Computer Science, IEEE, 289\u2013299, 1990.","DOI":"10.1109\/LICS.1990.113755"},{"key":"7_CR2","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1016\/S0747-7171(89)80025-2","volume":"8","author":"M. Clausen","year":"1989","unstructured":"Clausen, M., and Fortenbacher, A.: Efficient solution of linear Diophantine equations. J. Symbolic Computation, 8, 201\u2013216, 1989.","journal-title":"J. Symbolic Computation"},{"key":"7_CR3","unstructured":"Domenjoud, E.: Outils pour la D\u00e9duction Automatique dans les Th\u00e9ories Associatives-Commutatives. These de doctorat, Universit\u00e9 de Nancy I, 1991."},{"key":"7_CR4","first-page":"348","volume":"34","author":"E. B. Elliott","year":"1903","unstructured":"Elliott, E. B.: On linear homogenous Diophantine equations. Quart. J. Pure Appl. Math., 34, 348\u2013377, 1903.","journal-title":"Quart. J. Pure Appl. Math."},{"key":"7_CR5","doi-asserted-by":"crossref","unstructured":"Filgueiras, M., and Tom\u00e1s, A. P.: Fast Methods for Solving Linear Diophantine Equations. In M. Filgueiras, L. Damas (eds.) Progress in Artificial Intelligence \u2014 6th Portuguese Conference on Artificial Intelligence, Lecture Notes in Artificial Intelligence 727, Springer-Verlag, 297\u2013306, 1993.","DOI":"10.1007\/3-540-57287-2_55"},{"key":"7_CR6","doi-asserted-by":"crossref","first-page":"507","DOI":"10.1006\/jsco.1995.1029","volume":"19","author":"M. Filgueiras","year":"1995","unstructured":"Filgueiras, M., and Tomas, A. P.: A Fast Method for Finding the Basis of Nonnegative Solutions to a Linear Diophantine Equation. J. Symbolic Computation, 19, 507\u2013526, 1995.","journal-title":"J. Symbolic Computation"},{"issue":"3","key":"7_CR7","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1016\/0020-0190(78)90078-9","volume":"7","author":"G. Huet","year":"1978","unstructured":"Huet, G.: An algorithm to generate the basis of solutions to homogeneous linear Diophantine equations. Information Processing Letters, 7(3), pp. 21\u201378, 1978.","journal-title":"Information Processing Letters"},{"key":"7_CR8","unstructured":"Lambert, J.-L.: Une borne pour les g\u00e9n\u00e9rateurs des solutions enti\u00e8res positives d'une \u00e9quation diophantienne lin\u00e9aire. Comptes Rendus de l'Acad\u00e9mie des Sciences de Paris, t. 305, s\u00e9rie I, 39\u201340, 1987."},{"key":"7_CR9","doi-asserted-by":"crossref","unstructured":"MacMahon, P.: Combinatory Analysis, 2. Chelsea Publishing Co., 1918.","DOI":"10.1112\/plms\/s2-16.1.352"},{"key":"7_CR10","unstructured":"Moulinet-Ossola, C.: Algorithmique des R\u00e9seaux et des Syst\u00e8mes Diophantiens Lin\u00e9aires. These de doctorat, Universit\u00e9 de Nice Sophia-Antipolis, 1995."},{"key":"7_CR11","doi-asserted-by":"crossref","unstructured":"Pottier, L.: Minimal solutions of linear diophantine systems: bounds and algorithms. In R. V. Book (ed.), Proceedings of the 4th International Conference on Rewriting Techniques and Applications, Lecture Notes in Computer Science 488, Springer-Verlag, 162\u2013173, 1991.","DOI":"10.1007\/3-540-53904-2_94"},{"key":"7_CR12","unstructured":"A. Schrijver, Theory of Linear and Integer Programming, Wiley-Interscience, 1986."},{"key":"7_CR13","doi-asserted-by":"crossref","unstructured":"Stanley, R.P.: Enumerative Combinatorics, Vol I, The Wadsworth & Brooks\/Cole Mathematics Series, 1986.","DOI":"10.1007\/978-1-4615-9763-6"},{"key":"7_CR14","doi-asserted-by":"crossref","unstructured":"Tom\u00e1s, A. P., Filgueiras, M.: Solving linear Diophantine equations using the geometric structure of the solution space. In H. Common (ed.), Rewriting Techniques and Applications. Proceedings, Lecture Notes in Computer Science 1232, Springer-Verlag, 269\u2013283, 1997.","DOI":"10.1007\/3-540-62950-5_77"},{"key":"7_CR15","unstructured":"Tom\u00e1s, A. P.: On Solving Linear Diophantine Constraints. Tese de Doutoramento, Faculdade de Ci\u011bncias da Universidade do Porto, 1997."},{"key":"7_CR16","unstructured":"Tom\u00e1s, A. P., Filgueiras, M.: Exploiting the Geometric Structure of the Solution Space in Solving Linear Diophantine Equations. Internal Report, DCC & LIACC, Universidade do Porto, 1997."}],"container-title":["Lecture Notes in Computer Science","Progress in Artificial Intelligence"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BFb0023912","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,5]],"date-time":"2023-05-05T10:02:25Z","timestamp":1683280945000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BFb0023912"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1997]]},"ISBN":["9783540635864","9783540696056"],"references-count":16,"URL":"https:\/\/doi.org\/10.1007\/bfb0023912","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[1997]]}}}