{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,5,19]],"date-time":"2023-05-19T09:40:27Z","timestamp":1684489227837},"reference-count":17,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2008,7,25]],"date-time":"2008-07-25T00:00:00Z","timestamp":1216944000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["4OR-Q J Oper Res"],"published-print":{"date-parts":[[2009,6]]},"DOI":"10.1007\/s10288-008-0082-8","type":"journal-article","created":{"date-parts":[[2008,7,24]],"date-time":"2008-07-24T10:26:01Z","timestamp":1216895161000},"page":"145-167","source":"Crossref","is-referenced-by-count":8,"title":["Integer extended ABS algorithms and possible control of intermediate results for linear Diophantine systems"],"prefix":"10.1007","volume":"7","author":[{"given":"Mostafa","family":"Khorramizadeh","sequence":"first","affiliation":[]},{"given":"Nezam","family":"Mahdavi-Amiri","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2008,7,25]]},"reference":[{"key":"82_CR1","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1007\/BF01391414","volume":"45","author":"J Abaffy","year":"1984","unstructured":"Abaffy J, Broyden CG, Spedicato E (1984) A class of direct methods for linear equations. Numer Math 45: 361\u2013376","journal-title":"Numer Math"},{"key":"82_CR2","volume-title":"ABS projection algorithms: mathematical techniques for linear and nonlinear equations","author":"J Abaffy","year":"1989","unstructured":"Abaffy J, Spedicato E (1989) ABS projection algorithms: mathematical techniques for linear and nonlinear equations. Ellis Horwood, Chichester"},{"key":"82_CR3","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1080\/00207727408920109","volume":"5","author":"S Barnette","year":"1974","unstructured":"Barnette S, Pace IS (1974) Efficient algorithms for linear systems calculations: Part I-Smith form and common divisor of polynomial matrices. Int J Syst Sci 5: 403\u2013411","journal-title":"Int J Syst Sci"},{"key":"82_CR4","doi-asserted-by":"crossref","first-page":"514","DOI":"10.1145\/365719.365971","volume":"9","author":"WA Blankinship","year":"1966","unstructured":"Blankinship WA (1966) Algorithm 288, solution of simultaneous linear Diophantine equations. Comm ACM 9: 514","journal-title":"Comm ACM"},{"key":"82_CR5","doi-asserted-by":"crossref","first-page":"897","DOI":"10.1090\/S0025-5718-1971-0301909-X","volume":"25","author":"GH Bradley","year":"1971","unstructured":"Bradley GH (1971) Algorithms for Hermite and Smith normal matrices and linear Diophantine equations. Math Comp 25: 897\u2013907","journal-title":"Math Comp"},{"key":"82_CR6","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-62035-5","volume-title":"An introduction to the geometry of numbers","author":"JWS Cassels","year":"1959","unstructured":"Cassels JWS (1959) An introduction to the geometry of numbers. Springer, Berlin"},{"key":"82_CR7","first-page":"686","volume":"11","author":"TJ Chou","year":"1982","unstructured":"Chou TJ, Collins EE (1982) Algorithms for the solutions of systems of linear Diophantine equations. SIAM J Comput 11: 686\u2013708","journal-title":"SIAM J Comput"},{"key":"82_CR8","unstructured":"Chen Z, Deng NY, Xue Y (1992) A general algorithm for underdetermined linear systems. The Proceedings of the first international conference on ABS algorithms, pp 1\u201313"},{"key":"82_CR9","doi-asserted-by":"crossref","first-page":"481","DOI":"10.5486\/PMD.1956.4.3-4.48","volume":"4","author":"E Egervary","year":"1956","unstructured":"Egervary E (1956) Aufloesung eines homogenen linearen Diophantischen gleichungsystems mit hilf von projecytomatrizen. Publ Math Debrecen 4: 481\u2013483","journal-title":"Publ Math Debrecen"},{"key":"82_CR10","first-page":"376","volume":"9","author":"E Egervary","year":"1960","unstructured":"Egervary E (1960) On rank\u2013diminishing operations and their application to the solution of linear equations. ZAMP 9: 376\u2013386","journal-title":"ZAMP"},{"key":"82_CR11","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1007\/s002110100269","volume":"90","author":"H Esmaeili","year":"2001","unstructured":"Esmaeili H, Mahdavi-Amiri N, Spedicato E (2001a) A class of ABS Algorithms for Diophantine linear systems. Numer Math 90: 101\u2013115","journal-title":"Numer Math"},{"key":"82_CR12","first-page":"1","volume":"27","author":"H Esmaeili","year":"2001","unstructured":"Esmaeili H, Mahdavi-Amiri N, Spedicato E (2001b) Generating the integer null space and conditions for determination of an integer basis using the ABS algorithms. Bull Iran Math Soc 27: 1\u201318","journal-title":"Bull Iran Math Soc"},{"key":"82_CR13","doi-asserted-by":"crossref","first-page":"386","DOI":"10.1007\/3-540-08442-8_106","volume-title":"Fundamentals of computation theory, lecture notes in computer science, 56","author":"MA Frumkin","year":"1977","unstructured":"Frumkin MA (1977) Polynomial time algorithms in the theory of linear Diophantine equations. In: Karpinski M (eds) Fundamentals of computation theory, lecture notes in computer science, 56. Springer, New York, pp 386\u2013392"},{"key":"82_CR14","doi-asserted-by":"crossref","first-page":"499","DOI":"10.1137\/0208040","volume":"8","author":"R Kannan","year":"1979","unstructured":"Kannan R, Bachem A (1979) An polynomial algorithms for computing the Smith and Hermite normal forms of an integer matrix. SIAM J Comput 8: 499\u2013507","journal-title":"SIAM J Comput"},{"key":"82_CR15","unstructured":"Khorramizadeh M, Mahdavi-Amiri N (2008) On solving linear Diophantine systems using generalized Rosser\u2019s algorithm. Bull Iran Math Soc (in press)"},{"key":"82_CR16","doi-asserted-by":"crossref","first-page":"662","DOI":"10.1080\/00029890.1941.11991159","volume":"48","author":"JB Rosser","year":"1941","unstructured":"Rosser JB (1941) A note on the linear Diophantine equation. Am Math Mon 48: 662\u2013666","journal-title":"Am Math Mon"},{"key":"82_CR17","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1007\/s10288-002-0004-0","volume":"1","author":"E Spedicato","year":"2003","unstructured":"Spedicato E, Bodon E, Del Popolo A, Mahdavi-Amiri N (2003) ABS methods and ABSPACK for linear systems and optimization: a review. 4OR 1: 51\u201366","journal-title":"4OR"}],"container-title":["4OR"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10288-008-0082-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10288-008-0082-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10288-008-0082-8","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,19]],"date-time":"2023-05-19T09:19:52Z","timestamp":1684487992000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10288-008-0082-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,7,25]]},"references-count":17,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2009,6]]}},"alternative-id":["82"],"URL":"https:\/\/doi.org\/10.1007\/s10288-008-0082-8","relation":{},"ISSN":["1619-4500","1614-2411"],"issn-type":[{"value":"1619-4500","type":"print"},{"value":"1614-2411","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,7,25]]}}}