{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T14:13:20Z","timestamp":1775052800802,"version":"3.50.1"},"publisher-location":"Berlin, Heidelberg","reference-count":11,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783642626845","type":"print"},{"value":"9783642566660","type":"electronic"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2001]]},"DOI":"10.1007\/978-3-642-56666-0_31","type":"book-chapter","created":{"date-parts":[[2011,7,18]],"date-time":"2011-07-18T18:13:00Z","timestamp":1311012780000},"page":"401-415","source":"Crossref","is-referenced-by-count":2,"title":["Solution of Systems of Linear Diophantine Equations"],"prefix":"10.1007","author":[{"given":"Gennadi I.","family":"Malaschonok","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"31_CR1","first-page":"197","volume-title":"Proc. ISSAC\u201999","author":"J Abbott","year":"1999","unstructured":"Abbott, J., Bronstein, M., and Mulders, T.: Fast deterministic computation of determinants of dense matrices. In: Proc. ISSAC\u201999. ACM Press, Vancouver (1999) 197\u2013204"},{"key":"31_CR2","doi-asserted-by":"publisher","first-page":"68","DOI":"10.1093\/imamat\/10.1.68","volume":"10","author":"EH Bareiss","year":"1972","unstructured":"Bareiss, E. H.: Computational solutions of matrix problems over an integral domain. J. Inst. Maths Applics 10 (1972) 68\u2013104","journal-title":"J. Inst. Maths Applics"},{"key":"31_CR3","doi-asserted-by":"publisher","first-page":"251","DOI":"10.1016\/S0747-7171(08)80013-2","volume":"9","author":"D Coppersmith","year":"1990","unstructured":"Coppersmith, D. and Winograd, S.: Matrix multiplication via arithmetic progressions. J. Symbolic Computation 9 (1990) 251\u2013280","journal-title":"J. Symbolic Computation"},{"key":"31_CR4","doi-asserted-by":"publisher","first-page":"137","DOI":"10.1007\/BF01459082","volume":"40","author":"J Dixon","year":"1982","unstructured":"Dixon, J.: Exact solution of linear equations using p-adic expansions. Numer. Math. 40 (1982) 137\u2013141","journal-title":"Numer. Math."},{"key":"31_CR5","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-5242-9","volume-title":"Methods and Applications of Error-Free Computation","author":"RT Gregory","year":"1984","unstructured":"Gregory, R. T., Krishnamurthy E. V.: Methods and Applications of Error-Free Computation, Springer-Verlag, Berlin (1984)"},{"key":"31_CR6","doi-asserted-by":"publisher","first-page":"547","DOI":"10.1137\/0119053","volume":"10","author":"MF Hurt","year":"1970","unstructured":"Hurt, M. F., Waid, C. A.: A generalized inverse which give all the integral solutions to a system of linear equations. SIAM J. Appl0. Math. 10, (1970) 547\u2013550","journal-title":"SIAM J. Appl0. Math."},{"key":"31_CR7","first-page":"1497","volume":"23","author":"GI Malaschonok","year":"1983","unstructured":"Malaschonok, G. I.: Solution of a system of linear equations in an integral domain. USSR Journal of Computational Mathematics and Mathematical Physics 23 (1983) 1497\u20131500","journal-title":"USSR Journal of Computational Mathematics and Mathematical Physics"},{"key":"31_CR8","doi-asserted-by":"crossref","unstructured":"Malaschonok, G. I.: Algorithms for the solution of systems of linear equations in commutative rings. In: Mora, T. and Traverso, C. (eds.): Effective Methods in Algebraic Geometry. Progress in Mathematics 94, Birkhauser (1991) 289\u2013298","DOI":"10.1007\/978-1-4612-0441-1_19"},{"key":"31_CR9","first-page":"475","volume-title":"Computational Mathematics","author":"GI Malaschonok","year":"1997","unstructured":"Malaschonok, G. I.: Recursive Method for the Solution of Systems of Linear Equations. In: Sydow, A. (ed.): Computational Mathematics (Proceedings of the 15th IMACS World Congress, Vol. I, Berlin, August 1997). Wissenschaft & Technik Verlag, Berlin (1997) 475\u2013480"},{"key":"31_CR10","doi-asserted-by":"crossref","unstructured":"Malaschonok, G. I.: Effective Matrix Methods in Commutative Domains, In: Krob, D., Mikhalev, A. A., Mikhalev, A. V. (eds.): Formal Power Series and Algebraic Combinatorics. Springer (2000) 506\u2013517","DOI":"10.1007\/978-3-662-04166-6_48"},{"key":"31_CR11","first-page":"181","volume-title":"Proc. ISSAC\u201999","author":"T Mulders","year":"1999","unstructured":"Mulders, T., Storjohann, A.: Diophantine Linear System Solving. In: Proc. ISSAC\u201999. ACM Press, Vancouver (1999) 181\u2013188"}],"container-title":["Computer Algebra in Scientific Computing CASC 2001"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-56666-0_31","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,3,30]],"date-time":"2019-03-30T07:18:26Z","timestamp":1553930306000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-56666-0_31"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001]]},"ISBN":["9783642626845","9783642566660"],"references-count":11,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-56666-0_31","relation":{},"subject":[],"published":{"date-parts":[[2001]]}}}