{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T22:26:37Z","timestamp":1768775197784,"version":"3.49.0"},"publisher-location":"Cham","reference-count":22,"publisher":"Springer International Publishing","isbn-type":[{"value":"9783319663197","type":"print"},{"value":"9783319663203","type":"electronic"}],"license":[{"start":{"date-parts":[[2017,1,1]],"date-time":"2017-01-01T00:00:00Z","timestamp":1483228800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2017]]},"DOI":"10.1007\/978-3-319-66320-3_17","type":"book-chapter","created":{"date-parts":[[2017,8,29]],"date-time":"2017-08-29T11:34:27Z","timestamp":1504006467000},"page":"225-241","source":"Crossref","is-referenced-by-count":6,"title":["Computing the Integer Points of a Polyhedron, I: Algorithm"],"prefix":"10.1007","author":[{"given":"Rui-Juan","family":"Jing","sequence":"first","affiliation":[]},{"given":"Marc","family":"Moreno\u00a0Maza","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2017,8,30]]},"reference":[{"key":"17_CR1","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1006\/jsco.1999.0269","volume":"28","author":"P Aubry","year":"1999","unstructured":"Aubry, P., Lazard, D., Moreno Maza, M.: On the theories of triangular sets. J. Symb. Comput. 28, 105\u2013124 (1999)","journal-title":"J. Symb. Comput."},{"issue":"4","key":"17_CR2","doi-asserted-by":"crossref","first-page":"769","DOI":"10.1287\/moor.19.4.769","volume":"19","author":"AI Barvinok","year":"1994","unstructured":"Barvinok, A.I.: A polynomial time algorithm for counting integral points in polyhedra when the dimension is fixed. Math. Oper. Res. 19(4), 769\u2013779 (1994)","journal-title":"Math. Oper. Res."},{"key":"17_CR3","doi-asserted-by":"crossref","unstructured":"Barvinok, A.I.: Integer Points in Polyhedra. Contemporary Mathematics. European Mathematical Society (2008)","DOI":"10.4171\/052"},{"key":"17_CR4","doi-asserted-by":"crossref","unstructured":"Beck, M.: Integer Points in Polyhedra-Geometry, Number Theory, Representation Theory, Algebra, Optimization, Statistics: AMS-IMS-SIAM Joint Summer Research Conference, 11\u201315 June 2006, Snowbird. Utah. Contemporary mathematics - Amer. Math, Soc. (2008)","DOI":"10.1090\/conm\/452"},{"key":"17_CR5","unstructured":"Chen, C., Chen, X., Keita, A., Moreno Maza, M., Xie, N.: MetaFork: a compilation framework for concurrency models targeting hardware accelerators and its application to the generation of parametric CUDA kernels. In: Proceedings of CASCON 2015, pp. 70\u201379 (2015)"},{"key":"17_CR6","volume-title":"A Course in Computational Algebraic Number Theory","author":"H Cohen","year":"2013","unstructured":"Cohen, H.: A Course in Computational Algebraic Number Theory, vol. 138. Springer Science & Business Media, Heidelberg (2013)"},{"key":"17_CR7","unstructured":"Feautrier, P.: Parametric integer programming. RAIRO Recherche Op\u00e9rationnelle 22 (1988). http:\/\/citeseerx.ist.psu.edu\/viewdoc\/download?doi=10.1.1.30.9957&rep=rep.1&type=pdf"},{"key":"17_CR8","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1007\/3-540-61736-1_44","volume-title":"The Data Parallel Programming Model","author":"P Feautrier","year":"1996","unstructured":"Feautrier, P.: Automatic parallelization in the polytope model. In: Perrin, G.-R., Darte, A. (eds.) The Data Parallel Programming Model. LNCS, vol. 1132, pp. 79\u2013103. Springer, Heidelberg (1996). doi: 10.1007\/3-540-61736-1_44 . http:\/\/dl.acm.org\/citation.cfm?id=647429.723579"},{"key":"17_CR9","unstructured":"Fischer, M.J., Fischer, M.J., Rabin, M.O.: Super-exponential complexity of presburger arithmetic. Technical report, Cambridge, MA, USA (1974)"},{"key":"17_CR10","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4613-0019-9","volume-title":"Convex Polytops","author":"B Gr\u00fcnbaum","year":"2003","unstructured":"Gr\u00fcnbaum, B.: Convex Polytops. Springer, New York (2003)"},{"key":"17_CR11","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1016\/0024-3795(90)90228-5","volume":"140","author":"MS Hung","year":"1990","unstructured":"Hung, M.S., Rom, W.O.: An application of the hermite normal form in integer programming. Linear Algebra Appl. 140, 163\u2013179 (1990)","journal-title":"Linear Algebra Appl."},{"key":"17_CR12","unstructured":"Jing, R.-J., Yuan, C.-M., Gao, X.-S.: A polynomial-time algorithm to compute generalized hermite normal form of matrices over $${\\mathbb{Z}}[x]$$ . CoRR, abs\/1601.01067 (2016)"},{"issue":"2","key":"17_CR13","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1007\/s10957-008-9384-4","volume":"138","author":"CN Jones","year":"2008","unstructured":"Jones, C.N., Kerrigan, E.C., Maciejowski, J.M.: On polyhedral projection and parametric programming. J. Optim. Theory Appl. 138(2), 207\u2013220 (2008)","journal-title":"J. Optim. Theory Appl."},{"issue":"4","key":"17_CR14","doi-asserted-by":"crossref","first-page":"499","DOI":"10.1137\/0208040","volume":"8","author":"R Kannan","year":"1979","unstructured":"Kannan, R., Bachem, A.: Polynomial algorithms for computing the smith and hermite normal forms of an integer matrix. SIAM J. Comput. 8(4), 499\u2013507 (1979)","journal-title":"SIAM J. Comput."},{"key":"17_CR15","doi-asserted-by":"publisher","first-page":"1074","DOI":"10.1007\/978-0-387-74759-0_187","volume-title":"Encyclopedia of Optimization","author":"L Khachiyan","year":"2009","unstructured":"Khachiyan, L.: Fourier-motzkin elimination method. In: Floudas, C.A., Pardalos, P.M. (eds.) Encyclopedia of Optimization, 2nd edn, pp. 1074\u20131077. Springer, Heidelberg (2009). doi: 10.1007\/978-0-387-74759-0_187","edition":"2"},{"issue":"1","key":"17_CR16","doi-asserted-by":"crossref","first-page":"R16","DOI":"10.37236\/740","volume":"15","author":"M K\u00f6ppe","year":"2008","unstructured":"K\u00f6ppe, M., Verdoolaege, S.: Computing parametric rational generating functions with a primal Barvinok algorithm. Electr. J. Comb. 15(1), R16 (2008)","journal-title":"Electr. J. Comb."},{"key":"17_CR17","doi-asserted-by":"crossref","unstructured":"Pugh, W.: The omega test: a fast and practical integer programming algorithm for dependence analysis. In: Martin, J.L. (ed.) Proceedings Supercomputing 1991, Albuquerque, NM, USA, 18\u201322 November 1991, pp. 4\u201313. ACM (1991)","DOI":"10.1145\/125826.125848"},{"key":"17_CR18","doi-asserted-by":"crossref","unstructured":"Pugh, W.: Counting solutions to presburger formulas: how and why. In: Sarkar, V., Ryder, B.G., Soffa, M.L. (eds.) Proceedings of the ACM SIGPLAN 1994 Conference on Programming Language Design and Implementation (PLDI), Orlando, Florida, USA, 20\u201324 June 1994, pp. 121\u2013134. ACM (1994)","DOI":"10.1145\/178243.178254"},{"key":"17_CR19","volume-title":"Theory of Linear and Integer Programming","author":"A Schrijver","year":"1986","unstructured":"Schrijver, A.: Theory of Linear and Integer Programming. Wiley, New York (1986)"},{"key":"17_CR20","unstructured":"Storjohann, A.: A fast practical deterministic algorithm for triangularizing integer matrices. Citeseer (1996)"},{"key":"17_CR21","unstructured":"Storjohann, A.: Algorithms for matrix canonical forms. Ph.D. thesis, Swiss Federal Institute of Technology Z\u00fcrich (2000)"},{"key":"17_CR22","doi-asserted-by":"crossref","unstructured":"Wonnacott, D.: Omega test. In: Encyclopedia of Parallel Computing, pp. 1355\u20131365 (2011)","DOI":"10.1007\/978-0-387-09766-4_266"}],"container-title":["Lecture Notes in Computer Science","Computer Algebra in Scientific Computing"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-66320-3_17","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,10,16]],"date-time":"2020-10-16T13:44:52Z","timestamp":1602855892000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-319-66320-3_17"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017]]},"ISBN":["9783319663197","9783319663203"],"references-count":22,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-66320-3_17","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017]]}}}