{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T14:21:10Z","timestamp":1775053270190,"version":"3.50.1"},"reference-count":19,"publisher":"Pleiades Publishing Ltd","issue":"3","license":[{"start":{"date-parts":[[2007,5,1]],"date-time":"2007-05-01T00:00:00Z","timestamp":1177977600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2007,5,1]],"date-time":"2007-05-01T00:00:00Z","timestamp":1177977600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Program Comput Soft"],"published-print":{"date-parts":[[2007,5]]},"DOI":"10.1134\/s0361768807030048","type":"journal-article","created":{"date-parts":[[2007,6,5]],"date-time":"2007-06-05T01:34:25Z","timestamp":1181007265000},"page":"147-153","source":"Crossref","is-referenced-by-count":5,"title":["On selection of nonmultiplicative prolongations in computation of Janet bases"],"prefix":"10.1134","volume":"33","author":[{"given":"V. P.","family":"Gerdt","sequence":"first","affiliation":[]},{"given":"Yu. A.","family":"Blinkov","sequence":"additional","affiliation":[]}],"member":"137","reference":[{"key":"3004_CR1","doi-asserted-by":"publisher","first-page":"519","DOI":"10.1016\/S0378-4754(97)00127-4","volume":"45","author":"V. P. Gerdt","year":"1998","unstructured":"Gerdt, V. P. and Blinkov, Yu. A., Involutive Bases of Polynomial Ideals, Math. Comput. Simulation, 1998, vol. 45, pp. 519\u2013542, http:\/\/arXiv.org\/math.AC\/9912027; Minimal Involutive Bases, Math. Comput. Simulation, 1998, vol. 45, pp. 543\u2013560, http:\/\/arXiv.org\/math.AC\/9912029.","journal-title":"Math. Comput. Simulation"},{"issue":"6","key":"3004_CR2","first-page":"283","volume":"24","author":"V. P. Gerdt","year":"1998","unstructured":"Gerdt, V. P. and Blinkov, Yu. A., Involutive Division of Monomials, Programmirovanie, 1998, vol. 24, no. 6, pp. 283\u2013285.","journal-title":"Programmirovanie"},{"key":"3004_CR3","volume-title":"Cahiers Scientifiques, IV","author":"M. Janet","year":"1929","unstructured":"Janet, M., Le\u00e7ons sur les syst\u00e9mes d\u2019equations aux d\u00e9riv\u00e9es partielles, Cahiers Scientifiques, IV, Paris: Gauthier-Villars, 1929."},{"key":"3004_CR4","volume-title":"Proc. of the 4th Int. Conf. Computer Algebra in Scientific Computing CASC-2001","author":"V. P. Gerdt","year":"2001","unstructured":"Gerdt, V. P., Blinkov, Yu. A., and Yanovich, D. A., Construction of Janet Bases. I. Monomial Bases, Proc. of the 4th Int. Conf. Computer Algebra in Scientific Computing CASC-2001 (Konstanz, Germany, 2001), Ganzha, V. G., Mayr, E. W., and Vorozhtsov, E. V., Eds., Berlin: Springer, 2001, pp. 233\u2013247; II. Polynomial Bases, pp. 249\u2013263."},{"key":"3004_CR5","unstructured":"Gerdt, V. P., Involutive Algorithms for Computing Gr\u00f6bner Bases, Computational Commutative and Non-Commutative Algebraic Geometry, Cojocaru, S., Pfister, G., and Ufnarovski, V., Eds., NATO Science Series, IOS, 2005, vol. 196, pp. 199\u2013225; http:\/\/arXiv.org\/math.AC\/0501111."},{"key":"3004_CR6","first-page":"174","volume-title":"Lecture Notes in Computer Science (Proc. of the 8th Int. Conf. Computer Algebra in Scientific Computing CASC-2005)","author":"V. P. Gerdt","year":"2005","unstructured":"Gerdt, V. P. and Blinkov, Yu. A., Janet-Like Monomial Division. Janet-Like Gr\u00f6bner Bases, Lecture Notes in Computer Science (Proc. of the 8th Int. Conf. Computer Algebra in Scientific Computing CASC-2005), Berlin: Springer, 2005, pp. 174\u2013195."},{"key":"3004_CR7","unstructured":"http:\/\/www-sop.inria.fr\/saga\/POL."},{"key":"3004_CR8","unstructured":"http:\/\/www.math.uic.edu\/:_jan\/demo.html."},{"key":"3004_CR9","doi-asserted-by":"crossref","first-page":"184","DOI":"10.1007\/978-94-009-5225-6_6","volume-title":"Recent Trends in Multidimensional System Theory","author":"B. Buchberger","year":"1985","unstructured":"Buchberger, B., Gr\u00f6bner Bases: An Algorithmic Method in Polynomial Ideal Theory, in Recent Trends in Multidimensional System Theory, Bose, N.K., Ed., Dordrecht: Reidel, 1985, pp. 184\u2013232."},{"key":"3004_CR10","first-page":"49","volume-title":"Proc. of ISSAC\u201991","author":"A. Giovinni","year":"1991","unstructured":"Giovinni, A., Mora, T., Niesi, G., Robbiano, L., and Traverso, C., One Sugar Cube, Please, or Selection Strategies in the Buchberger Algorithm, Proc. of ISSAC\u201991, New York: ACM, 1991, pp. 49\u201354."},{"key":"3004_CR11","unstructured":"Gerdt, V. P. and Blinkov, Yu. A., On Computing Janet Bases for Degree-Compatible Orderings, Proc. of 10th Rhine Workshop on Computer Algebra (Basel, Switzerland, 2006), Basel, 2006, pp. 107\u2013117, http:\/\/arXiv.org\/math.AC\/0603161."},{"key":"3004_CR12","doi-asserted-by":"publisher","first-page":"329","DOI":"10.1006\/jsco.1993.1051","volume":"16","author":"J. C. Faug\u00e8re","year":"1993","unstructured":"Faug\u00e8re, J. C., Gianni, P., Lazard, D., and Mora, T., Efficient Computation of Zero-Dimensional Gr\u00f6bner Bases by Change of Ordering, J. Symbolic Computation, 1993, vol. 16, pp. 329\u2013344.","journal-title":"J. Symbolic Computation"},{"key":"3004_CR13","doi-asserted-by":"publisher","first-page":"465","DOI":"10.1006\/jsco.1996.0145","volume":"24","author":"S. Collart","year":"1997","unstructured":"Collart, S., Kalkbrener, M., and Mall, D., Converting Bases with the Gr\u00f6bner Walk, J. Symbolic Computation, 1997, vol. 24, pp. 465\u2013469.","journal-title":"J. Symbolic Computation"},{"key":"3004_CR14","unstructured":"http:\/\/magma.maths.usyd.edu.au\/magma\/."},{"issue":"s.1\u20133","key":"3004_CR15","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1016\/S0022-4049(99)00005-5","volume":"139","author":"J. C. Faug\u00e8re","year":"1999","unstructured":"Faug\u00e8re, J. C., A New Efficient Algorithm for Computing Gr\u00f6bner Bases (F\n                  4), J. Pure Applied Algebra, 1999, vol. 139, nos. 1\u20133, pp. 61\u201368.","journal-title":"J. Pure Applied Algebra"},{"key":"3004_CR16","unstructured":"http:\/\/www.singular.uni-kl.de."},{"key":"3004_CR17","unstructured":"http:\/\/invo.jinr.ru."},{"key":"3004_CR18","doi-asserted-by":"publisher","first-page":"351","DOI":"10.1006\/jsco.1998.0256","volume":"27","author":"A. M. Bigatti","year":"1999","unstructured":"Bigatti, A. M., La Scala, R., and Robbiano, L., Computing Toric Ideals, J. Symbolic Computation, 1999, vol. 27, pp. 351\u2013365.","journal-title":"J. Symbolic Computation"},{"key":"3004_CR19","first-page":"130","volume-title":"Lecture Notes in Computer Science","author":"P. Conti","year":"1991","unstructured":"Conti, P. and Traverso, C., Buchberger Algorithm and Integer Programming, Lecture Notes in Computer Science (Proc. AAECC-9), Berlin: Springer, 1991, vol. 539, pp. 130\u2013139."}],"container-title":["Programming and Computer Software"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1134\/S0361768807030048.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1134\/S0361768807030048","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1134\/S0361768807030048","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1134\/S0361768807030048.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T03:07:43Z","timestamp":1775012863000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1134\/S0361768807030048"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,5]]},"references-count":19,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2007,5]]}},"alternative-id":["3004"],"URL":"https:\/\/doi.org\/10.1134\/s0361768807030048","relation":{},"ISSN":["0361-7688","1608-3261"],"issn-type":[{"value":"0361-7688","type":"print"},{"value":"1608-3261","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,5]]}}}