{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T14:18:25Z","timestamp":1775053105053,"version":"3.50.1"},"publisher-location":"Berlin, Heidelberg","reference-count":19,"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_19","type":"book-chapter","created":{"date-parts":[[2011,7,18]],"date-time":"2011-07-18T14:13:00Z","timestamp":1310998380000},"page":"249-263","source":"Crossref","is-referenced-by-count":5,"title":["Construction of Janet Bases II. Polynomial Bases"],"prefix":"10.1007","author":[{"given":"Vladimir P.","family":"Gerdt","sequence":"first","affiliation":[]},{"given":"Yuri A.","family":"Blinkov","sequence":"additional","affiliation":[]},{"given":"Denis A.","family":"Yanovich","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"19_CR1","doi-asserted-by":"publisher","first-page":"519","DOI":"10.1016\/S0378-4754(97)00127-4","volume":"45","author":"VP Gerdt","year":"1998","unstructured":"Gerdt, V. P., Blinkov, Yu. A.: Involutive bases of polynomial ideals. Math. Comp. Simul.\n              45 (1998) 519\u2013542","journal-title":"Math. Comp. Simul."},{"key":"19_CR2","doi-asserted-by":"publisher","first-page":"543","DOI":"10.1016\/S0378-4754(97)00128-6","volume":"45","author":"VP Gerdt","year":"1998","unstructured":"Gerdt, V. P., Blinkov, Yu. A.: Minimal involutive bases. Math. Comp. Simul. 45 (1998) 543\u2013560","journal-title":"Math. Comp. Simul."},{"key":"19_CR3","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1007\/978-3-642-60218-4_9","volume-title":"Computer Algebra in Scientific Computing \/ CASC\u201999","author":"VP Gerdt","year":"1999","unstructured":"Gerdt, V. P.: Completion of linear differential systems to involution. In: Computer Algebra in Scientific Computing \/ CASC\u201999, V.G. Ganzha, E.W. Mayr and E.V. Vorozhtsov (Eds.), Springer-Verlag, Berlin (1999) 115\u2013137"},{"key":"19_CR4","doi-asserted-by":"publisher","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.: Grobner bases: an algorithmic method in polynomial ideal theory. In: Recent Trends in Multidimensional System Theory, N.K. Bose (ed.), Reidel, Dordrecht (1985) 184\u2013232"},{"key":"19_CR5","volume-title":"Gr\u00f6bner bases. A computational approach to commutative algebra. Graduate Texts in Mathematics","author":"T Becker","year":"1993","unstructured":"Becker, T., Weispfenning, V., Kredel, H.: Gr\u00f6bner bases. A computational approach to commutative algebra. Graduate Texts in Mathematics\n              141, Springer-Verlag, New York (1993)"},{"key":"19_CR6","volume-title":"Le\u00e7ons sur les Syst\u00e8mes d\u2019Equations aux D\u00e9riv\u00e9es Partielles","author":"M Janet","year":"1929","unstructured":"Janet, M.: Le\u00e7ons sur les Syst\u00e8mes d\u2019Equations aux D\u00e9riv\u00e9es Partielles, Cahiers Scientifiques, IV, Gauthier-Villars, Paris (1929)"},{"key":"19_CR7","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-017-2539-2","volume-title":"Partial Differential Equations and Group Theory. New Perspectives for Applications","author":"J-F Pommaret","year":"1994","unstructured":"Pommaret, J.-F.: Partial Differential Equations and Group Theory. New Perspectives for Applications, Kluwer, Dordrecht (1994)"},{"key":"19_CR8","unstructured":"Seiler, W. M.: Analysis and Application of the Formal Theory of Partial Diferential Equations. PhD thesis, School of Physics and Materials, Lancaster University (1994)"},{"key":"19_CR9","first-page":"167","volume-title":"Computer Algebra in Scientific Computing\/ CASC 2000","author":"VP Gerdt","year":"2000","unstructured":"Gerdt, V. P.: On the relation between Pommaret and Janet bases. In: Computer Algebra in Scientific Computing\/ CASC 2000, V.G. Ganzha, E.W. Mayr, E.V. Vorozhtsov (Eds.), Springer-Verlag, Berlin (2000) 167\u2013181"},{"key":"19_CR10","first-page":"185","volume":"258","author":"VP Gerdt","year":"1999","unstructured":"Gerdt, V. P.: Involutive division technique: Some generalizations and optimizations, Zapiski Nauchnykh Seminarov POMI (St.Petersburg)\n              258 (1999) 185\u2013206. To be published in J. Math. Sci.","journal-title":"Zapiski Nauchnykh Seminarov POMI (St.Petersburg)"},{"key":"19_CR11","unstructured":"Gerdt, V. P., Blinkov, Yu. A., Yanovich, D. A.: Construction of Janet bases. I. Monomial bases. This volume."},{"key":"19_CR12","unstructured":"Greuel, G.-M., Pfister, G., Schoenemann, H.: Singular: A Computer Algebra System for Polynomial Computation, Department of Mathematics, University of Keiserslautern (2001) http:\/\/www.singular.uni-kl.de\/Manual\/2-0-0;."},{"key":"19_CR13","unstructured":"Bini, D., Mourrain, B.: Polynomial Test Suite (1996) http:\/\/www-sop.inria.fr\/saga\/POL."},{"key":"19_CR14","unstructured":"Verschelde, J.: The Database with Test Examples. http\/\/www.math.uic.edurjan\/demo.html"},{"key":"19_CR15","unstructured":"The GNU Multiple Precision Arithmetic Library. Edition 3.1.1, 18 September 2000 http:\/\/www.gnu.org\/manual\/gmp\/."},{"key":"19_CR16","unstructured":"Bachmann, O., Sch\u00f6nemann, H.: Monomial representations for Gr\u00f6bner bases computations. In: Proceedings of ISSAC\u201998, ACM Press (1998) 309\u2013321"},{"key":"19_CR17","unstructured":"Gerdt, V. P.: On Algorithmic Optimization in Computation of Involutive Bases. In preparation."},{"key":"19_CR18","unstructured":"Seiler, W. M.: A Combinatorial Approach to Involution and \u03b4-regularity. Preprint, Universit\u00e4t Mannheim (2000)"},{"key":"19_CR19","first-page":"43","volume":"3","author":"YuA Blinkov","year":"2001","unstructured":"Blinkov, Yu. A.: The Method of Separative Monomials for Involutive Divisions. Programming and Computer Software\n              3 (2001) 43\u201345","journal-title":"Programming and Computer Software"}],"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_19","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,3,30]],"date-time":"2019-03-30T03:20:44Z","timestamp":1553916044000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-56666-0_19"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001]]},"ISBN":["9783642626845","9783642566660"],"references-count":19,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-56666-0_19","relation":{},"subject":[],"published":{"date-parts":[[2001]]}}}