{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,26]],"date-time":"2025-05-26T17:29:07Z","timestamp":1748280547478},"reference-count":34,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2021,5,21]],"date-time":"2021-05-21T00:00:00Z","timestamp":1621555200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,5,21]],"date-time":"2021-05-21T00:00:00Z","timestamp":1621555200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Math.Comput.Sci."],"published-print":{"date-parts":[[2021,9]]},"DOI":"10.1007\/s11786-021-00513-4","type":"journal-article","created":{"date-parts":[[2021,5,21]],"date-time":"2021-05-21T19:02:40Z","timestamp":1621623760000},"page":"453-482","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Relative Gr\u00f6bner and Involutive Bases for Ideals in Quotient Rings"],"prefix":"10.1007","volume":"15","author":[{"given":"Amir","family":"Hashemi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Matthias","family":"Orth","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Werner M.","family":"Seiler","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,5,21]]},"reference":[{"key":"513_CR1","unstructured":"Becker, T., Weispfenning, V.: Gr\u00f6bner Bases: A Computational Approach to Commutative Algebra. In: Cooperation with Heinz Kredel, vol. 141. Springer, New York (1993)"},{"key":"513_CR2","unstructured":"Berkesch, C., Schreyer, F.-O.: Syzygies, finite length modules, and random curves. In: Commutative Algebra and Noncommutative Algebraic Geometry. Vol. I: Expository articles, pp. 25\u201352. Cambridge University Press, Cambridge (2015)"},{"key":"513_CR3","doi-asserted-by":"crossref","unstructured":"Buchberger, B.: A criterion for detecting unnecessary reductions in the construction of Gr\u00f6bner-bases. Symbolic and algebraic computation, EUROSAM \u201979, International Symposium, Marseille 1979, Lecture Notes Computer Science 72, 3\u201321 (1979)","DOI":"10.1007\/3-540-09519-5_52"},{"key":"513_CR4","unstructured":"Buchberger, B.: Ein Algorithmus zum Auffinden der Basiselemente des Restklassenringes nach einem nulldimensionalen Polynomideal. Ph.D. thesis, Universit\u00e4t Innsbruck (1965)"},{"key":"513_CR5","doi-asserted-by":"crossref","unstructured":"Buchberger, B.: Bruno Buchberger\u2019s Ph.D. thesis 1965: an algorithm for finding the basis elements of the residue class ring of a zero dimensional polynomial ideal. Translation from the German. J. Symb. Comput. 41(3\u20134), 475\u2013511 (2006)","DOI":"10.1016\/j.jsc.2005.09.007"},{"key":"513_CR6","doi-asserted-by":"publisher","first-page":"112","DOI":"10.1016\/j.jsc.2016.11.008","volume":"83","author":"M Ceria","year":"2017","unstructured":"Ceria, M., Mora, T.: Buchberger\u2013Weispfenning theory for effective associative rings. J. Symb. Comput. 83, 112\u2013146 (2017)","journal-title":"J. Symb. Comput."},{"key":"513_CR7","doi-asserted-by":"publisher","first-page":"359","DOI":"10.1007\/s00200-020-00448-6","volume":"31","author":"M Ceria","year":"2020","unstructured":"Ceria, M., Mora, T.: Toward involutive bases over effective rings. Appl. Algebra Eng. Commun. Comput. 31, 359\u2013387 (2020)","journal-title":"Appl. Algebra Eng. Commun. Comput."},{"key":"513_CR8","unstructured":"Cox, D.A., Little, J., O\u2019Shea, D.: Using Algebraic Geometry, vol. 185, 2nd edition. Springer, New York (2005)"},{"key":"513_CR9","doi-asserted-by":"crossref","unstructured":"Cox, D.A., Little, J., O\u2019Shea, D.: Ideals, Varieties, and Algorithms. An Introduction to Computational Algebraic Geometry and Commutative Algebra. 4th revised ed. Cham: Springer (2015)","DOI":"10.1007\/978-3-319-16721-3"},{"issue":"1\u20133","key":"513_CR10","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 $$(F_4)$$. J. Pure Appl. Algebra 139(1\u20133), 61\u201388 (1999)","journal-title":"J. Pure Appl. Algebra"},{"key":"513_CR11","doi-asserted-by":"crossref","unstructured":"Faug\u00e8re, J.-C.: A new efficient algorithm for computing Gr\u00f6bner bases without reduction to zero $$(F_5)$$. In: Proceedings of the 2002 International Symposium on Symbolic and Algebraic Computation, ISSAC 2002, Lille, France, July 07\u201310, 2002, pp. 75\u201383. New York, NY: ACM Press (2002)","DOI":"10.1145\/780506.780516"},{"issue":"297","key":"513_CR12","doi-asserted-by":"publisher","first-page":"449","DOI":"10.1090\/mcom\/2969","volume":"85","author":"S Gao","year":"2016","unstructured":"Gao, S., Volny, F.I.V., Wang, M.: A new framework for computing Gr\u00f6bner bases. Math. Comput. 85(297), 449\u2013465 (2016)","journal-title":"Math. Comput."},{"key":"513_CR13","unstructured":"Gerdt, V.P.: Involutive algorithms for computing Gr\u00f6bner bases. In: Computational Commutative and Non-commutative Algebraic Geometry. Proceedings of the NATO Advanced Research Workshop, 2004, pp. 199\u2013225. Amsterdam: IOS Press (2005)"},{"issue":"5\u20136","key":"513_CR14","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, Y.A.: Involutive bases of polynomial ideals. Math. Comput. Simul. 45(5\u20136), 519\u2013541 (1998)","journal-title":"Math. Comput. Simul."},{"issue":"5\u20136","key":"513_CR15","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, Y.A.: Minimal involutive bases. Math. Comput. Simul. 45(5\u20136), 543\u2013560 (1998)","journal-title":"Math. Comput. Simul."},{"key":"513_CR16","doi-asserted-by":"publisher","first-page":"20","DOI":"10.1016\/j.jsc.2017.03.008","volume":"86","author":"A Hashemi","year":"2018","unstructured":"Hashemi, A., Schweinfurter, M., Seiler, W.M.: Deterministic genericity for polynomial ideals. J. Symb. Comput. 86, 20\u201350 (2018)","journal-title":"J. Symb. Comput."},{"key":"513_CR17","first-page":"179","volume-title":"Global Integrability of Field Theories","author":"M Hausdorf","year":"2006","unstructured":"Hausdorf, M., Sahbi, M., Seiler, W.M.: $$\\delta $$- and quasi-regularity for polynomial ideals. In: Calmet, J., Seiler, W.M., Tucker, R.W. (eds.) Global Integrability of Field Theories, pp. 179\u2013200. Universit\u00e4tsverlag Karlsruhe, Karlsruhe (2006)"},{"key":"513_CR18","doi-asserted-by":"publisher","first-page":"163","DOI":"10.1007\/s002000200099","volume":"13","author":"M Hausdorf","year":"2002","unstructured":"Hausdorf, M., Seiler, W.M.: An efficient algebraic algorithm for the geometric completion to involution. Appl. Alg. Eng. Commun. Comput. 13, 163\u2013207 (2002)","journal-title":"Appl. Alg. Eng. Commun. Comput."},{"key":"513_CR19","unstructured":"Janet, M.: Sur les syst\u00e8mes d\u2019\u00e9quations aux d\u00e9riv\u00e9es partielles. C. R. Acad. Sci. Paris 170, 1101\u20131103 (1920)"},{"issue":"4","key":"513_CR20","doi-asserted-by":"publisher","first-page":"601","DOI":"10.1007\/s11786-009-0072-z","volume":"2","author":"D Kapur","year":"2009","unstructured":"Kapur, D., Cai, Y.: An algorithm for computing a Gr\u00f6bner basis of a polynomial ideal over a ring with zero divisors. Math. Comput. Sci. 2(4), 601\u2013634 (2009)","journal-title":"Math. Comput. Sci."},{"key":"513_CR21","doi-asserted-by":"crossref","unstructured":"La Scala, R., Stillman, M.: Strategies for computing minimal free resolutions. J. Symb. Comput. 26(4), 409\u2013431 (1998)","DOI":"10.1006\/jsco.1998.0221"},{"key":"513_CR22","doi-asserted-by":"crossref","unstructured":"M\u00f6ller, H.M., Mora, T., Traverso, C.: Gr\u00f6bner bases computation using syzygies. In: International Symposium on Symbolic and Algebraic Computation 92. ISSAC 92. Berkeley, CA, USA, July 27\u201329, 1992, pp. 320\u2013328. Baltimore, MD: ACM Press (1992)","DOI":"10.1145\/143242.143343"},{"key":"513_CR23","doi-asserted-by":"crossref","unstructured":"Mora, T.: De Nugis Groebnerialium 4: Zacharias, Spears, M\u00f6ller. In Proceedings of the 2015 international symposium on symbolic and algebraic computation, ISSAC 2015, Bath, United Kingdom, July 06\u20139, 2015., pages 191\u2013198. New York, NY: ACM Press, (2015)","DOI":"10.1145\/2755996.2756640"},{"key":"513_CR24","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1016\/j.jsc.2019.04.002","volume":"99","author":"T Mora","year":"2020","unstructured":"Mora, T.: Zacharias representation of effective associative rings. J. Symb. Comput. 99, 147\u2013188 (2020)","journal-title":"J. Symb. Comput."},{"issue":"3","key":"513_CR25","doi-asserted-by":"publisher","first-page":"505","DOI":"10.1017\/S0004972700019973","volume":"64","author":"GH Norton","year":"2001","unstructured":"Norton, G.H., S\u0103l\u0103gean, A.: Strong Gr\u00f6bner bases for polynomials over a principal ideal ring. Bull. Aust. Math. Soc. 64(3), 505\u2013528 (2001)","journal-title":"Bull. Aust. Math. Soc."},{"key":"513_CR26","unstructured":"Pommaret, J.-F.: Systems of Partial Differential Equations and Lie Pseudogroups. Gordon and Breach Science Publishers (1978)"},{"key":"513_CR27","unstructured":"Schreyer, F.-O.: Die Berechnung von Syzygien mit dem verallgemeinerten Weierstrass\u2019schen Divisionssatz. Master\u2019s thesis, University of Hamburg, Germany, (1980)"},{"issue":"3\u20134","key":"513_CR28","doi-asserted-by":"publisher","first-page":"261","DOI":"10.1007\/s00200-009-0101-9","volume":"20","author":"WM Seiler","year":"2009","unstructured":"Seiler, W.M.: A combinatorial approach to involution and $$\\delta $$-regularity. II: structure analysis of polynomial modules with Pommaret bases. Appl. Algebra Eng. Commun. Comput 20(3\u20134), 261\u2013338 (2009)","journal-title":"Appl. Algebra Eng. Commun. Comput"},{"key":"513_CR29","doi-asserted-by":"crossref","unstructured":"Seiler, W.M.: Involution. The Formal Theory of Differential Equations and its Applications in Computer Algebra. Springer, Berlin (2010)","DOI":"10.1007\/978-3-642-01287-7_2"},{"issue":"10","key":"513_CR30","doi-asserted-by":"publisher","first-page":"3933","DOI":"10.1080\/00927872.2011.599354","volume":"40","author":"WM Seiler","year":"2012","unstructured":"Seiler, W.M.: Effective genericity, $$\\delta $$-regularity and strong Noether position. Commun. Algebra 40(10), 3933\u20133949 (2012)","journal-title":"Commun. Algebra"},{"key":"513_CR31","doi-asserted-by":"crossref","unstructured":"Semenov, A.: On connection between constructive involutive divisions and monomial orderings. In: Computer Algebra in Scientific Computing. 9th International Workshop, CASC 2006, Chi\u015fin\u0103u, Moldova, September 11\u201315, 2006. Proceedings, pp. 261\u2013278. Berlin: Springer (2006)","DOI":"10.1007\/11870814_22"},{"key":"513_CR32","unstructured":"Spear, D.: A constructive approach to commutative ring theory. In: Proceedings of 1977 Macsyma Users\u2019 Conference, pp. 369\u2013376. NASA CP-2012 (1977)"},{"key":"513_CR33","unstructured":"Zacharias, G.: Generalized Gr\u00f6bner bases in commutative polynomial rings. Master\u2019s thesis, MIT, (1978)"},{"issue":"4","key":"513_CR34","doi-asserted-by":"publisher","first-page":"323","DOI":"10.1016\/S0378-4754(96)00006-7","volume":"42","author":"AY Zharkov","year":"1996","unstructured":"Zharkov, A.Y., Blinkov, Y.A.: Involution approach to investigating polynomial systems. Math. Comput. Simul. 42(4), 323\u2013332 (1996)","journal-title":"Math. Comput. Simul."}],"container-title":["Mathematics in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11786-021-00513-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11786-021-00513-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11786-021-00513-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,7,23]],"date-time":"2021-07-23T04:24:07Z","timestamp":1627014247000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11786-021-00513-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,5,21]]},"references-count":34,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2021,9]]}},"alternative-id":["513"],"URL":"https:\/\/doi.org\/10.1007\/s11786-021-00513-4","relation":{},"ISSN":["1661-8270","1661-8289"],"issn-type":[{"value":"1661-8270","type":"print"},{"value":"1661-8289","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,5,21]]},"assertion":[{"value":"28 September 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 February 2021","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 March 2021","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 May 2021","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}