{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,30]],"date-time":"2026-01-30T06:58:48Z","timestamp":1769756328699,"version":"3.49.0"},"reference-count":99,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2022,3,25]],"date-time":"2022-03-25T00:00:00Z","timestamp":1648166400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2022,3,25]],"date-time":"2022-03-25T00:00:00Z","timestamp":1648166400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["AAECC"],"published-print":{"date-parts":[[2023,9]]},"DOI":"10.1007\/s00200-022-00547-6","type":"journal-article","created":{"date-parts":[[2022,3,25]],"date-time":"2022-03-25T16:30:21Z","timestamp":1648225821000},"page":"793-885","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Jacobi\u2019s Bound: Jacobi\u2019s results translated in K\u0151nig\u2019s, Egerv\u00e1ry\u2019s and Ritt\u2019s mathematical languages"],"prefix":"10.1007","volume":"34","author":[{"given":"Fran\u00e7ois","family":"Ollivier","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,3,25]]},"reference":[{"key":"#cr-split#-547_CR1.1","unstructured":"Adelson-Velsky, G., Landis, E.: An algorithm for the organization of information. Doklady Akademiya Nauk SSSR 146, 263-266, 1962"},{"key":"#cr-split#-547_CR1.2","unstructured":"English translation, Soviet Math. 3, 1259-1263, (1962)"},{"issue":"2","key":"547_CR2","doi-asserted-by":"crossref","first-page":"257","DOI":"10.2140\/pjm.2016.283.257","volume":"283","author":"F Aroca","year":"2016","unstructured":"Aroca, F., Garay, C., Toghani, Z.: The fundamental theorem of tropical differential algebraic geometry. Pac. J. Math. 283(2), 257\u2013270 (2016)","journal-title":"Pac. J. Math."},{"issue":"2","key":"547_CR3","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1090\/S0273-0979-1982-15032-7","volume":"7","author":"H Bass","year":"1982","unstructured":"Bass, H., Connell, E.H., Wright, D.: The Jacobian conjecture: reduction of degree and formal expansion of the inverse. Bull. Am. Math. Soc. (New Ser.) 7(2), 287\u2013330 (1982)","journal-title":"Bull. Am. Math. Soc. (New Ser.)"},{"key":"547_CR4","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1090\/qam\/102435","volume":"16","author":"R Bellman","year":"1958","unstructured":"Bellman, R.: On a routing problem. Q. Appl. Math. 16, 87\u201390 (1958)","journal-title":"Q. Appl. Math."},{"key":"547_CR5","doi-asserted-by":"crossref","unstructured":"Boulier, F., Lemaire, F., Moreno Maza, M.: \u201cPARDI\u00a0!\u201d, ISSAC 2001, ACM Press, 38\u201347, (2001)","DOI":"10.1145\/384101.384108"},{"issue":"1","key":"547_CR6","first-page":"73","volume":"20","author":"F Boulier","year":"2009","unstructured":"Boulier, F., Lazard, D., Ollivier, F., Petitot, M.: Computing representations for radicals of finitely generated differential ideals. Spec. Issue Jacobi\u2019s Legacy AAECC 20(1), 73\u2013121 (2009)","journal-title":"Spec. Issue Jacobi\u2019s Legacy AAECC"},{"key":"547_CR7","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611972238","volume-title":"Assignment Problems","author":"R Burkard","year":"2012","unstructured":"Burkard, R., Dell\u2019Amico, M., Martello, S.: Assignment Problems. SIAM, Philadelphia (2012)"},{"key":"547_CR8","unstructured":"Briefwechsel Zwischen, C.G.J.,\u00a0Jacobi und, M.H.\u00a0Jacobi, Herausgegeben von W.\u00a0Ahrens, Abhandlungen zur Geschichte der Mathematischen Wissenschaften, XXII.\u00a0Heft, Leipzig, Druck und Verlag von B.G.\u00a0Teubner (1907)"},{"key":"547_CR9","doi-asserted-by":"crossref","unstructured":"Ferro, C.: Giuseppa: a resultant theory for ordinary algebraic differential equations. In: Mora, T., Mattson, H. (eds.) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, LNCS vol 1255, 55\u201365. Springer, Berlin (1997)","DOI":"10.1007\/3-540-63163-1_5"},{"key":"547_CR10","unstructured":"Castro-Jim\u00e9nez, F.-J.: Calculs effectifs pour les id\u00e9aux d\u2019op\u00e9rateurs diff\u00e9rentiels, Actas de la II Conferencia Internacional de Geometr\u00eda Algebraica, La R\u00e1bida, Travaux en Cours 24. Hermann, Paris (1987)"},{"key":"547_CR11","unstructured":"Castro-Jim\u00e9nez, F-J., Granger, M.: Explicit calculations in rings of differential operators. S\u00e9minaires & Congr\u00e8s, 8, 89\u2013128, SMF (2004)"},{"issue":"1","key":"547_CR12","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1017\/S0080456800033299","volume":"38","author":"G Chrystal","year":"1897","unstructured":"Chrystal, G.: A fundamental theorem regarding the equivalence of systems of differential equations, and its application to the determination of the order and the systematic solution of a determinate system of such equations. Trans. R. Soc. Edinb. 38(1), 163\u2013178 (1897)","journal-title":"Trans. R. Soc. Edinb."},{"issue":"5","key":"547_CR13","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1007\/s00200-002-0110-4","volume":"13","author":"T Cluzeau","year":"2003","unstructured":"Cluzeau, T., Hubert, \u00c9.: Resolvent representation for regular differential ideals. AAECC 13(5), 395\u2013425 (2003)","journal-title":"AAECC"},{"issue":"1","key":"547_CR14","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1090\/S0002-9939-1983-0677218-6","volume":"87","author":"RM Cohn","year":"1983","unstructured":"Cohn, R.M.: Order and dimension. Proc. Am. Math. Soc. 87(1), 1\u20136 (1983)","journal-title":"Proc. Am. Math. Soc."},{"issue":"3","key":"547_CR15","doi-asserted-by":"crossref","first-page":"396","DOI":"10.1016\/j.jco.2005.10.002","volume":"22","author":"L D\u2019Alfonso","year":"2006","unstructured":"D\u2019Alfonso, L., Jeronimo, G., Solern\u00f3, P.: On the complexity of the resolvent representation of some prime differential ideals. J. Complex. 22(3), 396\u2013430 (2006)","journal-title":"J. Complex."},{"issue":"6","key":"547_CR16","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1007\/s00200-008-0083-z","volume":"19","author":"L D\u2019Alfonso","year":"2008","unstructured":"D\u2019Alfonso, L., Jeronimo, G., Solern\u00f3, P.: A linear algebra approach to the differentiation index of generic DAE systems. AAECC 19(6), 441\u2013473 (2008)","journal-title":"AAECC"},{"key":"547_CR17","doi-asserted-by":"crossref","unstructured":"D\u2019Alfonso, L., Jeronimo, G.G., Ollivier, F., Sedoglavic, A., Solern\u00f3, P.: A geometric index reduction method for implicit systems of differential algebraic equations. J. Symb. Comput. 46(10), 1114\u20131138 (2011)","DOI":"10.1016\/j.jsc.2011.05.012"},{"key":"547_CR18","unstructured":"D\u2019Alfonso, M.E.: M\u00e9todos simb\u00f3licos para sistemas de ecuaciones \u00e1lgebro-diferenciales. PhD thesis, University of Buenos Aires (2006)"},{"key":"547_CR19","doi-asserted-by":"crossref","unstructured":"Dora, D., Jean, D., Claire, D.: Dominique: about a new method for computing in algebraic number fields. Eurocal\u201985. Springer, LNCS 204, 289\u2013290 (1985)","DOI":"10.1007\/3-540-15984-3_279"},{"key":"547_CR20","doi-asserted-by":"crossref","unstructured":"Dijkstra, E.W.: A note on two problems in connexion with graphs. Numerische Mathematik, 1, 269\u2013271, Springer (1959)","DOI":"10.1007\/BF01386390"},{"key":"547_CR21","unstructured":"Dinic, E.A., [Dinic (Yefim)], Kronrod, M.A.: An algorithm for the solution of the assignment problem. Soviet Math. Dokl. 69(6), 1324\u20131326 (1969)"},{"key":"547_CR22","doi-asserted-by":"crossref","unstructured":"Duan, R., Pettie, S.: Approximating maximum weight matching in near-linear time. Proceedings of the $$51^{rst}$$ Annual IEEE Symposium on Foundations of Computer Science (FOCS), 673\u2013682 (2010)","DOI":"10.1109\/FOCS.2010.70"},{"key":"547_CR23","doi-asserted-by":"crossref","first-page":"248","DOI":"10.1145\/321694.321699","volume":"19","author":"J Edmonds","year":"1972","unstructured":"Edmonds, J., Karp, R.M.: Theoretical improvements in algorithmic efficiency for network flow problems. J. ACM 19, 248\u2013264 (1972)","journal-title":"J. ACM"},{"key":"#cr-split#-547_CR24.1","unstructured":"Egerv\u00e1ry, J.: Matrixok kombinatorius tulajdons\u00e1gair\u00f3l. In: Hungarian: On combinatorial properties of matrices, Matematikai \u00e9s Fizikai Lapok, vol.\u00a038, 1931, 16-28"},{"key":"#cr-split#-547_CR24.2","unstructured":"translated by H.W.\u00a0Kuhn as Paper\u00a04, Issue 11 of Logistik Papers, Georges Washington University Research Project (1955)"},{"issue":"4","key":"547_CR25","doi-asserted-by":"crossref","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., Mora, T.: Efficient computation of zero-dimensional Gr\u00f6bner bases by change of ordering. J. Symb. Comput. 16(4), 329\u2013344 (1993)","journal-title":"J. Symb. Comput."},{"key":"547_CR26","unstructured":"Ford, L.R., Jr.: Network flow theory, Paper P-923. RAND Corporation, Santa Monica, California (1956)"},{"issue":"3","key":"547_CR27","doi-asserted-by":"crossref","first-page":"596","DOI":"10.1145\/28869.28874","volume":"34","author":"ML Fredman","year":"1987","unstructured":"Fredman, M.L., Tarjan, R.E.: Fibonacci heaps and their uses in improved network optimization algorithms. J. ACM 34(3), 596\u2013615 (1987)","journal-title":"J. ACM"},{"key":"547_CR28","unstructured":"Frobenius, F.G.: \u00dcber Matrizen aus nicht negativen Elementen. Sitzungsberichte der K\u00f6niglich Preu\u00dfischen Akademie der Wissenschaften zu Berlin, 456\u2013477 (1912)"},{"key":"547_CR29","unstructured":"Frobenius, F.G.: \u00dcber zerlegbare Determinanten. Sitzungsberichte der K\u00f6niglich Preu\u00dfischen Akademie der Wissenschaften zu Berlin, 274\u2013277 (1917)"},{"key":"547_CR30","doi-asserted-by":"crossref","first-page":"1013","DOI":"10.1137\/0218069","volume":"18","author":"HN Gabow","year":"1989","unstructured":"Gabow, H.N., Tarjan, R.E.: Faster scaling algorithms for network problems. SIAM J. Comput. 18, 1013\u20131036 (1989)","journal-title":"SIAM J. Comput."},{"issue":"1","key":"547_CR31","doi-asserted-by":"crossref","first-page":"154","DOI":"10.1006\/jcom.2000.0571","volume":"17","author":"M Giusti","year":"2001","unstructured":"Giusti, M., Lecerf, G., Salvy, B.: A Gr\u00f6bner free alternative for polynomial system solving. J. Complex. 17(1), 154\u2013211 (2001)","journal-title":"J. Complex."},{"key":"547_CR32","unstructured":"Golubitsky, O., Kondratieva, M., Moreno Maza, M., Ovchinnikov, A.: Bounds and algebraic algorithms in differential algebra: the ordinary case. In: Decker, W., Dewar, M., Kaltofen, E., Watt, S.M. (eds.) Challenges in Symbolic Computation Software, N$$^{{\\rm o}}$$ 06271 in Dagstuhl Seminar Proceedings, Internationales Begegnungs und Forschungszentrum f\u00fcr Informatik (IBFI). Schloss Dagstuhl, Germany (2007)"},{"key":"547_CR33","volume-title":"When Computers were Human","author":"DA Grier","year":"2005","unstructured":"Grier, D.A.: When Computers were Human. Princeton University Press, Princeton (2005)"},{"issue":"4","key":"547_CR34","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1137\/0202019","volume":"2","author":"JE Hopcroft","year":"1973","unstructured":"Hopcroft, J.E., Karp, R.M., et al.: An $$n^{5\/2}$$ algorithm for maximum matchings in bipartite graphs. SIAM J. Comput. 2(4), 225\u2013231 (1973)","journal-title":"SIAM J. Comput."},{"key":"547_CR35","unstructured":"Houtain, L.: Des solutions singuli\u00e8res des \u00e9quations diff\u00e9rentielles. Ann. des Universit\u00e9s de Belgique Ann\u00e9es 1851\u20131854, 973\u20131323"},{"key":"547_CR36","unstructured":"Hrushovski, E.: The elementary theory of Frobenius automorphisms, preprint, 1996, revised 2004, (2014) arXiv:math\/0406514"},{"key":"547_CR37","first-page":"1","volume":"21","author":"\u00c9 Hubert","year":"1999","unstructured":"Hubert, \u00c9.: Essential components of an algebraic differential equation. J. Symb. Comput. 21, 1\u201324 (1999)","journal-title":"J. Symb. Comput."},{"issue":"1","key":"547_CR38","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1016\/0020-0190(81)90142-3","volume":"13","author":"OH Ibarra","year":"1981","unstructured":"Ibarra, O.H., Moran, S.: Deterministic and probabilistic algorithms for maximum bipartite matching via fast matrix multiplication. Inform. Process. Lett. 13(1), 12\u201315 (1981)","journal-title":"Inform. Process. Lett."},{"key":"547_CR39","doi-asserted-by":"crossref","unstructured":"Jacobi, C.G., Jacob: De eliminatione variabilis e duabus aequationibus algebraicis. J. f\u00fcr die Reine und Angew. Mathematik 15, 101\u2013124 (1836)","DOI":"10.1515\/crll.1836.15.101"},{"key":"547_CR40","doi-asserted-by":"crossref","unstructured":"Jacobi, C.G., Jacob: De investigando ordine systematis aequationum differentialum vulgarium cujuscunque, [Crelle 65], 297\u2013320, [GW V], 193\u2013216. English translation, AAECC 20(1), 7\u201332 (2009)","DOI":"10.1007\/s00200-009-0087-3"},{"key":"547_CR41","doi-asserted-by":"crossref","unstructured":"Jacobi, C.G., Jacob: De aequationum differentialum systemate non normali ad formam normalem revocando, [VD], 550\u2013578 and [GW V], 485\u2013513. English translation, AAECC 20(1), 33\u201364 (2009)","DOI":"10.1007\/s00200-009-0088-2"},{"key":"547_CR42","unstructured":"Jacobi, C.G.J.: \u201cTheoria novi multiplicatoris systemati aequationum differentialium vulgarium applicandi\u201d, first published in [Crelle 27] Heft\u00a0III 199\u2013268 (part\u00a0I) and [Crelle 29] Heft\u00a0III 213\u2013279 and Heft\u00a0IV 333\u2013376 (part\u00a0II), reproduced in [GW IV], 317\u2013509"},{"key":"547_CR43","unstructured":"Jacobi, C.G.J.: Lettre adress\u00e9e \u00e0 M.\u00a0le pr\u00e9sident de l\u2019Acad\u00e9mie des sciences. J. de Math. Pures et Appl., V, 1840, 350\u2013351"},{"key":"547_CR44","unstructured":"Jacobi, C.G.J.: Sur un nouveau principe de la m\u00e9canique analytique. C. R. Acad. Sci. Paris, XV, 1842, 202\u2013205; [GW\u00a0IV], 289\u2013294"},{"key":"547_CR45","unstructured":"Jacobi, C.G.J.: Sul principo dell\u2019ultimo multiplicatore e suo uso como nuovo principio generale di meccanica. Giornale arcadico, XCIX, 129\u2013146, (1844); [GW\u00a0IV] 511\u2013522"},{"key":"547_CR46","unstructured":"Jacobi, C.G.J.: Sur un th\u00e9or\u00e8me de Poisson. C. R. Acad. Sci. Paris, XI, (1840), p.\u00a0529; [GW\u00a0IV], 143\u2013146"},{"key":"547_CR47","unstructured":"Jacobi, C.G.J.: Canon arithmeticus, sive talul\u00e6 quibus exhibentur pro singulis numeris primis. Berolini, typis academicis (1839)"},{"key":"547_CR48","unstructured":"Janet, M.: Sur les syst\u00e8mes d\u2019\u00e9quations aux d\u00e9riv\u00e9es partielles. J. de Math\u00e9Mat. Pures et Appl., 8e s\u00e9rie, tome 3, 65\u2013152. Gauthier-Villars, Paris (1920)"},{"issue":"1","key":"547_CR49","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/321992.321993","volume":"24","author":"DB Johnson","year":"1977","unstructured":"Johnson, D.B.: Efficient algorithms for shortest paths in sparse networks. J. ACM 24(1), 1\u201313 (1977)","journal-title":"J. ACM"},{"key":"547_CR50","first-page":"251","volume":"91","author":"J Johnson","year":"1969","unstructured":"Johnson, J.: Differential dimension polynomials and a fundamental theorem on differential modules. Am. J. Math. 91, 251\u2013257 (1969)","journal-title":"Am. J. Math."},{"issue":"1","key":"547_CR51","doi-asserted-by":"crossref","first-page":"92","DOI":"10.2307\/1970810","volume":"89","author":"J Johnson","year":"1969","unstructured":"Johnson, J.: K\u00e4hler differentials and differential algebra. Ann. Math. 89(1), 92\u201398 (1969)","journal-title":"Ann. Math."},{"key":"547_CR52","doi-asserted-by":"crossref","unstructured":"Johnson, J.: A notion of regularity for differential local algebras. Contributions to algebra, A Collection of Papers Dedicated to Ellis Kolchin, Edited by Hyman Bass, Phyllis J.\u00a0Cassidy and Jerald Kovacic, Elsevier, 211\u2013232 (1977)","DOI":"10.1016\/B978-0-12-080550-1.50021-4"},{"key":"547_CR53","first-page":"329","volume":"242","author":"J Johnson","year":"1978","unstructured":"Johnson, J.: Systems of $$n$$ partial differential equations in $$n$$ unknown functions: the conjecture of M. Janet. Trans. AMS 242, 329\u2013334 (1978)","journal-title":"Trans. AMS"},{"key":"547_CR54","unstructured":"Jordan, C.: Sur l\u2019ordre d\u2019un syst\u00e8me d\u2019\u00e9quations diff\u00e9rentielles. Ann. de la soci\u00e9t\u00e9 Sci. de Bruxelles, 7, B., 127\u2013130 (1883)"},{"key":"547_CR55","unstructured":"J\u00fcttner, A: On the efficiency of Egerv\u00e1ry\u2019s perfect matching algorithm. TR-2004-13, Egerv\u00e1ry Research Group, Budapest, (2004). ISSN 1587\u20134451"},{"key":"547_CR56","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1007\/BF01695502","volume":"47","author":"O-H Keller","year":"1939","unstructured":"Keller, O.-H.: Ganze Cremona-transformationen. Monatsh. Math. Phys. 47, 299\u2013306 (1939)","journal-title":"Monatsh. Math. Phys."},{"key":"547_CR57","volume-title":"The art of computer programming III. Sorting and searching","author":"DE Knuth","year":"1973","unstructured":"Knuth, D.E.: The art of computer programming III. Sorting and searching. Addison-Wesley, Reading (1973)"},{"key":"547_CR58","unstructured":"Koenigsberger, L.: Carl Gustav Jacob Jacobi. Festschrift zur Feier der hundertsten Wiederkehr seines Geburstages, B.G. Teubner, Leipzig (1904), xviii, 554\u00a0p"},{"key":"547_CR59","volume-title":"Differential Algebra and Algebraic Groups","author":"ER Kolchin","year":"1973","unstructured":"Kolchin, E.R.: Differential Algebra and Algebraic Groups. Academic Press, New York (1973)"},{"key":"547_CR60","unstructured":"Kondratieva, M.V., Mikhalev, A.V., Pankratiev, E.V.: Jacobi\u2019s bound for systems of differential polynomials. Algebra. M.: MGU, s. 79-85 (1982) (in Russian)"},{"issue":"1","key":"547_CR61","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1007\/s00200-009-0092-6","volume":"20","author":"MV Kondratieva","year":"2009","unstructured":"Kondratieva, M.V., Mikhalev, A.V., Pankratiev, E.V.: Jacobi\u2019s bound for independent systems of algebraic partial differential equations. AAECC 20(1), 65\u201371 (2009)","journal-title":"AAECC"},{"key":"547_CR62","first-page":"116","volume":"38","author":"D K\u0151nig","year":"1931","unstructured":"K\u0151nig, D.: Gr\u00e1fok \u00e9s m\u00e1trixok. Matematikai \u00e9s Fizikai Lapok 38, 116\u2013119 (1931)","journal-title":"Matematikai \u00e9s Fizikai Lapok"},{"key":"#cr-split#-547_CR63.1","unstructured":"K\u0151nig, D.: Theorie der endlichen und unendlichen Graphen, Math. in Monogr. und Lehrb. XVI., Akad. Verlagsges., Leipzig, (1936)"},{"key":"#cr-split#-547_CR63.2","unstructured":"AMS Chelsey Publishing, Rhode Island (2001)"},{"key":"547_CR64","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1002\/nav.3800020109","volume":"2","author":"HW Kuhn","year":"1955","unstructured":"Kuhn, H.W.: The Hungarian method for the assignment problem. Naval Res. Logist. Quart. 2, 83\u201397 (1955)","journal-title":"Naval Res. Logist. Quart."},{"key":"547_CR65","doi-asserted-by":"crossref","first-page":"641","DOI":"10.1016\/j.ejor.2011.11.008","volume":"219","author":"HW Kuhn","year":"2012","unstructured":"Kuhn, H.W.: A tale of three eras: the discovery and rediscovery of the Hungarian Method. Eur. J. Oper. Res. 219, 641\u2013651 (2012)","journal-title":"Eur. J. Oper. Res."},{"key":"547_CR66","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1137\/0105003","volume":"5","author":"J Munkres","year":"1957","unstructured":"Munkres, J.: Algorithms for the assignment and transportation problems. J. Soc. Industr. Appl. Math. 5, 32\u201338 (1957)","journal-title":"J. Soc. Industr. Appl. Math."},{"key":"547_CR67","unstructured":"Landau, L.D., Lifshitz, E.M: Theoretical physics, vol.\u00a01, Mechanics, 3$$^{rd}$$\u00a0ed., Pergamon Press, Oxford (1976)"},{"key":"547_CR68","first-page":"119","volume":"152","author":"BA Lando","year":"1970","unstructured":"Lando, B.A.: Jacobi\u2019s bound for the order of systems of first order differential equations. Trans. Am. Math. Soc. 152, 119\u2013135 (1970)","journal-title":"Trans. Am. Math. Soc."},{"key":"547_CR69","doi-asserted-by":"crossref","unstructured":"Le Gall, F.: Powers of tensors and fast matrix multiplication. In: Proceedings of ISSAC\u20192014, ACM Press, 296\u2013303 (2014)","DOI":"10.1145\/2608628.2608664"},{"issue":"2","key":"547_CR70","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1007\/s10208-015-9249-9","volume":"15","author":"W Li","year":"2015","unstructured":"Li, W., Yuan, C.-M., Gao, X.-S.: Sparse differential resultant for laurent differential polynomials. Found. Comput. Math. 15(2), 451\u2013517 (2015)","journal-title":"Found. Comput. Math."},{"key":"547_CR71","doi-asserted-by":"crossref","unstructured":"Maclagan, D., Sturmfels, B.: Introduction to Tropical Geometry, Graduate Studies in Mathematics\u00a0161, AMS, Providence, 363\u00a0p., (2015)","DOI":"10.1090\/gsm\/161"},{"issue":"1","key":"547_CR72","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1007\/s10100-009-0125-z","volume":"18","author":"S Martello","year":"2010","unstructured":"Martello, S.: Jen\u0151 Egerv\u00e1ry: from the origins of the Hungarian algorithm to satellite communication. Cent. Eur. J. Oper. Res. 18(1), 47\u201358 (2010)","journal-title":"Cent. Eur. J. Oper. Res."},{"issue":"3\u20134","key":"547_CR73","doi-asserted-by":"crossref","first-page":"473","DOI":"10.1016\/S0747-7171(03)00091-9","volume":"36","author":"G Matera","year":"2003","unstructured":"Matera, G., Sedoglavic, A.: Fast computation of discrete invariants associated to a differential rational mapping. J. Symb. Comput. 36(3\u20134), 473\u2013499 (2003)","journal-title":"J. Symb. Comput."},{"key":"547_CR74","doi-asserted-by":"crossref","first-page":"631","DOI":"10.1006\/jsco.1999.0318","volume":"28","author":"S Morrison","year":"1999","unstructured":"Morrison, S.: The differential ideal $$[P]:M^{\\infty }$$. J. Symb. Comput. 28, 631\u2013656 (1999)","journal-title":"J. Symb. Comput."},{"key":"547_CR75","unstructured":"Monge, G.: \u201cM\u00e9moire sur la th\u00e9orie des d\u00e9blais et des remblais\u201d, Histoire de l\u2019Acad\u00e9mie royale des Sciences, [ann\u00e9e 1781. Avec les M\u00e9moires de Math\u00e9matique & de Physique pour la m\u00eame Ann\u00e9e] (2e partie) (1784) [Histoire: 34\u201338, M\u00e9moires\u00a0:] 666\u2013704"},{"key":"547_CR76","first-page":"77","volume":"6","author":"EJ Nanson","year":"1876","unstructured":"Nanson, E.J.: On the number of arbitrary constants in the complete solution of ordinary simultaneous differential equations. Messenger Math. 6, 77\u201381 (1876)","journal-title":"Messenger Math."},{"key":"547_CR77","doi-asserted-by":"crossref","first-page":"7743","DOI":"10.1088\/0305-4470\/37\/31\/007","volume":"37","author":"MC Nucci","year":"2004","unstructured":"Nucci, M.C., Leach, P.G.L.: Jacobi\u2019s last multiplier and symmetries for the Kepler problem plus a lineal story. J. Phys. A Math. Gen. 37, 7743\u20137753 (2004)","journal-title":"J. Phys. A Math. Gen."},{"issue":"6","key":"547_CR78","doi-asserted-by":"crossref","first-page":"065011","DOI":"10.1088\/0031-8949\/78\/06\/065011","volume":"78","author":"MC Nucci","year":"2008","unstructured":"Nucci, M.C., Leach, P.G.L.: The Jacobi last multiplier and its applications in mechanics. Phys. Scr. 78(6), 065011 (2008)","journal-title":"Phys. Scr."},{"issue":"3","key":"547_CR79","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1016\/j.crma.2007.06.010","volume":"345","author":"F Ollivier","year":"2007","unstructured":"Ollivier, F., Sadik, B.: La borne de Jacobi pour une diffi\u00e9t\u00e9 d\u00e9finie par un syst\u00e8me quasi r\u00e9gulier (Jacobi\u2019s bound for a diffiety defined by a quasi-regular system). C. R. Math. 345(3), 139\u2013144 (2007)","journal-title":"C. R. Math."},{"key":"547_CR80","unstructured":"Ollivier, F.: Jacobi\u2019s bound and normal forms computations. A historical survey. World Scientific Publishing Company, Differential Algebra And Related Topics (2008)978-981-283-371-6"},{"key":"547_CR81","doi-asserted-by":"crossref","unstructured":"Pryce, J.D.: A simple structural analysis method for DAEs. BIT: Numerical Mathematics, vol.\u00a041, no.\u00a02, 364\u2013394, Swets & Zeitlinger (2001)","DOI":"10.1023\/A:1021998624799"},{"key":"547_CR82","doi-asserted-by":"crossref","unstructured":"Rabinowitsch, J.L.: [Rainich (George Yuri)], Zum Hilbertschen Nullstellensatz. Math. Ann. 102, 520 (1929)","DOI":"10.1007\/BF01782361"},{"key":"547_CR83","volume-title":"Les syst\u00e8mes d\u2019\u00e9quations aux d\u00e9riv\u00e9es partielles","author":"C Riquier","year":"1910","unstructured":"Riquier, C.: Les syst\u00e8mes d\u2019\u00e9quations aux d\u00e9riv\u00e9es partielles. Gauthier-Villars, Paris (1910)"},{"key":"547_CR84","doi-asserted-by":"crossref","unstructured":"Ritt, J.F.: Differential equations from the algebraic standpoint. Am. Math. Soc. Colloq. Publ., vol.\u00a0xiv. A.M.S., New-York (1932)","DOI":"10.1090\/coll\/014"},{"key":"547_CR85","doi-asserted-by":"crossref","first-page":"303","DOI":"10.2307\/1968572","volume":"36","author":"JF Ritt","year":"1935","unstructured":"Ritt, J.F.: Jacobi\u2019s problem on the order of a system of differential equations. Ann. Math. 36, 303\u2013312 (1935)","journal-title":"Ann. Math."},{"key":"547_CR86","doi-asserted-by":"crossref","unstructured":"Ritt, J.F.: Differential Algebra. Am. Math. Soc. Colloq. Publ., vol.\u00a0xxxiii. A.M.S., New-York (1950)","DOI":"10.1090\/coll\/033"},{"key":"547_CR87","unstructured":"Saltykow, N.N.: L\u2019\u0152uvre de Jacobi dans le domaine des \u00e9quations diff\u00e9rentielles du premier ordre. Bull. des Sci. Math\u00e9matiques, Gauthier-Villars, Paris, 213\u2013228 (1939)"},{"key":"547_CR88","doi-asserted-by":"crossref","unstructured":"Saltykow, N.N.: Ordre d\u2019un syst\u00e8me d\u2019\u00e9quations diff\u00e9rentielles ordinaires de la forme g\u00e9n\u00e9rale. Bulletin (Acad\u00e9mie serbe des sciences et des arts. Classe des sciences math\u00e9matiques et naturelles. Sciences math\u00e9matiques), n$$^{\\rm o}$$\u00a01, 141\u2013148 (1952)","DOI":"10.3406\/barb.1951.70576"},{"key":"547_CR89","doi-asserted-by":"crossref","first-page":"4480","DOI":"10.1016\/j.tcs.2009.07.028","volume":"410","author":"P Sankowski","year":"2009","unstructured":"Sankowski, P.: Maximum weight bipartite matching in matrix multiplication time. Theoret. Comput. Sci. 410, 4480\u20134488 (2009)","journal-title":"Theoret. Comput. Sci."},{"issue":"5","key":"547_CR90","doi-asserted-by":"crossref","first-page":"735","DOI":"10.1006\/jsco.2002.0532","volume":"33","author":"A Sedoglavic","year":"2002","unstructured":"Sedoglavic, A.: A probabilistic algorithm to test local algebraic observability in polynomial time. J. Symb. Comput. 33(5), 735\u2013755 (2002)","journal-title":"J. Symb. Comput."},{"key":"547_CR91","unstructured":"Shaleninov, A.A.: Removal of topological degeneracy in systems of differential evolution equations. Automation and Remote Control, 51, 1599\u20131605, 1991 (English version). Translation from Avtomatika i Telemekhanika, Issue 11, 163\u2013170 (1990)"},{"key":"547_CR92","unstructured":"Schrijver, A.: Combinatorial Optimization. Springer, Polyhedra and Efficiency (2003)"},{"key":"547_CR93","first-page":"1","volume-title":"Handbook of Discrete Optimization","author":"A Schrijver","year":"2005","unstructured":"Schrijver, A.: On the history of combinatorial optimization (till 1960). In: Aardal, K., Nemhauser, G.L., Weismantel, R. (eds.) Handbook of Discrete Optimization, pp. 1\u201368. Elsevier, Amsterdam (2005)"},{"key":"547_CR94","doi-asserted-by":"crossref","unstructured":"Schrijver, A.: On the history of the shortest path problem. Documenta Math. Extra Vol. Optim. Stories 155\u2013167 (2012)","DOI":"10.4171\/dms\/6\/19"},{"key":"547_CR95","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1002\/net.3230010206","volume":"1","author":"N Tomizawa","year":"1971","unstructured":"Tomizawa, N.: On some techniques useful for solution of transportation network problems. Networks 1, 173\u2013194 (1971)","journal-title":"Networks"},{"key":"547_CR96","unstructured":"Volevich, L.R.: On general systems of differential equations. Dokl. Akad. Nauk SSSR, 132(1) 20\u201323, (1960). English translation Soviet. Math., 1, 458\u2013465 (1960)"}],"container-title":["Applicable Algebra in Engineering, Communication and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00200-022-00547-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00200-022-00547-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00200-022-00547-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,7,25]],"date-time":"2023-07-25T16:06:10Z","timestamp":1690301170000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00200-022-00547-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,3,25]]},"references-count":99,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2023,9]]}},"alternative-id":["547"],"URL":"https:\/\/doi.org\/10.1007\/s00200-022-00547-6","relation":{},"ISSN":["0938-1279","1432-0622"],"issn-type":[{"value":"0938-1279","type":"print"},{"value":"1432-0622","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,3,25]]},"assertion":[{"value":"24 August 2016","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 September 2020","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 February 2022","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 March 2022","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}