{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,26]],"date-time":"2025-03-26T15:43:31Z","timestamp":1743003811863,"version":"3.40.3"},"publisher-location":"Cham","reference-count":23,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319663197"},{"type":"electronic","value":"9783319663203"}],"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_23","type":"book-chapter","created":{"date-parts":[[2017,8,29]],"date-time":"2017-08-29T07:34:27Z","timestamp":1503992067000},"page":"313-328","source":"Crossref","is-referenced-by-count":1,"title":["Algorithms for Zero-Dimensional Ideals Using Linear Recurrent Sequences"],"prefix":"10.1007","author":[{"given":"Vincent","family":"Neiger","sequence":"first","affiliation":[]},{"given":"Hamid","family":"Rahkooy","sequence":"additional","affiliation":[]},{"given":"\u00c9ric","family":"Schost","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2017,8,30]]},"reference":[{"key":"23_CR1","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1016\/j.jsc.2016.11.005","volume":"83","author":"J Berthomieu","year":"2016","unstructured":"Berthomieu, J., Boyer, B., Faug\u00e8re, J.-C.: Linear algebra for computing Gr\u00f6bner bases of linear recursive multidimensional sequences. J. Symb. Comput. 83, 36\u201367 (2016)","journal-title":"J. Symb. Comput."},{"key":"23_CR2","doi-asserted-by":"crossref","unstructured":"Berthomieu, J., Faug\u00e8re, J.-C.: Guessing linear recurrence relations of sequence tuples and P-recursive sequences with linear algebra. In: ISSAC 2016, pp. 95\u2013102. ACM (2016)","DOI":"10.1145\/2930889.2930926"},{"key":"23_CR3","unstructured":"Berthomieu, J., Faug\u00e8re, J.-C.: In-depth comparison of the Berlekamp-Massey-Sakata and the Scalar-FGLM algorithms: the non adaptive variants. hal-01516708, May 2017"},{"key":"23_CR4","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1007\/s00200-003-0133-5","volume":"14","author":"A Bostan","year":"2003","unstructured":"Bostan, A., Salvy, B., Schost, \u00c9.: Fast algorithms for zero-dimensional polynomial systems using duality. AAECC 14, 239\u2013272 (2003)","journal-title":"AAECC"},{"issue":"11","key":"23_CR5","doi-asserted-by":"crossref","first-page":"1851","DOI":"10.1016\/j.laa.2010.06.046","volume":"433","author":"J Brachat","year":"2010","unstructured":"Brachat, J., Comon, P., Mourrain, B., Tsigaridas, E.: Symmetric tensor decomposition. Linear Algebra Appl. 433(11), 1851\u20131872 (2010)","journal-title":"Linear Algebra Appl."},{"key":"23_CR6","doi-asserted-by":"crossref","unstructured":"Dahan, X., Moreno Maza, M., Schost, \u00c9., Xie, Y.: On the complexity of the D5 principle. In: Transgressive Computing, pp. 149-168 (2006)","DOI":"10.1145\/1113439.1113457"},{"key":"23_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"289","DOI":"10.1007\/3-540-15984-3_279","volume-title":"EUROCAL \u201985","author":"J Della Dora","year":"1985","unstructured":"Della Dora, J., Dicrescenzo, C., Duval, D.: About a new method for computing in algebraic number fields. In: Caviness, B.F. (ed.) EUROCAL 1985. LNCS, vol. 204, pp. 289\u2013290. Springer, Heidelberg (1985). doi: 10.1007\/3-540-15984-3_279"},{"key":"23_CR8","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-5350-1","volume-title":"Commutative Algebra: With a View Toward Algebraic Geometry","author":"D Eisenbud","year":"2013","unstructured":"Eisenbud, D.: Commutative Algebra: With a View Toward Algebraic Geometry, vol. 150. Springer Science & Business Media, New York (2013). doi: 10.1007\/978-1-4612-5350-1"},{"key":"23_CR9","unstructured":"Faug\u00e8re, J.-C., Gaudry, P., Huot, L., Renault, G.: Polynomial Systems Solving by Fast Linear Algebra (2013). https:\/\/hal.archives-ouvertes.fr\/hal-00816724"},{"key":"23_CR10","doi-asserted-by":"crossref","unstructured":"Faug\u00e8re, J.-C., Gaudry, P., Huot, L., Renault, G.: Sub-cubic change of ordering for Gr\u00f6bner basis: a probabilistic approach. In: ISSAC 2014, pp. 170-177. ACM (2014)","DOI":"10.1145\/2608628.2608669"},{"issue":"4","key":"23_CR11","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."},{"issue":"3","key":"23_CR12","doi-asserted-by":"crossref","first-page":"538","DOI":"10.1016\/j.jsc.2016.07.025","volume":"80","author":"J-C Faug\u00e8re","year":"2017","unstructured":"Faug\u00e8re, J.-C., Mou, C.: Sparse FGLM algorithms. J. Symb. Comput. 80(3), 538\u2013569 (2017)","journal-title":"J. Symb. Comput."},{"key":"23_CR13","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9781139856065","volume-title":"Modern Computer Algebra","author":"J Gathen von zur","year":"2013","unstructured":"von zur Gathen, J., Gerhard, J.: Modern Computer Algebra, 3rd edn. Cambridge University Press, Cambridge (2013)","edition":"3"},{"key":"23_CR14","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"247","DOI":"10.1007\/3-540-51082-6_83","volume-title":"Applied Algebra, Algebraic Algorithms and Error-Correcting Codes","author":"P Gianni","year":"1989","unstructured":"Gianni, P., Mora, T.: Algebrric solution of systems of polynomirl equations using Groebher bases. In: Huguet, L., Poli, A. (eds.) AAECC 1987. LNCS, vol. 356, pp. 247\u2013257. Springer, Heidelberg (1989). doi: 10.1007\/3-540-51082-6_83"},{"issue":"1","key":"23_CR15","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1007\/BF01448025","volume":"110","author":"W Gr\u00f6bner","year":"1935","unstructured":"Gr\u00f6bner, W.: \u00dcber irreduzible Ideale in kommutativen Ringen. Math. Ann. 110(1), 197\u2013222 (1935)","journal-title":"Math. Ann."},{"issue":"1","key":"23_CR16","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1017\/S0305004100012354","volume":"30","author":"FS Macaulay","year":"1934","unstructured":"Macaulay, F.S.: Modern algebra and polynomial ideals. Math. Proc. Camb. Philos. Soc. 30(1), 27\u201346 (1934)","journal-title":"Math. Proc. Camb. Philos. Soc."},{"key":"23_CR17","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1007\/BF01386834","volume":"4","author":"MG Marinari","year":"1993","unstructured":"Marinari, M.G., Mora, T., M\u00f6ller, H.M.: Gr\u00f6bner bases of ideals defined by functionals with an application to ideals of projective points. AAECC 4, 103\u2013145 (1993)","journal-title":"AAECC"},{"key":"23_CR18","unstructured":"Moreno-Soc\u00edas, G.: Autour de la fonction de Hilbert-Samuel (escaliers d\u2019ideaux polynomiaux). Ph.D. thesis, \u00c9cole polytechnique (1991)"},{"key":"23_CR19","doi-asserted-by":"crossref","unstructured":"Mourrain, B.: Fast algorithm for border bases of Artinian Gorenstein algebras. ArXiv e-prints, May 2017","DOI":"10.1145\/3087604.3087632"},{"key":"23_CR20","unstructured":"Neiger, V.: Bases of relations in one or several variables: fast algorithms and applications. Ph.D. thesis, \u00c9cole Normale Sup\u00e9rieure de Lyon, November 2016"},{"issue":"5","key":"23_CR21","doi-asserted-by":"crossref","first-page":"433","DOI":"10.1007\/s002000050114","volume":"9","author":"F Rouillier","year":"1999","unstructured":"Rouillier, F.: Solving zero-dimensional systems through the rational univariate representation. AAECC 9(5), 433\u2013461 (1999)","journal-title":"AAECC"},{"issue":"2","key":"23_CR22","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1016\/0890-5401(90)90039-K","volume":"84","author":"S Sakata","year":"1990","unstructured":"Sakata, S.: Extension of the Berlekamp-Massey algorithm to $$N$$ dimensions. Inform. Comput. 84(2), 207\u2013239 (1990)","journal-title":"Inform. Comput."},{"issue":"4","key":"23_CR23","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1006\/jsco.1995.1055","volume":"20","author":"V Shoup","year":"1995","unstructured":"Shoup, V.: A new polynomial factorization algorithm and its implementation. J. Symb. Comput. 20(4), 363\u2013397 (1995)","journal-title":"J. Symb. Comput."}],"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_23","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,10,2]],"date-time":"2019-10-02T17:55:39Z","timestamp":1570038939000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-319-66320-3_23"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017]]},"ISBN":["9783319663197","9783319663203"],"references-count":23,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-66320-3_23","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2017]]}}}