{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,6]],"date-time":"2024-09-06T22:59:23Z","timestamp":1725663563681},"publisher-location":"Berlin, Heidelberg","reference-count":13,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540510840"},{"type":"electronic","value":"9783540461531"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[1989]]},"DOI":"10.1007\/3-540-51084-2_15","type":"book-chapter","created":{"date-parts":[[2012,2,25]],"date-time":"2012-02-25T20:42:32Z","timestamp":1330202552000},"page":"162-176","source":"Crossref","is-referenced-by-count":1,"title":["Greater easy common divisor and standard basis completion algorithms"],"prefix":"10.1007","author":[{"given":"Andr\u00e9","family":"Galligo","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lo\u00efc","family":"Pottier","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Carlo","family":"Traverso","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2005,5,27]]},"reference":[{"key":"15_CR1","unstructured":"Bayer, D. A., The division algorithm and the Hilbert scheme, Ph.D. thesis, Harvard (1982)."},{"key":"15_CR2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1215\/S0012-7094-87-05517-7","volume":"55","author":"D. A. Bayer","year":"1987","unstructured":"Bayer, D. A., Stillman, M., A theorem on refining division orders by the reverse lexicographic order, Duke Math. J. 55 (1987;), 1\u201311.","journal-title":"Duke Math. J."},{"key":"15_CR3","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-7091-3406-1","volume-title":"Computer Algebra","author":"B. Buchberger","year":"1982","unstructured":"Buchberger, B., Collins, G. E., Loos, R., \u201cComputer Algebra,\u201d Springer Verlag, Wien-New York, 1982."},{"key":"15_CR4","doi-asserted-by":"crossref","first-page":"374","DOI":"10.1007\/BF01844169","volume":"4","author":"B. Buchberger","year":"1970","unstructured":"Buchberger, B., An Algorithm for Finding a Basis for the Residue Class Ring of a Zero-Dimensional Polynomial Ideal, Aequationes Mathematicae 4 (1970), 374\u2013383. (Ph.D. Thesis, Math. Inst. Univ. Innsbruck, 1965).","journal-title":"Aequationes Mathematicae"},{"key":"15_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/3-540-09519-5_52","volume-title":"EUROSAM 1979","author":"B. Buchberger","year":"1979","unstructured":"\u2014, A Criterion for Detecting Unnecessary Reductions in the Construction of Gr\u00f6bner Bases, in \u201cEUROSAM 1979,\u201d Lecture Notes in Computer Science 72, Springer Verlag, Berlin-Heidelberg-New York, 1979, pp. 3\u201321."},{"key":"15_CR6","unstructured":"Galligo, A., Algorithmes de calcul de base standard, Universit\u00e9 de Nice (preprint) (1982)."},{"key":"15_CR7","unstructured":"Galligo, A., Traverso, C., Pottier,L., Appendix to: Greater Easy Common Divisor and standard basis completion algorithms, Rapports de Recherche (1988), INRIA, centre de Sophia Antipolis."},{"key":"15_CR8","unstructured":"Gebauer, R., M\u00f6ller, H. M., An installation of of Buchberger's algorithm, J. of Symbolic Computation (to appear)."},{"key":"15_CR9","doi-asserted-by":"crossref","unstructured":"Loos, R., Generalized polynomial remainder sequences, in \u201cComputer Algebra,\u201d (BCL), pp. 115\u2013137.","DOI":"10.1007\/978-3-7091-7551-4_9"},{"key":"15_CR10","unstructured":"Pottier, L., Algorithmes de completion, constructions, preuves, strat\u00e9gies, applications. (to appear); (submitted to \u201c1988 IEEE Symposium on Logic in;Computer Science\u201d)"},{"key":"15_CR11","unstructured":"Traverso, C., Gr\u00f6bner trace algorithms, (these proceedings)."},{"key":"15_CR12","unstructured":"\u2014, AIPi: a package to test different versions of the Gr\u00f6bner basis completion algorithm. (to appear)"},{"key":"15_CR13","unstructured":"van der Waerden, B. L., \u201cModerne Algebra,\u201d Springer Verlag, Berlin-Heidelberg-New York."}],"container-title":["Lecture Notes in Computer Science","Symbolic and Algebraic Computation"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/3-540-51084-2_15.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,11,17]],"date-time":"2020-11-17T21:19:50Z","timestamp":1605647990000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/3-540-51084-2_15"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1989]]},"ISBN":["9783540510840","9783540461531"],"references-count":13,"URL":"https:\/\/doi.org\/10.1007\/3-540-51084-2_15","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[1989]]}}}