{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,2]],"date-time":"2026-10-02T01:00:57Z","timestamp":1790902857812,"version":"4.1.0"},"publisher-location":"Berlin, Heidelberg","reference-count":20,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783540128687","type":"print"},{"value":"9783540387565","type":"electronic"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[1983]]},"DOI":"10.1007\/3-540-12868-9_98","type":"book-chapter","created":{"date-parts":[[2012,2,25]],"date-time":"2012-02-25T12:55:32Z","timestamp":1330174532000},"page":"137-145","source":"Crossref","is-referenced-by-count":21,"title":["A note on the complexity of constructing Gr\u00f6bner-bases"],"prefix":"10.1007","author":[{"given":"B.","family":"Buchberger","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2005,5,29]]},"reference":[{"key":"14_CR1","unstructured":"Bayer, D.A., 82: The Division Algorithm and the Hilbert Scheme. Harvard University, Cambridge, Mass., Math. Dptmt: Ph.D. Thesis, June 1982."},{"key":"14_CR2","unstructured":"Buchberger, B., 65: An Algorithm for Finding a Basis for the Residue Class Ring of a Zero-Dimensional Polynomial Ideal (German). Univ. of Innsbruck, Austria: Math. Inst., Ph.D. Thesis 1965."},{"issue":"3","key":"14_CR3","doi-asserted-by":"crossref","first-page":"374","DOI":"10.1007\/BF01844169","volume":"4","author":"B. Buchberger","year":"1970","unstructured":"Buchberger, B., 70: An Algorithmical Criterion for the Sovability of Algebraic Systems of Equations (German). Aequationes mathematicae 4\/3, 374\u2013383 (1970).","journal-title":"Aequationes mathematicae"},{"issue":"3","key":"14_CR4","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1145\/1088216.1088219","volume":"10","author":"B. Buchberger","year":"1976","unstructured":"Buchberger, B., 76a: A Theoretical Basis for the Reduction of Polynomials to Canonical Form. ACM SIGSAM Bull. 10\/3, 19\u201329 (1976).","journal-title":"ACM SIGSAM Bull."},{"issue":"4","key":"14_CR5","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1145\/1088222.1088224","volume":"10","author":"B. Buchberger","year":"1976","unstructured":"Buchberger, B., 76b: Some Properties of Gr\u00f6bner-Bases for Polynomial Ideals. ACM SIGSAM Bull. 10\/4, 19\u201324 (1976).","journal-title":"ACM SIGSAM Bull."},{"key":"14_CR6","first-page":"3","volume":"72","author":"B. Buchberger","year":"1979","unstructured":"Buchberger, B., 79: A Criterion for Detecting Unnecessary Reductions in the Construction of Gr\u00f6bner-Bases. Proc. EUROSAM 1979, Marseille, Lect. Notes Comput. Sci. 72, 3\u201321 (1979).","journal-title":"Proc. EUROSAM 1979, Marseille, Lect. Notes Comput. Sci."},{"key":"14_CR7","unstructured":"Buchberger, B., 82: Miscellaneous Results on Gr\u00f6bner-Bases for Polynomial Ideals II. Technical Report, Dpmt. of Computer and Information Sciences, University of Delaware, to appear (1982)."},{"key":"14_CR8","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1007\/978-3-7091-3406-1_2","volume-title":"Computer Algebra","author":"B. Buchberger","year":"1982","unstructured":"Buchberger, B., Loos, R., 82: Algebraic Simplification. In: Computer Algebra (B. Buchberger, G. Collins, R. Loos eds.), Springer, Wien-New York, 1982, 11\u201343."},{"key":"14_CR9","series-title":"Technical Report","volume-title":"Miscellaneous Results on the Construction of Gr\u00f6bner-Bases for Polynomial Ideals I","author":"B. Buchberger","year":"1979","unstructured":"Buchberger, B., Winkler, F., 79: Miscellaneous Results on the Construction of Gr\u00f6bner-Bases for Polynomial Ideals I. Technical Report Nr. 137, Mathematisches Institut, Universit\u00e4t Linz, Austria (1979)."},{"key":"14_CR10","doi-asserted-by":"crossref","unstructured":"Cardoza, E., Lipton, R., Meyer, A.R., 76: Exponential Space Complete Problems for Petri Nets and Commutative Semigroups. Conf. Record of the 8th Annual ACM Symp. on Theory of Computing, 50\u201354 (1976).","DOI":"10.1145\/800113.803630"},{"key":"14_CR11","unstructured":"Guiver, J.P., 82: Contributions to Two-Dimensional System Theory. Univ. of Pittsburgh, Math. Depmt.: Ph.D. Thesis 1982."},{"key":"14_CR12","doi-asserted-by":"crossref","first-page":"736","DOI":"10.1007\/BF01206635","volume":"95","author":"G. Hermann","year":"1926","unstructured":"Hermann, G., 26: Die Frage der endlich vielen Schritte in der Theorie der Polynomideale. Math. Ann. 95, 736\u2013788 (1926).","journal-title":"Math. Ann."},{"key":"14_CR13","unstructured":"Lazard, D., 83: Gr\u00f6bner bases, Gaussian Elimination and Resolution of Systems of Algebraic Equations. These proceedings."},{"key":"14_CR14","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1007\/978-3-7091-3406-1_9","volume-title":"Computer Algebra","author":"R. Loos","year":"1982","unstructured":"Loos, R., 82: Generalized Polynomial Remainder Sequences. In: Computer Algebra (B. Buchberger, G. Collins, R. Loos eds.), Springer, Wien-New York, 1982, 115\u2013137."},{"key":"14_CR15","unstructured":"Mayr, E.W., Meyer, A.R., 81: The Complexity of the Word Problems for Commutative Semigroups and Polynomial Ideals. M.I.T.: Lab. Comput. Sci. Rep. LCS\/TM-199 (1981)."},{"key":"14_CR16","doi-asserted-by":"crossref","unstructured":"Pohst, M., Yun, D.Y.Y., 81: On Solving Systems of Algebraic Equations Via Ideal Bases and Elimination Theory SYMSAC 1981, 206\u2013211.","DOI":"10.1145\/800206.806397"},{"key":"14_CR17","doi-asserted-by":"crossref","unstructured":"Sakata, S., 81: On Determining the Independent Point Set for Doubly Periodic Arrays and Encoding Two-Dimensional Cyclic Codes and Their Duals. IEEE Trans. on Information Theory, IT-27\/5, 556\u2013565.","DOI":"10.1109\/TIT.1981.1056396"},{"key":"14_CR18","unstructured":"Schaller, S., 79: Algorithmic Aspects of Polynomial Residue Class Rings. University of Wisconsin, Madison: Ph.D. Thesis, Comput. Sci. Tech. Rep. 370, 1979."},{"key":"14_CR19","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1090\/S0002-9947-1974-0349648-2","volume":"197","author":"A. Seidenberg","year":"1974","unstructured":"Seidenberg, A., 74: Constructions in Algebra. Trans. AMS 197, 273\u2013313 (1974).","journal-title":"Trans. AMS"},{"issue":"4","key":"14_CR20","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1016\/0022-314X(78)90019-7","volume":"10","author":"W. Trinks","year":"1978","unstructured":"Trinks, W., 78: On B. Buchberger's method of Solving Algebraic Equations (German). J. Number Theory 10\/4, 475\u2013488 (1978).","journal-title":"J. Number Theory"}],"container-title":["Lecture Notes in Computer Science","Computer Algebra"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/3-540-12868-9_98.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,11,17]],"date-time":"2020-11-17T15:06:34Z","timestamp":1605625594000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/3-540-12868-9_98"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1983]]},"ISBN":["9783540128687","9783540387565"],"references-count":20,"URL":"https:\/\/doi.org\/10.1007\/3-540-12868-9_98","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[1983]]}}}