{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T11:04:40Z","timestamp":1776769480117,"version":"3.51.2"},"reference-count":23,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2000,3,1]],"date-time":"2000-03-01T00:00:00Z","timestamp":951868800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2000,3,1]],"date-time":"2000-03-01T00:00:00Z","timestamp":951868800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Advances in Computational Mathematics"],"published-print":{"date-parts":[[2000,3]]},"DOI":"10.1023\/a:1018937723499","type":"journal-article","created":{"date-parts":[[2003,2,19]],"date-time":"2003-02-19T22:07:13Z","timestamp":1045692433000},"page":"335-362","source":"Crossref","is-referenced-by-count":41,"title":["H-bases for polynomial interpolation and system solving"],"prefix":"10.1007","volume":"12","author":[{"given":"H. Michael","family":"M\u00f6ller","sequence":"first","affiliation":[]},{"given":"Thomas","family":"Sauer","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"325383_CR1","doi-asserted-by":"crossref","unstructured":"W.W. Adams and P. Loustauneau, An Introduction to Gr\u00f6bner Bases, Graduate Studies in Mathematics, Vol. 3(Amer. Math. Soc., Providence, RI, 1994).","DOI":"10.1090\/gsm\/003"},{"key":"325383_CR2","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1007\/978-3-0348-6303-2_2","volume":"86","author":"W. Auzinger","year":"1988","unstructured":"W. Auzinger and H.J. Stetter, An elimination algorithm for the computation of all zeros of a system of multivariate polynomial equations, in: International Series in Numerical Mathematics, Vol. 86 (1988) pp. 11\u201330.","journal-title":"International Series in Numerical Mathematics"},{"key":"325383_CR3","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-0913-3","volume-title":"Gr\u00f6bner Bases: A Computational Approach to Commutative Algebra","author":"T. Becker","year":"1993","unstructured":"T. Becker and V. Weispfenning, Gr\u00f6bner Bases: A Computational Approach to Commutative Algebra (Springer, Berlin\/New York, 1993)."},{"key":"325383_CR4","first-page":"345","volume-title":"Constructive Approaches to Mathematical Models","author":"G. Birkhoff","year":"1979","unstructured":"G. Birkhoff, The algebra of multivariate interpolation, in: Constructive Approaches to Mathematical Models, eds. C.V. Coffman and G.J. Fix (Academic Press, New York, 1979) pp. 345\u2013363."},{"key":"325383_CR5","doi-asserted-by":"crossref","unstructured":"B. Buchberger, Gr\u00f6bner bases: An algorithmic method in polynomial ideal theory, in: Multidimensional Systems Theory, ed. N.K. Bose (D. Reidel, 1985) pp. 184\u2013232.","DOI":"10.1007\/978-94-009-5225-6_6"},{"key":"325383_CR6","first-page":"24","volume-title":"Lecture Notes in Computer Science","author":"B. Buchberger","year":"1982","unstructured":"B. Buchberger and H.M. M\u00f6ller, The construction of multivariate polynomials with preassigned zeros, in: Lecture Notes in Computer Science, Vol. 144(Springer, Berlin, 1982) pp. 24\u201331."},{"key":"325383_CR7","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-2181-2","volume-title":"Ideals, Varieties, and Algorithms","author":"D. Cox","year":"1992","unstructured":"D. Cox, J. Little and D. O'shea, Ideals, Varieties, and Algorithms (Springer, New York, 1992)."},{"key":"325383_CR8","doi-asserted-by":"publisher","first-page":"287","DOI":"10.1007\/BF01890412","volume":"6","author":"C. d. Boor","year":"1990","unstructured":"C. de Boor and A. Ron, On multivariate polynomial interpolation, Constr. Approx. 6(1990) 287\u2013302.","journal-title":"Constr. Approx."},{"key":"325383_CR9","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1007\/BF02571803","volume":"210","author":"C. d. Boor","year":"1992","unstructured":"C. de Boor and A. Ron, The least solution for the polynomial interpolation problem, Math. Z. 210 (1992) 347\u2013378.","journal-title":"Math. Z"},{"key":"325383_CR10","volume-title":"Commutative Algebra with a View toward Algebraic Geometry","author":"D. Eisenbud","year":"1995","unstructured":"D. Eisenbud, Commutative Algebra with a View toward Algebraic Geometry (Springer, New York, 1995)."},{"key":"325383_CR11","volume-title":"An Introduction to Gr\u00f6bner Bases","author":"R. Fr\u00f6berg","year":"1997","unstructured":"R. Fr\u00f6berg, An Introduction to Gr\u00f6bner Bases (Wiley, Chichester, 1997)."},{"key":"325383_CR12","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-7091-5740-4","volume-title":"Moderne Algebraische Geometrie","author":"W. Gr\u00f6bner","year":"1949","unstructured":"W. Gr\u00f6bner, Moderne Algebraische Geometrie (Springer, Wien\/Innsbruck, 1949)."},{"key":"325383_CR13","unstructured":"W. Gr\u00f6bner, Algebraische Geometrie II (Bibliographisches Institut, Mannheim\/Wien\/Zfv\u00fcrich, 1970)."},{"key":"325383_CR14","unstructured":"F.S. Macaulay, The Algebraic Theory of Modular Systems, Cambridge Tracts in Mathematics and Mathematical Physics, Vol. 19(Cambridge Univ. Press, 1916)."},{"key":"325383_CR15","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1112\/plms\/s2-26.1.531","volume":"26","author":"F.S. Macaulay","year":"1927","unstructured":"F.S. Macaulay, Some properties of enumeration in the theory of modular systems, Proc. London Math. Soc. 26(1927) 531\u2013555.","journal-title":"Proc. London Math. Soc."},{"key":"325383_CR16","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1007\/BF01214700","volume":"148","author":"H.M. M\u00f6ller","year":"1976","unstructured":"H.M. M\u00f6ller, Mehrdimensionale Hermite-Interpolation und numerische Integration, Math. Z. 148 (1976) 107\u2013118.","journal-title":"Math. Z."},{"key":"325383_CR17","doi-asserted-by":"publisher","first-page":"345","DOI":"10.1016\/S0747-7171(88)80052-X","volume":"6","author":"H.M. M\u00f6ller","year":"1988","unstructured":"H.M. M\u00f6ller, On the construction of Gr\u00f6bner bases using syzygies, J. Symbolic Comput. 6(1988) 345\u2013359.","journal-title":"J. Symbolic Comput."},{"key":"325383_CR18","doi-asserted-by":"crossref","unstructured":"H.M. M\u00f6ller, Gr\u00f6bner bases and Numerical Analysis, in: Groebner Bases and Applications (Proc. of the Conf. 33 Years of Groebner Bases), eds. B. Buchberger and F. Winkler, London Mathematical Society Lecture Notes, Vol. 251(Cambridge University Press, 1998) pp. 159\u2013178.","DOI":"10.1017\/CBO9780511565847.009"},{"key":"325383_CR19","doi-asserted-by":"publisher","first-page":"138","DOI":"10.1016\/0021-8693(86)90071-2","volume":"100","author":"H.M. M\u00f6ller","year":"1986","unstructured":"H.M. M\u00f6ller and F. Mora, New constructive methods in classical ideal theory, J. Algebra 100(1986) 138\u2013178.","journal-title":"J. Algebra"},{"key":"325383_CR20","doi-asserted-by":"publisher","first-page":"311","DOI":"10.1007\/s002110050122","volume":"70","author":"H.M. M\u00f6ller","year":"1995","unstructured":"H.M. M\u00f6ller and H.J. Stetter, Multivariate polynomial equations with multiple zeros solved by matrix eigenproblems, Numer. Math. 70(1995) 311\u2013329.","journal-title":"Numer. Math"},{"key":"325383_CR21","doi-asserted-by":"publisher","first-page":"59","DOI":"10.1007\/s002110050304","volume":"78","author":"T. Sauer","year":"1997","unstructured":"T. Sauer, Polynomial interpolation of minimal degree, Numer. Math. 78(1997) 59\u201385.","journal-title":"Numer. Math"},{"key":"325383_CR22","doi-asserted-by":"crossref","unstructured":"T. Sauer, Polynomial interpolation of minimal degree and Gr\u00f6bner bases, in: Groebner Bases and Applications (Proc. of the Conf. 33 Years of Groebner Bases), eds. B. Buchberger and F. Winkler, London Mathematical Society Lecture Notes, Vol. 251(Cambridge University Press, 1998) pp. 483\u2013494.","DOI":"10.1017\/CBO9780511565847.030"},{"key":"325383_CR23","doi-asserted-by":"crossref","unstructured":"T. Sauer, Gr\u00f6bner bases, H-bases and interpolation, Proc. Amer. Math. Soc. (1999, to appear).","DOI":"10.1090\/S0002-9947-00-02646-5"}],"container-title":["Advances in Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1018937723499.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1023\/A:1018937723499\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1018937723499.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,16]],"date-time":"2025-05-16T23:11:09Z","timestamp":1747437069000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1023\/A:1018937723499"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,3]]},"references-count":23,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2000,3]]}},"alternative-id":["325383"],"URL":"https:\/\/doi.org\/10.1023\/a:1018937723499","relation":{},"ISSN":["1019-7168","1572-9044"],"issn-type":[{"value":"1019-7168","type":"print"},{"value":"1572-9044","type":"electronic"}],"subject":[],"published":{"date-parts":[[2000,3]]}}}