{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,5]],"date-time":"2024-09-05T15:09:22Z","timestamp":1725548962648},"publisher-location":"Berlin, Heidelberg","reference-count":14,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540249986"},{"type":"electronic","value":"9783540318569"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2005]]},"DOI":"10.1007\/978-3-540-31856-9_20","type":"book-chapter","created":{"date-parts":[[2010,3,2]],"date-time":"2010-03-02T13:06:19Z","timestamp":1267535179000},"page":"244-255","source":"Crossref","is-referenced-by-count":3,"title":["Computing Minimal Multi-homogeneous B\u00e9zout Numbers Is Hard"],"prefix":"10.1007","author":[{"given":"Gregorio","family":"Malajovich","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Klaus","family":"Meer","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"volume-title":"Handbook of mathematical functions with formulas, graphs, and mathematical tables","year":"1992","key":"20_CR1","unstructured":"Abramowitz, M., Stegun, I.A. (eds.): Handbook of mathematical functions with formulas, graphs, and mathematical tables. Dover Publications Inc., New York (1992)"},{"key":"20_CR2","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-58412-1","volume-title":"Complexity and approximation","author":"G. Ausiello","year":"1999","unstructured":"Ausiello, G., Crescenzi, P., Gambosi, G., Kann, V., Marchetti-Spaccamela, A., Protasi, M.: Complexity and approximation. Springer, Berlin (1999)"},{"key":"20_CR3","doi-asserted-by":"crossref","unstructured":"Bernstein, D.N.: The number of roots of a system of equations (in russian). Funkcional. Anal. i Prilo\u017een.\u00a09(3) (1975)","DOI":"10.1007\/BF01075595"},{"key":"20_CR4","unstructured":"Dedieu, J.P., Malajovich, G., Shub, M.: On the curvature of the central path of linear programming theory (2003) (preprint)"},{"issue":"267","key":"20_CR5","first-page":"179","volume":"44, 3","author":"L.G. Khachiyan","year":"1989","unstructured":"Khachiyan, L.G.: The problem of calculating the volume of a polyhedron is enumeratively hard (in Russian). Uspekhi Mat. Nauk\u00a044, 3(267), 179\u2013180 (1989)","journal-title":"Uspekhi Mat. Nauk"},{"key":"20_CR6","doi-asserted-by":"publisher","first-page":"233","DOI":"10.1007\/BF01075534","volume":"10","author":"A.G. Kushnirenko","year":"1976","unstructured":"Kushnirenko, A.G.: Newton Polytopes and the B\u00e9zout Theorem. Funct. Anal. Appl.\u00a010, 233\u2013235 (1976)","journal-title":"Funct. Anal. Appl."},{"key":"20_CR7","doi-asserted-by":"publisher","first-page":"399","DOI":"10.1017\/S0962492900002749","volume":"6","author":"T.Y. Li","year":"1997","unstructured":"Li, T.Y.: Numerical solution of multivariate polynomial systems by homotopy continuation methods. Acta numerica\u00a06, 399\u2013436 (1997)","journal-title":"Acta numerica"},{"issue":"234","key":"20_CR8","doi-asserted-by":"publisher","first-page":"767","DOI":"10.1090\/S0025-5718-00-01303-X","volume":"70","author":"T. Li","year":"2001","unstructured":"Li, T., Bai, F.: Minimizing multi-homogeneous B\u00e9zout numbers by a local search method. Math. Comp.\u00a070(234), 767\u2013787 (2001)","journal-title":"Math. Comp."},{"issue":"1","key":"20_CR9","doi-asserted-by":"publisher","first-page":"237","DOI":"10.1016\/S0096-3003(02)00540-4","volume":"146","author":"T. Li","year":"2003","unstructured":"Li, T., Lin, Z., Bai, F.: Heuristic methods for computing the minimal multi-homogeneous B\u00e9zout number. Appl. Math. Comput.\u00a0146(1), 237\u2013256 (2003)","journal-title":"Appl. Math. Comput."},{"key":"20_CR10","volume-title":"Solving polynomial systems using continuation for engineering and scientific problems","author":"A. Morgan","year":"1987","unstructured":"Morgan, A.: Solving polynomial systems using continuation for engineering and scientific problems. Prentice Hall Inc., Englewood Cliffs (1987)"},{"issue":"2","key":"20_CR11","doi-asserted-by":"publisher","first-page":"101","DOI":"10.1016\/0096-3003(87)90063-4","volume":"24","author":"A. Morgan","year":"1987","unstructured":"Morgan, A., Sommese, A.: A homotopy for solving general polynomial systems that respects m-homogeneous structures. Appl. Math. Comput.\u00a024(2), 101\u2013113 (1987)","journal-title":"Appl. Math. Comput."},{"key":"20_CR12","volume-title":"Basic algebraic geometry","author":"I.R. Shafarevich","year":"1977","unstructured":"Shafarevich, I.R.: Basic algebraic geometry, Springer Study Edition. Springer, Berlin (1977)"},{"key":"20_CR13","doi-asserted-by":"publisher","first-page":"59","DOI":"10.1115\/1.2912579","volume":"112","author":"C. Wampler","year":"1990","unstructured":"Wampler, C., Morgan, A., Sommese, A.: Numerical continuation methods for solving polynomial systems arising in kinematics. Journal Mechanical Design\u00a0112, 59\u201368 (1990)","journal-title":"Journal Mechanical Design"},{"issue":"2","key":"20_CR14","doi-asserted-by":"publisher","first-page":"660","DOI":"10.1006\/jcom.2001.0610","volume":"18","author":"A.G. Werschulz","year":"2002","unstructured":"Werschulz, A.G., Wo\u017aniakowski, H.: What is the complexity of volume calculation? Journal of Complexity\u00a018(2), 660\u2013678 (2002)","journal-title":"Journal of Complexity"}],"container-title":["Lecture Notes in Computer Science","STACS 2005"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-540-31856-9_20.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,11,18]],"date-time":"2020-11-18T23:29:45Z","timestamp":1605742185000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-540-31856-9_20"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005]]},"ISBN":["9783540249986","9783540318569"],"references-count":14,"URL":"https:\/\/doi.org\/10.1007\/978-3-540-31856-9_20","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2005]]}}}