{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,4]],"date-time":"2024-09-04T22:54:24Z","timestamp":1725490464070},"publisher-location":"Berlin, Heidelberg","reference-count":21,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540751861"},{"type":"electronic","value":"9783540751878"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"DOI":"10.1007\/978-3-540-75187-8_24","type":"book-chapter","created":{"date-parts":[[2007,9,1]],"date-time":"2007-09-01T15:13:38Z","timestamp":1188659618000},"page":"316-327","source":"Crossref","is-referenced-by-count":0,"title":["Ruppert Matrix as Subresultant Mapping"],"prefix":"10.1007","author":[{"given":"Kosaku","family":"Nagasaka","sequence":"first","affiliation":[]}],"member":"297","reference":[{"key":"24_CR1","doi-asserted-by":"publisher","first-page":"801","DOI":"10.1090\/S0025-5718-02-01428-X","volume":"72","author":"S. Gao","year":"2003","unstructured":"Gao, S.: Factoring multivariate polynomials via partial differential equations. Math. Comp.\u00a072, 801\u2013822 (2003)","journal-title":"Math. Comp."},{"key":"24_CR2","doi-asserted-by":"publisher","first-page":"4","DOI":"10.1145\/1005285.1005289","volume-title":"ISSAC 2004","author":"F.A. Salem","year":"2004","unstructured":"Salem, F.A., Gao, S., Lauder, A.G.B.: Factoring polynomials via polytopes. In: ISSAC 2004, pp. 4\u201311. ACM, New York (2004)"},{"key":"24_CR3","doi-asserted-by":"publisher","first-page":"167","DOI":"10.1016\/S0022-314X(01)92763-5","volume":"95","author":"M. Hoeij van","year":"2002","unstructured":"van Hoeij, M.: Factoring polynomials and the knapsack problem. J. Number Theory\u00a095, 167\u2013189 (2002)","journal-title":"J. Number Theory"},{"key":"24_CR4","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1145\/1005285.1005300","volume-title":"ISSAC 2004","author":"G. Ch\u00e8ze","year":"2004","unstructured":"Ch\u00e8ze, G.: Absolute polynomial factorization in two variables and the knapsack problem. In: ISSAC 2004, pp. 87\u201394. ACM, New York (2004)"},{"key":"24_CR5","doi-asserted-by":"crossref","unstructured":"Sasaki, T.: Approximate multivariate polynomial factorization based on zero-sum relations. In: ISSAC 2001. Proceedings of the 2001 International Symposium on Symbolic and Algebraic Computation, pp. 284\u2013291 (2001)","DOI":"10.1145\/384101.384139"},{"key":"24_CR6","doi-asserted-by":"crossref","unstructured":"Gao, S., Kaltofen, E., May, J., Yang, Z., Zhi, L.: Approximate factorization of multivariate polynomials via differential equations. In: ISSAC 2004. Proceedings of the 2004 International Symposium on Symbolic and Algebraic Computation, pp. 167\u2013174 (2004)","DOI":"10.1145\/1005285.1005311"},{"key":"24_CR7","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1145\/1145768.1145783","volume-title":"ISSAC 2006","author":"H. Cheng","year":"2006","unstructured":"Cheng, H., Labahn, G.: On computing polynomial gcds in alternate bases. In: ISSAC 2006. Proceedings of the 2006 international symposium on Symbolic and algebraic computation, pp. 47\u201354. ACM Press, New York, NY, USA (2006)"},{"key":"24_CR8","doi-asserted-by":"publisher","first-page":"126","DOI":"10.2307\/2689124","volume":"42","author":"M.A. Laidacker","year":"1969","unstructured":"Laidacker, M.A.: Another theorem relating Sylvester\u2019s matrix and the greatest common divisor. Math. Mag.\u00a042, 126\u2013128 (1969)","journal-title":"Math. Mag."},{"key":"24_CR9","doi-asserted-by":"publisher","first-page":"3394","DOI":"10.1109\/TSP.2004.837413","volume":"52","author":"R.M. Corless","year":"2004","unstructured":"Corless, R.M., Watt, S.M., Zhi, L.: QR factoring to compute the GCD of univariate approximate polynomials. IEEE Trans. Signal Process\u00a052, 3394\u20133402 (2004)","journal-title":"IEEE Trans. Signal Process"},{"key":"24_CR10","doi-asserted-by":"publisher","first-page":"320","DOI":"10.1145\/1005285.1005331","volume-title":"ISSAC 2004","author":"Z. Zeng","year":"2004","unstructured":"Zeng, Z., Dayton, B.H.: The approximate GCD of inexact polynomials. II. A multivariate algorithm. In: ISSAC 2004, pp. 320\u2013327. ACM, New York (2004)"},{"key":"24_CR11","doi-asserted-by":"publisher","first-page":"169","DOI":"10.1145\/1145768.1145799","volume-title":"ISSAC 2006","author":"E. Kaltofen","year":"2006","unstructured":"Kaltofen, E., Yang, Z., Zhi, L.: Approximate greatest common divisors of several polynomials with linearly constrained coefficients and singular polynomials. In: ISSAC 2006. Proceedings of the 2006 international symposium on Symbolic and algebraic computation, pp. 169\u2013176. ACM Press, New York, NY, USA (2006)"},{"key":"24_CR12","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1006\/inco.2001.3032","volume":"167","author":"V.Y. Pan","year":"2001","unstructured":"Pan, V.Y.: Computation of approximate polynomial GCDs and an extension. Inform. and Comput.\u00a0167, 71\u201385 (2001)","journal-title":"Inform. and Comput."},{"key":"24_CR13","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1007\/BF01195333","volume":"6","author":"T.C.Y. Lee","year":"1995","unstructured":"Lee, T.C.Y., Vanstone, S.A.: Subspaces and polynomial factorizations over finite fields. Appl. Algebra Engrg. Comm. Comput.\u00a06, 147\u2013157 (1995)","journal-title":"Appl. Algebra Engrg. Comm. Comput."},{"key":"24_CR14","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1145\/1060328.1060330","volume":"38","author":"K. Nagasaka","year":"2004","unstructured":"Nagasaka, K.: Towards more accurate separation bounds of empirical polynomials. SIGSAM\/CCA\u00a038, 119\u2013129 (2004)","journal-title":"SIGSAM\/CCA"},{"key":"24_CR15","series-title":"Lecture Notes Ser. Comput.","doi-asserted-by":"crossref","first-page":"288","DOI":"10.1142\/9789812704436_0024","volume-title":"Computer mathematics","author":"L. Zhi","year":"2003","unstructured":"Zhi, L.: Displacement structure in computing approximate GCD of univariate polynomials. In: Computer mathematics. Lecture Notes Ser. Comput., vol.\u00a010, pp. 288\u2013298. World Sci. Publ., River Edge, NJ (2003)"},{"key":"24_CR16","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1016\/S0022-4049(99)00014-6","volume":"139","author":"D. Rupprecht","year":"1999","unstructured":"Rupprecht, D.: An algorithm for computing certified approximate GCD of n univariate polynomials. J. Pure Appl. Algebra\u00a0139, 255\u2013284 (1999)","journal-title":"J. Pure Appl. Algebra"},{"key":"24_CR17","doi-asserted-by":"publisher","first-page":"62","DOI":"10.1006\/jnth.1999.2381","volume":"77","author":"W.M. Ruppert","year":"1999","unstructured":"Ruppert, W.M.: Reducibility of polynomials f(x,y) modulo p. J. Number Theory\u00a077, 62\u201370 (1999)","journal-title":"J. Number Theory"},{"key":"24_CR18","doi-asserted-by":"publisher","first-page":"32","DOI":"10.1016\/S0022-314X(03)00044-1","volume":"101","author":"S. Gao","year":"2003","unstructured":"Gao, S., Rodrigues, V.M.: Irreducibility of polynomials modulo p via newton polytopes. J. Number Theory\u00a0101, 32\u201347 (2003)","journal-title":"J. Number Theory"},{"key":"24_CR19","doi-asserted-by":"crossref","unstructured":"Kaltofen, E., May, J.: On approximate irreducibility of polynomials in several variables. In: ISSAC 2003. Proceedings of the 2003 International Symposium on Symbolic and Algebraic Computation, pp. 161\u2013168 (2003)","DOI":"10.1145\/860854.860893"},{"key":"24_CR20","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"318","DOI":"10.1007\/11555964_27","volume-title":"Computer Algebra in Scientific Computing","author":"K. Nagasaka","year":"2005","unstructured":"Nagasaka, K.: Towards more accurate separation bounds of empirical polynomials II. In: Ganzha, V.G., Mayr, E.W., Vorozhtsov, E.V. (eds.) CASC 2005. LNCS, vol.\u00a03718, pp. 318\u2013329. Springer, Heidelberg (2005)"},{"key":"24_CR21","unstructured":"May, J.P.: Approximate Factorization of Polynomials in Many Variables and Other Problems in Approximate Algebra via Singular Value Decomposition Methods. PhD thesis, North Carolina State Univ., Raleigh, North Carolina (2005)"}],"container-title":["Lecture Notes in Computer Science","Computer Algebra in Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-540-75187-8_24.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,27]],"date-time":"2021-04-27T10:54:46Z","timestamp":1619520886000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-540-75187-8_24"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[null]]},"ISBN":["9783540751861","9783540751878"],"references-count":21,"URL":"https:\/\/doi.org\/10.1007\/978-3-540-75187-8_24","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[]}}