{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,4,7]],"date-time":"2024-04-07T01:36:07Z","timestamp":1712453767294},"reference-count":32,"publisher":"Elsevier BV","issue":"2-3","license":[{"start":{"date-parts":[[2004,5,1]],"date-time":"2004-05-01T00:00:00Z","timestamp":1083369600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2013,8,22]],"date-time":"2013-08-22T00:00:00Z","timestamp":1377129600000},"content-version":"vor","delay-in-days":3400,"URL":"https:\/\/www.elsevier.com\/open-access\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Theoretical Computer Science"],"published-print":{"date-parts":[[2004,5]]},"DOI":"10.1016\/j.tcs.2004.01.011","type":"journal-article","created":{"date-parts":[[2004,2,12]],"date-time":"2004-02-12T10:15:06Z","timestamp":1076580906000},"page":"651-669","source":"Crossref","is-referenced-by-count":22,"title":["Numerical factorization of multivariate complex polynomials"],"prefix":"10.1016","volume":"315","author":[{"given":"Andrew J.","family":"Sommese","sequence":"first","affiliation":[]},{"given":"Jan","family":"Verschelde","sequence":"additional","affiliation":[]},{"given":"Charles W.","family":"Wampler","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"issue":"2","key":"10.1016\/j.tcs.2004.01.011_BIB1","doi-asserted-by":"crossref","first-page":"318","DOI":"10.1137\/0222024","article-title":"Factoring rational polynomials over the complex numbers","volume":"22","author":"Bajaj","year":"1993","journal-title":"SIAM J. Comput."},{"key":"10.1016\/j.tcs.2004.01.011_BIB2","series-title":"Proc. 2002 Internat. Symp. on Symbolic and Algebraic Computation (ISSAC 2002)","article-title":"A geometric-numeric algorithm for factoring multivariate polynomials","author":"Corless","year":"2002"},{"key":"10.1016\/j.tcs.2004.01.011_BIB3","series-title":"Proc. 2001 Internat. Symp. on Symbolic and Algebraic Computation (ISSAC 2001)","first-page":"85","article-title":"Towards factoring bivariate approximate polynomials","author":"Corless","year":"2001"},{"key":"10.1016\/j.tcs.2004.01.011_BIB4","series-title":"Computer Algebra Handbook","first-page":"112","article-title":"Hybrid methods","author":"Corless","year":"2002"},{"key":"10.1016\/j.tcs.2004.01.011_BIB5","series-title":"Proc. 2001 Internat. Symp. on Symbolic and Algebraic Computation (ISSAC 2001)","first-page":"137","article-title":"Semi-numerical determination of irreducible branches of a reduced space curve","author":"Galligo","year":"2001"},{"issue":"5","key":"10.1016\/j.tcs.2004.01.011_BIB6","doi-asserted-by":"crossref","first-page":"661","DOI":"10.1006\/jsco.2000.0528","article-title":"Irreducible decomposition of curves","volume":"33","author":"Galligo","year":"2002","journal-title":"J. Symbolic Comput."},{"key":"10.1016\/j.tcs.2004.01.011_BIB7","series-title":"Accuracy and Stability of Numerical Algorithms","author":"Higham","year":"1996"},{"key":"10.1016\/j.tcs.2004.01.011_BIB8","series-title":"Proc. 2000 Internat. Symp. on Symbolic and Algebraic Computation (ISSAC 2000)","first-page":"161","article-title":"Pseudofactors of multivariate polynomials","author":"Huang","year":"2000"},{"key":"10.1016\/j.tcs.2004.01.011_BIB9","series-title":"Analysis of Numerical Methods","author":"Isaacson","year":"1994"},{"issue":"6","key":"10.1016\/j.tcs.2004.01.011_BIB10","doi-asserted-by":"crossref","first-page":"891","DOI":"10.1006\/jsco.2000.0370","article-title":"Challenges of symbolic computation","volume":"29","author":"Kaltofen","year":"2000","journal-title":"J. Symbolic Comput."},{"key":"10.1016\/j.tcs.2004.01.011_BIB11","article-title":"The geometry of the zeroes of a polynomial in a complex variable","volume":"Vol. 3","author":"Marden","year":"1949"},{"issue":"3","key":"10.1016\/j.tcs.2004.01.011_BIB12","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1177\/02783640022066860","article-title":"Singularity analysis and representation of the general Gough\u2013Stewart platform","volume":"19","author":"Mayer St-Onge","year":"2000","journal-title":"Internat. J. Robotics Res."},{"issue":"5","key":"10.1016\/j.tcs.2004.01.011_BIB13","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1177\/027836498900800504","article-title":"Singular configurations of parallel manipulators and Grassmann geometry","volume":"8","author":"Merlet","year":"1999","journal-title":"Internat. J. Robotics Res."},{"key":"10.1016\/j.tcs.2004.01.011_BIB14","series-title":"Parallel Robots","author":"Merlet","year":"2000"},{"issue":"2","key":"10.1016\/j.tcs.2004.01.011_BIB15","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1137\/S0036144595288554","article-title":"Solving a polynomial equation","volume":"39","author":"Pan","year":"1997","journal-title":"SIAM Rev."},{"key":"10.1016\/j.tcs.2004.01.011_BIB16","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1006\/inco.2001.3032","article-title":"Computation of approximate polynomial GCDs and an extension","volume":"167","author":"Pan","year":"2001","journal-title":"Inform. Comput."},{"issue":"169","key":"10.1016\/j.tcs.2004.01.011_BIB17","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1090\/S0025-5718-1985-0771036-6","article-title":"A globally convergent method for simultaneously finding polynomial roots","volume":"44","author":"Pasquini","year":"1985","journal-title":"Math. Comput."},{"key":"10.1016\/j.tcs.2004.01.011_BIB18","doi-asserted-by":"crossref","unstructured":"F. Pernkopf, M.L. Husty, Singularity analysis of spatial Stewart\u2013Gough platforms with planar base and platform, Proc. ASME Design Eng. Tech. Conf. Montreal, Canada, September 30\u2013October 2, 2002.","DOI":"10.1115\/DETC2002\/MECH-34267"},{"key":"10.1016\/j.tcs.2004.01.011_BIB19","unstructured":"D. Rupprecht, Semi-numerical absolute factorization of polynomials with integer coefficients, manuscript."},{"key":"10.1016\/j.tcs.2004.01.011_BIB20","series-title":"Proc. 2001 Internat. Symp. on Symbolic and Algebraic Computation (ISSAC 2001)","first-page":"284","article-title":"Approximate multivariate polynomial factorization based on zero-sum relations","author":"Sasaki","year":"2001"},{"issue":"3","key":"10.1016\/j.tcs.2004.01.011_BIB21","doi-asserted-by":"crossref","first-page":"572","DOI":"10.1006\/jcom.2000.0554","article-title":"Numerical homotopies to compute generic points on positive dimensional algebraic sets","volume":"16","author":"Sommese","year":"2000","journal-title":"J. Complexity"},{"issue":"6","key":"10.1016\/j.tcs.2004.01.011_BIB22","doi-asserted-by":"crossref","first-page":"2022","DOI":"10.1137\/S0036142900372549","article-title":"Numerical decomposition of the solution sets of polynomial systems into irreducible components","volume":"38","author":"Sommese","year":"2001","journal-title":"SIAM J. Numer. Anal."},{"key":"10.1016\/j.tcs.2004.01.011_BIB23","series-title":"Journal of Symbolic Computation: Solving Equations in Algebra, Geometry, and Engineering","first-page":"37","article-title":"Numerical irreducible decomposition using projections from points on the components","volume":"Vol. 286","author":"Sommese","year":"2001"},{"key":"10.1016\/j.tcs.2004.01.011_BIB24","series-title":"Application of Algebraic Geometry to Coding Theory, Physics and Computation, Proc. NATO Conf., Eilat, Israel","first-page":"297","article-title":"Using monodromy to decompose solution sets of polynomial systems into irreducible components","author":"Sommese","year":"2001"},{"issue":"6","key":"10.1016\/j.tcs.2004.01.011_BIB25","doi-asserted-by":"crossref","first-page":"2026","DOI":"10.1137\/S0036142901397101","article-title":"Symmetric functions applied to decomposing solution sets of polynomial systems","volume":"40","author":"Sommese","year":"2002","journal-title":"SIAM J. Numer. Anal."},{"key":"10.1016\/j.tcs.2004.01.011_BIB26","series-title":"Algebraic Geometry, a Volume in Memory of Paolo Francia","first-page":"329","article-title":"A method for tracking singular paths with application to the numerical irreducible decomposition","author":"Sommese","year":"2002"},{"key":"10.1016\/j.tcs.2004.01.011_BIB27","doi-asserted-by":"crossref","unstructured":"A.J. Sommese, J. Verschelde, C.W. Wampler, Advances in polynomial continuation for solving problems in kinematics, in: Proc. ASME Design Engineering Tech. Conf. (CDROM), Paper DETC2002\/MECH-34254, Montreal, Quebec, September 29\u2013October 2, 2002 (A revised version will appear in the ASME Journal of Mechanical Design).","DOI":"10.1115\/DETC2002\/MECH-34254"},{"key":"10.1016\/j.tcs.2004.01.011_BIB28","series-title":"Algebra, Geometry, and Software Systems","first-page":"109","article-title":"Numerical irreducible decomposition using PHCpack","author":"Sommese","year":"2003"},{"key":"10.1016\/j.tcs.2004.01.011_BIB29","unstructured":"A.J. Sommese, J. Verschelde, C.W. Wampler, Introduction to numerical algebraic geometry, in: Graduate School on Systems of Polynomial Equations: From Algebraic Geometry to Industrial Applications, 2003, pp. 229\u2013247 (Organized by A. Dickenstein, I. Emiris, 14\u201325 July 2003, Buenos Aires, Argentina. Notes published by INRIA)."},{"key":"10.1016\/j.tcs.2004.01.011_BIB30","unstructured":"A.J. Sommese, C.W. Wampler, Numerical algebraic geometry, in: J. Renegar, M. Shub, S. Smale (Eds.), The Mathematics of Numerical Analysis, Lectures in Applied Mathematics, Vol. 32, Proc. AMS-SIAM Summer Seminar in Applied Mathematics, Park City, Utah, July 17\u2013August 11, 1995, Park City, UT, 1996, pp. 749\u2013763."},{"issue":"2","key":"10.1016\/j.tcs.2004.01.011_BIB31","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1145\/317275.317286","article-title":"Algorithm 795: PHCpack","volume":"25","author":"Verschelde","year":"1999","journal-title":"ACM Transactions on Mathematical Software"},{"issue":"3","key":"10.1016\/j.tcs.2004.01.011_BIB32","doi-asserted-by":"crossref","first-page":"603","DOI":"10.1006\/jcom.2000.0555","article-title":"Finding a cluster of zeros of univariate polynomials","volume":"16","author":"Yakoubsohn","year":"2000","journal-title":"J. Complexity"}],"container-title":["Theoretical Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S030439750400043X?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S030439750400043X?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2019,2,15]],"date-time":"2019-02-15T03:56:54Z","timestamp":1550203014000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S030439750400043X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,5]]},"references-count":32,"journal-issue":{"issue":"2-3","published-print":{"date-parts":[[2004,5]]}},"alternative-id":["S030439750400043X"],"URL":"http:\/\/dx.doi.org\/10.1016\/j.tcs.2004.01.011","relation":{},"ISSN":["0304-3975"],"issn-type":[{"value":"0304-3975","type":"print"}],"subject":[],"published":{"date-parts":[[2004,5]]}}}