{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T00:21:54Z","timestamp":1740097314912,"version":"3.37.3"},"publisher-location":"Cham","reference-count":39,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319456409"},{"type":"electronic","value":"9783319456416"}],"license":[{"start":{"date-parts":[[2016,1,1]],"date-time":"2016-01-01T00:00:00Z","timestamp":1451606400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2016]]},"DOI":"10.1007\/978-3-319-45641-6_31","type":"book-chapter","created":{"date-parts":[[2016,9,8]],"date-time":"2016-09-08T06:30:29Z","timestamp":1473316229000},"page":"489-503","source":"Crossref","is-referenced-by-count":2,"title":["Pruning Algorithms for Pretropisms of Newton Polytopes"],"prefix":"10.1007","author":[{"given":"Jeff","family":"Sommars","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jan","family":"Verschelde","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2016,9,9]]},"reference":[{"key":"31_CR1","doi-asserted-by":"crossref","unstructured":"Adrovic, D., Verschelde, J.: Computing Puiseux series for algebraic surfaces. In: van der Hoeven, J., van Hoeij, M. (eds.) Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation (ISSAC 2012), pp. 20\u201327. ACM (2012)","DOI":"10.1145\/2442829.2442837"},{"key":"31_CR2","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1007\/978-3-319-02297-0_2","volume-title":"Computer Algebra in Scientific Computing","author":"D Adrovic","year":"2013","unstructured":"Adrovic, D., Verschelde, J.: Polyhedral methods for space curves exploiting symmetry applied to the cyclic n-roots problem. In: Gerdt, V.P., Koepf, W., Mayr, E.W., Vorozhtsov, E.V. (eds.) CASC 2013. LNCS, vol. 8136, pp. 10\u201329. Springer, Heidelberg (2013)"},{"key":"31_CR3","unstructured":"Assarf, B., Gawrilow, E., Herr, K., Joswig, M., Lorenz, B., Paffenholz, A., Rehn, T.: Computing convex hulls and counting integer points with polymake. arXiv:1408.4653v2"},{"issue":"3","key":"31_CR4","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1007\/BF02293050","volume":"8","author":"D Avis","year":"1992","unstructured":"Avis, D., Fukuda, K.: A pivoting algorithm for convex hulls and vertex enumeration of arrangements and polyhedra. Discrete Comput. Geom. 8(3), 295\u2013313 (1992)","journal-title":"Discrete Comput. Geom."},{"key":"31_CR5","unstructured":"Backelin, J.: Square multiples n give infinitely many cyclic n-roots. Reports, Matematiska Institutionen 8, Stockholms universitet (1989)"},{"issue":"1\u20132","key":"31_CR6","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/j.scico.2007.08.001","volume":"72","author":"R Bagnara","year":"2008","unstructured":"Bagnara, R., Hill, P., Zaffanella, E.: The Parma Polyhedral Library: toward a complete set of numerical abstractions for the analysis and verification of hardware and software systems. Sci. Comput. Program. 72(1\u20132), 3\u201321 (2008)","journal-title":"Sci. Comput. Program."},{"issue":"3","key":"31_CR7","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1007\/BF01075595","volume":"9","author":"D Bernshte\u01d0n","year":"1975","unstructured":"Bernshte\u01d0n, D.: The number of roots of a system of equations. Funct. Anal. Appl. 9(3), 183\u2013185 (1975)","journal-title":"Funct. Anal. Appl."},{"key":"31_CR8","first-page":"319","volume":"320","author":"G Bj\u00f6ck","year":"1995","unstructured":"Bj\u00f6ck, G., Saffari, B.: New classes of finite unimodular sequences with unimodular Fourier transforms. Circulant Hadamard matrices with complex entries. C.R. Acad. Sci. Paris S\u00e9rie I 320, 319\u2013324 (1995)","journal-title":"C.R. Acad. Sci. Paris S\u00e9rie I"},{"key":"31_CR9","doi-asserted-by":"crossref","unstructured":"Bliss, N., Verschelde, J.: Computing all space curve solutions of polynomial systems by polyhedral methods. In: Gerdt, V.P., Koepf, W., Seiler, W.M., Vorozhtsov, E.V. (eds.) CASC 2016. LNCS, vol. 9890, pp. 73\u201386. Springer, Heidelberg (2016)","DOI":"10.1007\/978-3-319-45641-6_6"},{"issue":"1","key":"31_CR10","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1016\/j.jsc.2006.02.004","volume":"42","author":"T Bogart","year":"2007","unstructured":"Bogart, T., Jensen, A., Speyer, D., Sturmfels, B., Thomas, R.: Computing tropical varieties. J. Symbolic Comput. 42(1), 54\u201373 (2007)","journal-title":"J. Symbolic Comput."},{"key":"31_CR11","unstructured":"Braun, V., Hampton, M.: Polyhedra module of Sage, The Sage Development Team (2011)"},{"key":"31_CR12","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1007\/978-3-0348-8438-9_6","volume-title":"Polytopes -Combinatorics and Computation, DMV Seminar","author":"B B\u00fceler","year":"2000","unstructured":"B\u00fceler, B., Enge, A., Fukuda, K.: Exact volume computation for polytopes:a practical study. In: Kalai, G., Ziegler, G. (eds.) Polytopes -Combinatorics and Computation, DMV Seminar, vol. 29, pp. 131\u2013154. Springer, Heidelberg (2000)"},{"key":"31_CR13","series-title":"Algorithms and Computation in Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-12971-1","volume-title":"Triangulations, Structures for Algorithms and Applications","author":"J Loera De","year":"2010","unstructured":"De Loera, J., Rambau, J., Santos, F.: Triangulations, Structures for Algorithms and Applications. Algorithms and Computation in Mathematics, vol. 25. Springer, Heidelberg (2010)"},{"key":"31_CR14","unstructured":"Emiris, I.: Sparse Elimination and Applications in Kinematics. Ph.D. thesis, University of California at Berkeley, Berkeley (1994)"},{"issue":"2","key":"31_CR15","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1006\/jsco.1995.1041","volume":"20","author":"I Emiris","year":"1995","unstructured":"Emiris, I., Canny, J.: Efficient incremental algorithms for the sparse resultant and the mixed volume. J. Symbolic Comput. 20(2), 117\u2013149 (1995)","journal-title":"J. Symbolic Comput."},{"key":"31_CR16","doi-asserted-by":"crossref","unstructured":"Emiris, I., Fisikopoulos, V.: Efficient random-walk methods for approximating polytope volume. In: Proceedings of the Thirtieth Annual Symposium on Computational Geometry (SoCG 2014), pp. 318\u2013327. ACM (2014)","DOI":"10.1145\/2582112.2582133"},{"key":"31_CR17","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1016\/j.jsc.2015.06.001","volume":"73","author":"I Emiris","year":"2016","unstructured":"Emiris, I., Fisikopoulos, V., G\u00e4rtner, B.: Efficient edge-skeleton computation for polytopes defined by oracles. J. Symbolic Comput. 73, 139\u2013152 (2016)","journal-title":"J. Symbolic Comput."},{"key":"31_CR18","unstructured":"Emiris, I., Fisikopoulos, V., Konaxis, C.: Exact and approximate algorithms for resultant polytopes. In: Proceedings of the 28th European Workshop on Computational Geometry (EuroCG 2012) (2012)"},{"key":"31_CR19","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1016\/j.laa.2015.06.019","volume":"484","author":"H F\u00fchr","year":"2015","unstructured":"F\u00fchr, H., Rzeszotnik, Z.: On biunimodular vectors for unitary matrices. Linear Algebra Appl. 484, 86\u2013129 (2015)","journal-title":"Linear Algebra Appl."},{"key":"31_CR20","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1007\/3-540-61576-8_77","volume-title":"Combinatorics and Computer Science","author":"K Fukuda","year":"1996","unstructured":"Fukuda, K., Prodon, A.: Double description method revisited. In: Deza, M., Manoussakis, I., Euler, R. (eds.) CCS 1995. LNCS, vol. 1120, pp. 91\u2013111. Springer, Heidelberg (1996)"},{"issue":"2","key":"31_CR21","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1007\/s00454-002-2837-x","volume":"29","author":"T Gao","year":"2003","unstructured":"Gao, T., Li, T.: Mixed volume computation for semi-mixed systems. Discrete Comput. Geom. 29(2), 257\u2013277 (2003)","journal-title":"Discrete Comput. Geom."},{"issue":"4","key":"31_CR22","doi-asserted-by":"crossref","first-page":"555","DOI":"10.1145\/1114268.1114274","volume":"31","author":"T Gao","year":"2005","unstructured":"Gao, T., Li, T., Wu, M.: Algorithm 846: MixedVol: a software package for mixed-volume computation. ACM Trans. Math. Softw. 31(4), 555\u2013560 (2005)","journal-title":"ACM Trans. Math. Softw."},{"issue":"1","key":"31_CR23","doi-asserted-by":"crossref","first-page":"35","DOI":"10.3934\/jgm.2015.7.35","volume":"7","author":"M Hampton","year":"2015","unstructured":"Hampton, M., Jensen, A.: Finiteness of relative equilibria in the planar generalized n-body problem with fixed subconfigurations. J. Geom. Mech. 7(1), 35\u201342 (2015)","journal-title":"J. Geom. Mech."},{"issue":"3","key":"31_CR24","doi-asserted-by":"crossref","first-page":"1317","DOI":"10.1090\/S0002-9947-08-04685-0","volume":"361","author":"M Hampton","year":"2009","unstructured":"Hampton, M., Moeckel, R.: Finiteness of stationary configurations of the four-vortex problem. Trans. Am. Math. Soci. 361(3), 1317\u20131332 (2009)","journal-title":"Trans. Am. Math. Soci."},{"key":"31_CR25","unstructured":"Jensen, A.: Gfan, a software system for Gr\u00f6bner fans and tropical varieties. http:\/\/home.imf.au.dk\/jensen\/software\/gfan\/gfan.html"},{"key":"31_CR26","series-title":"The IMA Volumes in Mathematics and its Applications","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1007\/978-0-387-78133-4_3","volume-title":"Software for Algebraic Geometry","author":"A Jensen","year":"2008","unstructured":"Jensen, A.: Computing Gr\u00f6bner fans and tropical varieties in Gfan. In: Stillman, M., Takayama, N., Verschelde, J. (eds.) Software for Algebraic Geometry. The IMA Volumes in Mathematics and its Applications, vol. 148, pp. 33\u201346. Springer, Heidelberg (2008)"},{"key":"31_CR27","doi-asserted-by":"crossref","DOI":"10.1090\/gsm\/161","volume-title":"Introduction to Tropical Geometry, Graduate Studies in Mathematics","author":"D Maclagan","year":"2015","unstructured":"Maclagan, D., Sturmfels, B.: Introduction to Tropical Geometry, Graduate Studies in Mathematics, vol. 161. American Mathematical Society, Providence (2015)"},{"key":"31_CR28","doi-asserted-by":"crossref","unstructured":"Malajovich, G.: Computing mixed volume and all mixed cells in quermassintegral time, to appear in Found. Comput. Math. http:\/\/dx.doi.org\/10.1007\/s10208-016-9320-1","DOI":"10.1007\/s10208-016-9320-1"},{"key":"31_CR29","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1007\/BF01298184","volume":"32","author":"J Maurer","year":"1980","unstructured":"Maurer, J.: Puiseux expansion for space curves. Manuscripta Math. 32, 91\u2013100 (1980)","journal-title":"Manuscripta Math."},{"key":"31_CR30","series-title":"The IMA Volumes in Mathematics and Its Applications","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1007\/978-0-387-78133-4_5","volume-title":"Software for Algebraic Geometry","author":"T Mizutani","year":"2008","unstructured":"Mizutani, T., Takeda, A.: DEMiCs: a software package for computing the mixed volume via dynamic enumeration of all mixed cells. In: Stillman, M., Takayama, N., Verschelde, J. (eds.) Software for Algebraic Geometry. The IMA Volumes in Mathematics and Its Applications, vol. 148, pp. 59\u201379. Springer, New York (2008)"},{"issue":"3","key":"31_CR31","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1007\/s00454-006-1300-9","volume":"37","author":"T Mizutani","year":"2007","unstructured":"Mizutani, T., Takeda, A., Kojima, M.: Dynamic enumeration of all mixed cells. Discrete Comput. Geom. 37(3), 351\u2013367 (2007)","journal-title":"Discrete Comput. Geom."},{"key":"31_CR32","unstructured":"Novoseltsev, A.: lattice_polytope module of Sage, The Sage Development Team (2011)"},{"key":"31_CR33","unstructured":"R Development Core Team: R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria (2008). http:\/\/www.R-project.org , ISBN 3-900051-07-0"},{"key":"31_CR34","unstructured":"Sommars, J., Verschelde, J.: Exact gift wrapping to prune the tree of edges of Newton polytopes to compute pretropisms. arXiv:1512.01594"},{"key":"31_CR35","unstructured":"Sommars, J., Verschelde, J.: Computing pretropisms for the cyclic n-roots problem. In: 32nd European Workshop on Computational Geometry (EuroCG 2016), pp. 235\u2013238 (2016)"},{"key":"31_CR36","unstructured":"Stein, W., et al.: Sage Mathematics Software (Version 6.9). The Sage Development Team (2015). http:\/\/www.sagemath.org"},{"issue":"2","key":"31_CR37","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1145\/317275.317286","volume":"25","author":"J Verschelde","year":"1999","unstructured":"Verschelde, J.: Algorithm 795: PHCpack: a general-purpose solver for polynomial systems by homotopy continuation. ACM Trans. Math. Softw. 25(2), 251\u2013276 (1999)","journal-title":"ACM Trans. Math. Softw."},{"key":"31_CR38","doi-asserted-by":"crossref","unstructured":"Verschelde, J.: Polyhedral methods in numerical algebraic geometry. In: Bates, D., Besana, G., Di Rocco, S., Wampler, C. (eds.) Interactions of Classical and Numerical Algebraic Geometry, Contemporary Mathematics, vol. 496, pp. 243\u2013263. AMS (2009)","DOI":"10.1090\/conm\/496\/09727"},{"key":"31_CR39","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4613-8431-1","volume-title":"Lectures on Polytopes, Graduate Texts in Mathematics","author":"G Ziegler","year":"1995","unstructured":"Ziegler, G.: Lectures on Polytopes, Graduate Texts in Mathematics, vol. 152. Springer, New York (1995)"}],"container-title":["Lecture Notes in Computer Science","Computer Algebra in Scientific Computing"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-45641-6_31","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,13]],"date-time":"2019-09-13T04:12:41Z","timestamp":1568347961000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-319-45641-6_31"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016]]},"ISBN":["9783319456409","9783319456416"],"references-count":39,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-45641-6_31","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2016]]}}}