{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,28]],"date-time":"2026-03-28T01:25:46Z","timestamp":1774661146404,"version":"3.50.1"},"reference-count":15,"publisher":"Association for Computing Machinery (ACM)","issue":"3\/4","license":[{"start":{"date-parts":[[2011,1,28]],"date-time":"2011-01-28T00:00:00Z","timestamp":1296172800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Commun. Comput. Algebra"],"published-print":{"date-parts":[[2011,1,28]]},"abstract":"<jats:p>PHCpack is a software package to solve polynomial systems via homotopy continuation methods. In the last twenty years (since the start of the development of PHCpack), the notion of solving a polynomial system by PHCpack evolved from approximating all isolated complex solutions for systems with as many equations as variables into providing tools for a numerical irreducible decomposition. This document provides the outline for a software demonstration highlighting recent additions to the software, such as accepting polynomials with negative exponents and sweeping for real points that lie isolated on complex solution curves.<\/jats:p>","DOI":"10.1145\/1940475.1940524","type":"journal-article","created":{"date-parts":[[2011,2,8]],"date-time":"2011-02-08T13:21:01Z","timestamp":1297171261000},"page":"217-220","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":29,"title":["Polynomial homotopy continuation with PHCpack"],"prefix":"10.1145","volume":"44","author":[{"given":"Jan","family":"Verschelde","sequence":"first","affiliation":[{"name":"University of Illinois at Chicago, Chicago, IL"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2011,1,28]]},"reference":[{"key":"e_1_2_1_1_1","unstructured":"D.J. Bates J.D. Hauenstein A.J. Sommese and C.W. Wampler. Bertini: Software for numerical algebraic geometry. Available at http:\/\/www.nd.edu\/?sommese\/bertini\/.  D.J. Bates J.D. Hauenstein A.J. Sommese and C.W. Wampler. Bertini: Software for numerical algebraic geometry. Available at http:\/\/www.nd.edu\/?sommese\/bertini\/."},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1006\/jsco.1995.1041"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/1114268.1114274"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1006\/jsco.2000.0369"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00607-003-0032-4"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00607-008-0015-6"},{"key":"e_1_2_1_7_1","unstructured":"A. Leykin. Numerical algebraic geometry for Macaulay2. arXiv:0911.1783v1 {math.AG}.  A. Leykin. Numerical algebraic geometry for Macaulay2. arXiv:0911.1783v1 {math.AG}."},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1007\/11832225_35"},{"key":"e_1_2_1_9_1","doi-asserted-by":"crossref","unstructured":"T.\n       \n      Mizutani\n     and \n      \n      \n      A.\n       \n      Takeda\n      \n  \n  . \n  DEMiCs: A software package for computing the mixed\n   volume via dynamic enumeration of all mixed cells. In M.E. Stillman N. Takayama and J. Verschelde editors Software for Algebraic Geometry volume \n  148\n   of \n  The IMA Volumes in Mathematics and its Applications pages \n  59\n  --\n  79\n  . \n  Springer-Verlag 2008\n  . Software at http:\/\/www.is.titech.ac.jp\/?mizutan8\/DEMiCs.  T. Mizutani and A. Takeda. DEMiCs: A software package for computing the mixed volume via dynamic enumeration of all mixed cells. In M.E. Stillman N. Takayama and J. Verschelde editors Software for Algebraic Geometry volume 148 of The IMA Volumes in Mathematics and its Applications pages 59--79. Springer-Verlag 2008. Software at http:\/\/www.is.titech.ac.jp\/?mizutan8\/DEMiCs.","DOI":"10.1007\/978-0-387-78133-4_5"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.5555\/1717962"},{"key":"e_1_2_1_11_1","volume-title":"Springer-Verlag","author":"Sommese A.J.","year":"2003"},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1142\/5763"},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1145\/1186785.1186789"},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1145\/317275.317286"},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1145\/347837.347885"}],"container-title":["ACM Communications in Computer Algebra"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1940475.1940524","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1940475.1940524","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T10:52:55Z","timestamp":1750243975000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1940475.1940524"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,1,28]]},"references-count":15,"journal-issue":{"issue":"3\/4","published-print":{"date-parts":[[2011,1,28]]}},"alternative-id":["10.1145\/1940475.1940524"],"URL":"https:\/\/doi.org\/10.1145\/1940475.1940524","relation":{},"ISSN":["1932-2240"],"issn-type":[{"value":"1932-2240","type":"print"}],"subject":[],"published":{"date-parts":[[2011,1,28]]},"assertion":[{"value":"2011-01-28","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}