{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,1,4]],"date-time":"2024-01-04T16:01:51Z","timestamp":1704384111963},"reference-count":23,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2018,10,12]],"date-time":"2018-10-12T00:00:00Z","timestamp":1539302400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Math.Comput.Sci."],"published-print":{"date-parts":[[2019,6]]},"DOI":"10.1007\/s11786-018-0387-8","type":"journal-article","created":{"date-parts":[[2018,10,12]],"date-time":"2018-10-12T05:51:17Z","timestamp":1539323477000},"page":"79-93","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["On Multivariate Hermitian Quadratic Forms"],"prefix":"10.1007","volume":"13","author":[{"given":"Ryoya","family":"Fukasaku","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hidenao","family":"Iwane","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yosuke","family":"Sato","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2018,10,12]]},"reference":[{"key":"387_CR1","doi-asserted-by":"crossref","unstructured":"Arai, N.H., Matsuzaki, T., Iwane, H., Anai, H.: Mathematics by machine. In: Proceedings of International Symposium on Symbolic and Algebraic Computation, pp. 1\u20138, ACM-Press (2014)","DOI":"10.1145\/2608628.2627488"},{"key":"387_CR2","doi-asserted-by":"crossref","unstructured":"Becker, E., W\u00f6rmann, T.: On the trace formula for quadratic forms. In: Proceedings of Recent Advances in Real Algebraic Geometry and Quadratic Forms, Contemporary Mathematics, vol. 155, pp. 271\u2013291. American Mathematical Society (1994)","DOI":"10.1090\/conm\/155\/01385"},{"key":"387_CR3","unstructured":"Brown, C., et al.: QEPCAD. \n                    https:\/\/urldefense.proofpoint.com\/v2\/url?u=https-3A__www.usna.edu_CS_qepcadweb_B_QEPCAD.html&d=DwICAg&c=vh6FgFnduejNhPPD0fl_yRaSfZy8CWbWnIf4XJhSqx8&r=UpNksRRkQEKvUbblp9QRYTuemGLwQgpW1U7iMCFPZ8k&m=mWR4kwzCQJx99sfByc_Wd_NtOKrvA94px0mf4a_qj_8&s=fs72Aj2MHHkrUbt5MXeOF0B3iyfTQkLWYjPboUB-RSA&e=\n                    \n                  . Accessed 8 Oct 2017"},{"key":"387_CR4","unstructured":"Fukasaku, R.: 2016 Version of CGSQE Package. \n                    https:\/\/urldefense.proofpoint.com\/v2\/url?u=http-3A__www.rs.tus.ac.jp_fukasaku_software_CGSQE-2D20160509_&d=DwICAg&c=vh6FgFnduejNhPPD0fl_yRaSfZy8CWbWnIf4XJhSqx8&r=UpNksRRkQEKvUbblp9QRYTuemGLwQgpW1U7iMCFPZ8k&m=mWR4kwzCQJx99sfByc_Wd_NtOKrvA94px0mf4a_qj_8&s=ExGbD7jMK0fzhZjaF_9DQ2vYfqv6alRkPjcYhRzkADk&e=\n                    \n                  . Accessed 8 Oct 2017"},{"key":"387_CR5","unstructured":"Fukasaku, R.: 2017 Version of CGSQE Package. \n                    https:\/\/urldefense.proofpoint.com\/v2\/url?u=http-3A__www.rs.tus.ac.jp_fukasaku_software_CGSQE-2D2017_&d=DwICAg&c=vh6FgFnduejNhPPD0fl_yRaSfZy8CWbWnIf4XJhSqx8&r=UpNksRRkQEKvUbblp9QRYTuemGLwQgpW1U7iMCFPZ8k&m=mWR4kwzCQJx99sfByc_Wd_NtOKrvA94px0mf4a_qj_8&s=E-8Gmc7etlgpy1LN6yFA1qKUNLLB65V2URmVednn2Rg&e=\n                    \n                  . Accessed 8 Oct 2017"},{"key":"387_CR6","doi-asserted-by":"crossref","unstructured":"Collins, G.E.: Quantifier elimination for real closed fields by cylindrical algebraic decomposition. In: Proceedings of Automata Theory and Formal Languages, LNCS vol. 33, pp. 134\u2013183. Springer, Berlin (1975)","DOI":"10.1007\/3-540-07407-4_17"},{"key":"387_CR7","doi-asserted-by":"crossref","unstructured":"Fukasaku, R.: QE software based on comprehensive Gr\u00f6bner systems. In: Proceedings of Mathematical Software\u2014ICMS 2014\u20144th International Congress, LNCS vol. 8592, pp. 512\u2013517. Springer, Berlin (2014)","DOI":"10.1007\/978-3-662-44199-2_77"},{"key":"387_CR8","doi-asserted-by":"crossref","unstructured":"Fukasaku, R., Iwane, H., Sato, Y: Real quantifier elimination by computation of comprehensive Gr\u00f6bner systems. In: Proceedings of International Symposium on Symbolic and Algebraic Computation, pp. 173\u2013180. ACM-Press (2015)","DOI":"10.1145\/2755996.2756646"},{"key":"387_CR9","doi-asserted-by":"crossref","unstructured":"Fukasaku, R., Iwane, H., Sato, Y: On the Implementation of CGS Real QE. In: Proceedings of Mathematical Software\u2014ICMS 2016\u20145th International Conference, LNCS vol. 9725, pp. 165\u2013172. Springer, Berlin (2016)","DOI":"10.1007\/978-3-319-42432-3_21"},{"key":"387_CR10","unstructured":"Iwane, H.: SyNRAC Package. \n                    https:\/\/urldefense.proofpoint.com\/v2\/url?u=http-3A__www.fujitsu.com_jp_group_labs_en_resources_tech_freeware_synrac_&d=DwICAg&c=vh6FgFnduejNhPPD0fl_yRaSfZy8CWbWnIf4XJhSqx8&r=UpNksRRkQEKvUbblp9QRYTuemGLwQgpW1U7iMCFPZ8k&m=mWR4kwzCQJx99sfByc_Wd_NtOKrvA94px0mf4a_qj_8&s=ohEYZdyMb9fiZ7ajsP8WnI6QvqhisstydbZQtD1hGkM&e=\n                    \n                  . Accessed 8 Oct 2017"},{"key":"387_CR11","doi-asserted-by":"crossref","unstructured":"Kapur, D., Sun, Y., Wang, D.: A new algorithm for computing comprehensive Gr\u00f6bner systems. In: Proceedings of International Symposium on Symbolic and Algebraic Computation, pp. 29\u201336. ACM-Press (2010)","DOI":"10.1145\/1837934.1837946"},{"key":"387_CR12","first-page":"39","volume":"1","author":"Y Kurata","year":"2011","unstructured":"Kurata, Y.: Improving Suzuki\u2013Sato\u2019s CGS algorithm by using stability of Gr\u00f6bner bases and basic manipulations for efficient implementation. Commun. Jpn. Soc. Symb. Algebr. Comput. 1, 39\u201366 (2011)","journal-title":"Commun. Jpn. Soc. Symb. Algebr. Comput."},{"key":"387_CR13","unstructured":"Maza, M.-M. et al.: RegularChains Package. \n                    https:\/\/urldefense.proofpoint.com\/v2\/url?u=http-3A__www.regularchains.org_&d=DwICAg&c=vh6FgFnduejNhPPD0fl_yRaSfZy8CWbWnIf4XJhSqx8&r=UpNksRRkQEKvUbblp9QRYTuemGLwQgpW1U7iMCFPZ8k&m=mWR4kwzCQJx99sfByc_Wd_NtOKrvA94px0mf4a_qj_8&s=NJ2uBtKt_hCxEF7lQWZjZVvTVQSMTWIHFjDD-FsbidA&e=\n                    \n                  . Accessed 8 Oct 2017"},{"key":"387_CR14","doi-asserted-by":"crossref","unstructured":"Nabeshima, K.: A speed-up of the algorithm for computing comprehensive Gr\u00f6bner systems. In: Proceedings of the International Symposium on Symbolic and Algebraic Computation, pp. 299\u2013306. ACM-Press (2007)","DOI":"10.1145\/1277548.1277589"},{"key":"387_CR15","doi-asserted-by":"crossref","unstructured":"Nabeshima, K.: Stability conditions of monomial bases and comprehensive Gr\u00f6bner systems. In: Proceedings of Computer Algebra in Scientific Computing, LNCS vol. 7442, pp. 248\u2013259. Springer, Berlin (2012)","DOI":"10.1007\/978-3-642-32973-9_21"},{"key":"387_CR16","doi-asserted-by":"crossref","unstructured":"Pedersen, P., Roy, M.-F., Szpirglas, A.: Counting real zeroes in the multivariate case. In: Proceedings of Effective Methods in Algebraic Geometry, Progress in Mathematics vol. 109, pp. 203\u2013224. Springer, Berlin (1993)","DOI":"10.1007\/978-1-4612-2752-6_15"},{"key":"387_CR17","doi-asserted-by":"crossref","unstructured":"Sato, S., Fukasaku, R., Sekigawa, H.: On continuity of the roots of a parametric zero dimensional multivariate polynomial ideal. In: Proceedings of the International Symposium on Symbolic and Algebraic Computation, pp. 359\u2013365. ACM-Press (2018)","DOI":"10.1145\/3208976.3209004"},{"key":"387_CR18","unstructured":"Strzebonski, A.: Reduce of Mathematica. \n                    https:\/\/urldefense.proofpoint.com\/v2\/url?u=https-3A__reference.wolfram.com_language_ref_Reduce.html&d=DwICAg&c=vh6FgFnduejNhPPD0fl_yRaSfZy8CWbWnIf4XJhSqx8&r=UpNksRRkQEKvUbblp9QRYTuemGLwQgpW1U7iMCFPZ8k&m=mWR4kwzCQJx99sfByc_Wd_NtOKrvA94px0mf4a_qj_8&s=4EgFsOWDHosP2kivGNaEgtF21HCLwzXqfkkgmrzY7SI&e=\n                    \n                  . Accessed 8 Oct 2017"},{"key":"387_CR19","unstructured":"Strzebonski, A.: Resolve of Mathematica. \n                    https:\/\/urldefense.proofpoint.com\/v2\/url?u=https-3A__reference.wolfram.com_language_ref_Resolve.html&d=DwICAg&c=vh6FgFnduejNhPPD0fl_yRaSfZy8CWbWnIf4XJhSqx8&r=UpNksRRkQEKvUbblp9QRYTuemGLwQgpW1U7iMCFPZ8k&m=mWR4kwzCQJx99sfByc_Wd_NtOKrvA94px0mf4a_qj_8&s=f-nt87scWnkm1Ct-Hg0T9_eYCwKRzyOsZBx-bnIlD10&e=\n                    \n                  . Accessed 8 Oct 2017"},{"issue":"3","key":"387_CR20","doi-asserted-by":"publisher","first-page":"471","DOI":"10.1006\/jsco.1999.0327","volume":"29","author":"A Strzebonski","year":"2000","unstructured":"Strzebonski, A.: Solving systems of strict polynomial inequalities. J. Symb. Comput. 29(3), 471\u2013480 (2000)","journal-title":"J. Symb. Comput."},{"key":"387_CR21","unstructured":"Sturm, T. et al.: Redlog package. \n                    https:\/\/urldefense.proofpoint.com\/v2\/url?u=http-3A__www.redlog.eu_&d=DwICAg&c=vh6FgFnduejNhPPD0fl_yRaSfZy8CWbWnIf4XJhSqx8&r=UpNksRRkQEKvUbblp9QRYTuemGLwQgpW1U7iMCFPZ8k&m=mWR4kwzCQJx99sfByc_Wd_NtOKrvA94px0mf4a_qj_8&s=IYEAxvdgb7Rlopn5s55MJGTASSLXMa0Tr395COkW5Ww&e=\n                    \n                  . Accessed 8 Oct 2017"},{"key":"387_CR22","doi-asserted-by":"crossref","unstructured":"Suzuki, A., Sato, Y.: A simple algorithm to compute comprehensive Gr\u00f6bner bases using Gr\u00f6bner bases. In: Proceedings of International Symposium on Symbolic and Algebraic Computation, pp. 326\u2013331. ACM-Press (2006)","DOI":"10.1145\/1145768.1145821"},{"key":"387_CR23","doi-asserted-by":"crossref","unstructured":"Weispfenning, V.: A new approach to quantifier elimination for real algebra. In: Quantifier Elimination and Cylindrical Algebraic Decomposition, pp. 376\u2013392. Springer, Berlin (1998)","DOI":"10.1007\/978-3-7091-9459-1_20"}],"container-title":["Mathematics in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11786-018-0387-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11786-018-0387-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11786-018-0387-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,10,11]],"date-time":"2019-10-11T23:27:39Z","timestamp":1570836459000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11786-018-0387-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,10,12]]},"references-count":23,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2019,6]]}},"alternative-id":["387"],"URL":"https:\/\/doi.org\/10.1007\/s11786-018-0387-8","relation":{},"ISSN":["1661-8270","1661-8289"],"issn-type":[{"value":"1661-8270","type":"print"},{"value":"1661-8289","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,10,12]]},"assertion":[{"value":"8 November 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 April 2018","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 September 2018","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 October 2018","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}