{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,19]],"date-time":"2026-02-19T07:21:38Z","timestamp":1771485698801,"version":"3.50.1"},"reference-count":18,"publisher":"World Scientific Pub Co Pte Ltd","issue":"06","funder":[{"name":"the Basque Government","award":["IT1483-22"],"award-info":[{"award-number":["IT1483-22"]}]},{"name":"the Spanish Government","award":["PID2019-107444GA-I00"],"award-info":[{"award-number":["PID2019-107444GA-I00"]}]},{"name":"the Spanish Government","award":["PID2020-117281GB-I00"],"award-info":[{"award-number":["PID2020-117281GB-I00"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2023,9]]},"abstract":"<jats:p> For a finitely generated group G, the Diophantine problem over G is the algorithmic problem of deciding whether a given equation [Formula: see text] (perhaps restricted to a fixed subclass of equations) has a solution in G. In this paper, we investigate the algorithmic complexity of the Diophantine problem for the class [Formula: see text] of quadratic equations over the metabelian Baumslag\u2013Solitar groups [Formula: see text]. We prove that this problem is [Formula: see text]-complete whenever [Formula: see text], and determine the algorithmic complexity for various subclasses (orientable, nonorientable, etc.) of\u00a0[Formula: see text]. <\/jats:p>","DOI":"10.1142\/s0218196723500558","type":"journal-article","created":{"date-parts":[[2023,7,20]],"date-time":"2023-07-20T01:48:25Z","timestamp":1689817705000},"page":"1195-1216","source":"Crossref","is-referenced-by-count":6,"title":["Quadratic equations in metabelian Baumslag\u2013Solitar groups"],"prefix":"10.1142","volume":"33","author":[{"given":"Richard","family":"Mandel","sequence":"first","affiliation":[{"name":"Department of Science and Technology, University of the Basque Country, Barrio Sarriena s\/n, 48940 Leioa, Bizkaia, Spain"}]},{"given":"Alexander","family":"Ushakov","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, Stevens Institute of Technology, Hoboken, NJ 07030, USA"}]}],"member":"219","published-online":{"date-parts":[[2023,8,21]]},"reference":[{"key":"S0218196723500558BIB001","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1090\/S0002-9904-1962-10745-9","volume":"68","author":"Baumslag G.","year":"1962","journal-title":"Bull. 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