{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T07:01:16Z","timestamp":1776841276680,"version":"3.51.2"},"reference-count":43,"publisher":"American Mathematical Society (AMS)","issue":"359","license":[{"start":{"date-parts":[[2026,12,10]],"date-time":"2026-12-10T00:00:00Z","timestamp":1796860800000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    An isotropic vector of a given quadratic form is a nonzero vector where the form vanishes. Geometrically, it is a vector that is self-orthogonal with respect to this form. On the other hand, from the arithmetical point of view, an isotropic vector forms a solution to a multivariate quadratic equation. The problem of constructing isotropic vectors is one of the leading forces in the computational theory of quadratic forms. In this paper, we present algorithms for finding isotropic vectors of quadratic forms (of any dimension) over an arbitrary global field of characteristic distinct from\u00a0\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"2\">\n                        <mml:semantics>\n                          <mml:mn>2<\/mml:mn>\n                          <mml:annotation encoding=\"application\/x-tex\">2<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    .\n                  <\/p>","DOI":"10.1090\/mcom\/4165","type":"journal-article","created":{"date-parts":[[2025,12,10]],"date-time":"2025-12-10T19:38:16Z","timestamp":1765395496000},"page":"1541-1567","source":"Crossref","is-referenced-by-count":0,"title":["Isotropic vectors over global fields"],"prefix":"10.1090","volume":"95","author":[{"given":"Przemys\u0142aw","family":"Koprowski","sequence":"first","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2025,12,10]]},"reference":[{"key":"1","series-title":"Algorithms and Computation in Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-05355-3","volume-title":"Algorithms in real algebraic geometry","volume":"10","author":"Basu, Saugata","year":"2003","ISBN":"https:\/\/id.crossref.org\/isbn\/3540009736"},{"issue":"1","key":"2","doi-asserted-by":"publisher","first-page":"19","DOI":"10.5802\/jtnb.433","article-title":"Topics in computational algebraic number theory","volume":"16","author":"Belabas, Karim","year":"2004","journal-title":"J. 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