{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T14:16:09Z","timestamp":1777644969002,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"4","license":[{"start":{"date-parts":[[2018,2,9]],"date-time":"2018-02-09T00:00:00Z","timestamp":1518134400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Fundamenta Informaticae"],"published-print":{"date-parts":[[2018,2,9]]},"abstract":"<jats:p>\n                    Inflations algorithm is a procedure that appears implicitly in Ovsienko\u2019s classical proof for the classification of positive definite integral quadratic forms. The best known upper asymptotic bound for its time complexity is an exponential one. In this paper we show that this bound can be tightened to\n                    <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"math0005\" overflow=\"scroll\" altimg=\"eq-00001.gif\">\n                      <mml:mrow>\n                        <mml:mtext>O<\/mml:mtext>\n                        <mml:mrow>\n                          <mml:mo>(<\/mml:mo>\n                          <mml:mrow>\n                            <mml:msup>\n                              <mml:mi>n<\/mml:mi>\n                              <mml:mn>6<\/mml:mn>\n                            <\/mml:msup>\n                          <\/mml:mrow>\n                          <mml:mo>)<\/mml:mo>\n                        <\/mml:mrow>\n                      <\/mml:mrow>\n                    <\/mml:math>\n                    for the naive implementation. Also, we propose a new approach to show how to decide whether an admissible quasi-Cartan matrix is positive definite and compute the Dynkin type in just\n                    <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"math0010\" overflow=\"scroll\" altimg=\"eq-00002.gif\">\n                      <mml:mrow>\n                        <mml:mtext>O<\/mml:mtext>\n                        <mml:mrow>\n                          <mml:mo>(<\/mml:mo>\n                          <mml:mrow>\n                            <mml:msup>\n                              <mml:mi>n<\/mml:mi>\n                              <mml:mn>3<\/mml:mn>\n                            <\/mml:msup>\n                          <\/mml:mrow>\n                          <mml:mo>)<\/mml:mo>\n                        <\/mml:mrow>\n                      <\/mml:mrow>\n                    <\/mml:math>\n                    operations taking an integer matrix as input.\n                  <\/jats:p>","DOI":"10.3233\/fi-2018-1653","type":"journal-article","created":{"date-parts":[[2018,2,9]],"date-time":"2018-02-09T11:42:24Z","timestamp":1518176544000},"page":"369-384","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":5,"title":["Cubic Algorithm to Compute the Dynkin Type of a Positive Definite Quasi-Cartan Matrix"],"prefix":"10.1177","volume":"158","author":[{"given":"Claudia","family":"P\u00e9rez","sequence":"first","affiliation":[{"name":"Instituto de Investigaci\u00f3n en Ciencias B\u00e1sicas y Aplicadas, Centro de Investigaci\u00f3n en Ciencias, Universidad Aut\u00f3noma del Estado de Morelos, Av. Universidad 1001, Cuernavaca, Mor. Mexico."}]},{"given":"Mario","family":"Abarca","sequence":"additional","affiliation":[{"name":"Instituto de Investigaci\u00f3n en Ciencias B\u00e1sicas y Aplicadas, Centro de Investigaci\u00f3n en Ciencias, Universidad Aut\u00f3noma del Estado de Morelos, Av. Universidad 1001, Cuernavaca, Mor. Mexico."}]},{"given":"Daniel","family":"Rivera","sequence":"additional","affiliation":[{"name":"Instituto de Investigaci\u00f3n en Ciencias B\u00e1sicas y Aplicadas, Centro de Investigaci\u00f3n en Ciencias, Universidad Aut\u00f3noma del Estado de Morelos, Av. Universidad 1001, Cuernavaca, Mor. Mexico."}]}],"member":"179","published-online":{"date-parts":[[2018,2,9]]},"container-title":["Fundamenta Informaticae"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-2018-1653","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-2018-1653","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T06:30:50Z","timestamp":1777444250000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/FI-2018-1653"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,2,9]]},"references-count":0,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2018,2,9]]}},"alternative-id":["10.3233\/FI-2018-1653"],"URL":"https:\/\/doi.org\/10.3233\/fi-2018-1653","relation":{},"ISSN":["0169-2968","1875-8681"],"issn-type":[{"value":"0169-2968","type":"print"},{"value":"1875-8681","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,2,9]]}}}