{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:08:37Z","timestamp":1750306117058,"version":"3.41.0"},"reference-count":9,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2017,2,22]],"date-time":"2017-02-22T00:00:00Z","timestamp":1487721600000},"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":[[2017,2,22]]},"abstract":"<jats:p>\n            Let (\n            <jats:italic>K<\/jats:italic>\n            ,\n            <jats:italic>\u03c3<\/jats:italic>\n            ) be a difference field. We define the set of constants by const\n            <jats:italic>K<\/jats:italic>\n            = {\n            <jats:italic>c<\/jats:italic>\n            \u2208\n            <jats:italic>K<\/jats:italic>\n            |\n            <jats:italic>\u03c3<\/jats:italic>\n            (\n            <jats:italic>c<\/jats:italic>\n            ) =\n            <jats:italic>c<\/jats:italic>\n            }. A \u03a0\u03a3*-\n            <jats:italic>extension<\/jats:italic>\n            of\n            <jats:italic>K<\/jats:italic>\n            is a field of rational functions\n            <jats:italic>K<\/jats:italic>\n            (\n            <jats:italic>t<\/jats:italic>\n            ) over\n            <jats:italic>K<\/jats:italic>\n            together with an extension of\n            <jats:italic>\u03c3<\/jats:italic>\n            to\n            <jats:italic>K<\/jats:italic>\n            (\n            <jats:italic>t<\/jats:italic>\n            ) given by either\n            <jats:italic>\u03c3<\/jats:italic>\n            (\n            <jats:italic>t<\/jats:italic>\n            ) =\n            <jats:italic>at<\/jats:italic>\n            (\u03a0 case) or\n            <jats:italic>\u03c3<\/jats:italic>\n            (\n            <jats:italic>t<\/jats:italic>\n            ) =\n            <jats:italic>t<\/jats:italic>\n            +\n            <jats:italic>b<\/jats:italic>\n            (\u03a3* case) for some non-zero\n            <jats:italic>a<\/jats:italic>\n            or\n            <jats:italic>b<\/jats:italic>\n            \u2208\n            <jats:italic>K<\/jats:italic>\n            such that const\n            <jats:italic>K<\/jats:italic>\n            (\n            <jats:italic>t<\/jats:italic>\n            ) = const\n            <jats:italic>K<\/jats:italic>\n            holds. See, for example, [8, 9] for more details on \u03a0\u03a3*-extensions.\n          <\/jats:p>","DOI":"10.1145\/3055282.3055298","type":"journal-article","created":{"date-parts":[[2017,2,27]],"date-time":"2017-02-27T13:06:52Z","timestamp":1488200812000},"page":"185-187","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Denominator bounds for higher order systems of linear recurrence equations"],"prefix":"10.1145","volume":"50","author":[{"given":"Johannes","family":"Middeke","sequence":"first","affiliation":[{"name":"Research Institute for Symbolic Computation (RISC), Linz, Austria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Carsten","family":"Schneider","sequence":"additional","affiliation":[{"name":"Research Institute for Symbolic Computation (RISC), Linz, Austria"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2017,2,22]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cpc.2016.01.002"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0041-5553(89)80002-3"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/281508.281593"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1134\/S0361768812020028"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jsc.2005.10.002"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1006\/jsco.2000.0368"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.aam.2007.11.004"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1145\/322248.322255"},{"key":"e_1_2_1_10_1","first-page":"2","volume":"42","author":"Schneider Carsten","year":"2004","unstructured":"Carsten Schneider , A collection of denominator bounds to solve parameterized linear difference equations in \u03a0\u03a3-extensions , An. Univ. Timi\u015foara Ser. Mat.-Inform. 42 ( 2004 ), no. 2 , 163--179, Extended version of Proc. SYNASC'04. Carsten Schneider, A collection of denominator bounds to solve parameterized linear difference equations in \u03a0\u03a3-extensions, An. Univ. Timi\u015foara Ser. Mat.-Inform. 42 (2004), no. 2, 163--179, Extended version of Proc. SYNASC'04.","journal-title":"An. Univ. Timi\u015foara Ser. Mat.-Inform."}],"container-title":["ACM Communications in Computer Algebra"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3055282.3055298","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3055282.3055298","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T03:36:37Z","timestamp":1750217797000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3055282.3055298"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,2,22]]},"references-count":9,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2017,2,22]]}},"alternative-id":["10.1145\/3055282.3055298"],"URL":"https:\/\/doi.org\/10.1145\/3055282.3055298","relation":{},"ISSN":["1932-2240"],"issn-type":[{"type":"print","value":"1932-2240"}],"subject":[],"published":{"date-parts":[[2017,2,22]]},"assertion":[{"value":"2017-02-22","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}