{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,17]],"date-time":"2026-03-17T06:36:26Z","timestamp":1773729386697,"version":"3.50.1"},"reference-count":9,"publisher":"Association for Computing Machinery (ACM)","issue":"2","license":[{"start":{"date-parts":[[2019,11,8]],"date-time":"2019-11-08T00:00:00Z","timestamp":1573171200000},"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":[[2019,11,8]]},"abstract":"<jats:p>Matrices or linear operators and their identities can be modelled algebraically by noncommutative polynomials in the free algebra. For proving new identities of matrices or operators from given ones, computations are done formally with noncommutative polynomials. Computations in the free algebra, however, are not necessarily compatible with formats of matrices resp. with domains and codomains of operators. For ensuring validity of such computations in terms of operators, in principle, one would have to inspect every step of the computation. In [9], an algebraic framework is developed that allows to rigorously justify such computations without restricting the computation to compatible expressions. The main result of that paper reduces the proof of an operator identity to verifying membership of the corresponding polynomial in the ideal generated by the polynomials corresponding to the assumptions and verifying compatibility of this polynomial and of the generators of the ideal.<\/jats:p>","DOI":"10.1145\/3371991.3371996","type":"journal-article","created":{"date-parts":[[2019,11,8]],"date-time":"2019-11-08T20:27:58Z","timestamp":1573244878000},"page":"49-52","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":12,"title":["Certifying operator identities via noncommutative Gr\u00f6bner bases"],"prefix":"10.1145","volume":"53","author":[{"given":"Clemens","family":"Hofstadler","sequence":"first","affiliation":[{"name":"Johannes Kepler Universit\u00e4t Linz, , Austria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Clemens G.","family":"Raab","sequence":"additional","affiliation":[{"name":"Johannes Kepler Universit\u00e4t Linz, , Austria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Georg","family":"Regensburger","sequence":"additional","affiliation":[{"name":"Johannes Kepler Universit\u00e4t Linz, , Austria"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2019,11,8]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1016\/0001-8708(78)90010-5"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1006\/jsco.1996.0125"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jsc.2005.09.007"},{"key":"e_1_2_1_4_1","unstructured":"The GAP Group GAP - Groups Algorithms and Programming Version 4.10.1 2019.  The GAP Group GAP - Groups Algorithms and Programming Version 4.10.1 2019."},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1006\/jfan.1998.3249"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jsc.2009.03.002"},{"key":"e_1_2_1_7_1","doi-asserted-by":"crossref","unstructured":"Viktor Levandovskyy Karim Abou Zeid and Hans Sch\u00f6nemann Singular:Letterplace --- A Singular Subsystem for Non-commutative Finitely Presented Algebras 2019. http:\/\/www.singular.uni-kl.de  Viktor Levandovskyy Karim Abou Zeid and Hans Sch\u00f6nemann Singular:Letterplace --- A Singular Subsystem for Non-commutative Finitely Presented Algebras 2019. http:\/\/www.singular.uni-kl.de","DOI":"10.1145\/3373207.3404056"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(94)90283-6"},{"key":"e_1_2_1_9_1","unstructured":"Clemens G. Raab Georg Regensburger and Jamal Hossein Poor. Formal proofs of operator identities by a single formal computation. In preparation.  Clemens G. Raab Georg Regensburger and Jamal Hossein Poor. Formal proofs of operator identities by a single formal computation. In preparation."}],"container-title":["ACM Communications in Computer Algebra"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3371991.3371996","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3371991.3371996","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,17]],"date-time":"2025-06-17T23:44:19Z","timestamp":1750203859000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3371991.3371996"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,11,8]]},"references-count":9,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2019,11,8]]}},"alternative-id":["10.1145\/3371991.3371996"],"URL":"https:\/\/doi.org\/10.1145\/3371991.3371996","relation":{},"ISSN":["1932-2240"],"issn-type":[{"value":"1932-2240","type":"print"}],"subject":[],"published":{"date-parts":[[2019,11,8]]},"assertion":[{"value":"2019-11-08","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}