{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,1]],"date-time":"2022-04-01T07:32:27Z","timestamp":1648798347751},"reference-count":9,"publisher":"World Scientific Pub Co Pte Lt","issue":"07","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2013,11]]},"abstract":"<jats:p> Given a collection [Formula: see text] of k<jats:sup>2<\/jats:sup> commutative polynomials in 2k<jats:sup>2<\/jats:sup> variables, the objective is to find a condensed representation for these polynomials in terms of a single non-commutative (nc) polynomial p(X, Y) in two k \u00d7 k matrix variables X and Y. In this paper, we develop algorithms that will generically determine whether the given family [Formula: see text] has a nc representation and will produce such a representation if it exists. In particular, we determine an open, dense subset of the space of nc polynomials in two variables that satisfies the following property: if a family [Formula: see text] of polynomials admits a nc representation in this subset, then our algorithms will determine this representation. <\/jats:p>","DOI":"10.1142\/s0218196713500422","type":"journal-article","created":{"date-parts":[[2013,11,12]],"date-time":"2013-11-12T06:59:36Z","timestamp":1384239576000},"page":"1685-1753","source":"Crossref","is-referenced-by-count":0,"title":["NON-COMMUTATIVE REPRESENTATIONS OF FAMILIES OF k<sup>2<\/sup> COMMUTATIVE POLYNOMIALS IN 2k<sup>2<\/sup> COMMUTING VARIABLES"],"prefix":"10.1142","volume":"23","author":[{"given":"HARRY","family":"DYM","sequence":"first","affiliation":[{"name":"Department of Mathematics, The Weizmann Institute of Science, Rehovot 7610001, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J. WILLIAM","family":"HELTON","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of California San Diego, 9500 Gilman Drive, La Jolla, CA 92093, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"CALEB","family":"MEIER","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of California San Diego, 9500 Gilman Drive, La Jolla, CA 92093, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2013,12]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1950-0036751-9"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1007\/s00020-008-1626-1"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-10-10324-4"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-09686-5_2"},{"key":"rf5","unstructured":"G.\u00a0Golub and C.\u00a0van, Loan Matrix Computations (Johns Hopkins Press, 1983)\u00a0pp. 99\u2013103."},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1006\/jfan.1998.3249"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2008.08.027"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1512\/iumj.2010.59.4107"},{"key":"rf11","first-page":"334","volume":"1","author":"Levitski J.","year":"1950","journal-title":"Proc. Amer. Math. Soc."}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196713500422","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T13:52:42Z","timestamp":1565099562000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196713500422"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,11]]},"references-count":9,"journal-issue":{"issue":"07","published-online":{"date-parts":[[2013,12]]},"published-print":{"date-parts":[[2013,11]]}},"alternative-id":["10.1142\/S0218196713500422"],"URL":"https:\/\/doi.org\/10.1142\/s0218196713500422","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,11]]}}}