{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,12,29]],"date-time":"2022-12-29T05:19:07Z","timestamp":1672291147601},"reference-count":9,"publisher":"Association for Computing Machinery (ACM)","issue":"2","content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Commun. Comput. Algebra"],"published-print":{"date-parts":[[2006,6]]},"abstract":"<jats:p>In differential algebra [1], rankings on partial derivatives play the same role as admissible term orders in the theory of Gr\u00f6bner bases. In fact, an admissible term order is a particular case of a ranking on partial derivatives of a single differential indeterminate. The introduction of a ranking allows to select leading derivatives in differential polynomials, define a pseudo-reduction relation, and consider autoreduced sets; the latter are the a tool for representing differential ideals.<\/jats:p>","DOI":"10.1145\/1182553.1182557","type":"journal-article","created":{"date-parts":[[2007,1,17]],"date-time":"2007-01-17T18:32:02Z","timestamp":1169058722000},"page":"38-42","update-policy":"http:\/\/dx.doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Construction of rankings on partial derivatives"],"prefix":"10.1145","volume":"40","author":[{"given":"Oleg","family":"Golubitsky","sequence":"first","affiliation":[{"name":"Queen's University, Kingston, Ontario, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2006,6]]},"reference":[{"key":"e_1_2_1_1_1","unstructured":"E. R. Kolchin Differential Algebra and Algebraic Groups. Acad. press 1973.  E. R. Kolchin Differential Algebra and Algebraic Groups. Acad. press 1973."},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/258726.258737"},{"key":"e_1_2_1_3_1","doi-asserted-by":"crossref","unstructured":"M. Caboara M. Silvestri: Classification of compatible module orderings. Journal of Pure and Applied Algebra No. 142 1999 13--24.  M. Caboara M. Silvestri: Classification of compatible module orderings. Journal of Pure and Applied Algebra No. 142 1999 13--24.","DOI":"10.1016\/S0022-4049(98)00054-1"},{"key":"e_1_2_1_4_1","unstructured":"Communicated to the author by Hoon Hong.  Communicated to the author by Hoon Hong."},{"key":"e_1_2_1_5_1","volume-title":"University Lecture Series","volume":"8","author":"Sturmfels B.","year":"1995"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1137\/0406019"},{"key":"e_1_2_1_7_1","unstructured":"Private communication with Roman Pearce.  Private communication with Roman Pearce."},{"key":"e_1_2_1_8_1","volume-title":"Proc. CASC","author":"Golubitsky O.","year":"2004"},{"key":"e_1_2_1_9_1","volume-title":"Preprint","author":"Golubitsky O.","year":"2006"}],"container-title":["ACM Communications in Computer Algebra"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1182553.1182557","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,12,28]],"date-time":"2022-12-28T19:04:35Z","timestamp":1672254275000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1182553.1182557"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,6]]},"references-count":9,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2006,6]]}},"alternative-id":["10.1145\/1182553.1182557"],"URL":"https:\/\/doi.org\/10.1145\/1182553.1182557","relation":{},"ISSN":["1932-2240"],"issn-type":[{"value":"1932-2240","type":"print"}],"subject":[],"published":{"date-parts":[[2006,6]]},"assertion":[{"value":"2006-06-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}