{"id":157920,"date":"2009-07-30T00:00:00","date_gmt":"2009-07-30T00:00:00","guid":{"rendered":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/msr-research-item\/superfluous-s-polynomials-in-strategy-independent-grobner-bases\/"},"modified":"2018-10-16T19:56:15","modified_gmt":"2018-10-17T02:56:15","slug":"superfluous-s-polynomials-in-strategy-independent-grobner-bases","status":"publish","type":"msr-research-item","link":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/publication\/superfluous-s-polynomials-in-strategy-independent-grobner-bases\/","title":{"rendered":"Superfluous S-polynomials in Strategy-Independent Grobner Bases"},"content":{"rendered":"<div class=\"asset-content\">\n<p>Using the machinery of proof orders originally introduced by Bachmair and Dershowitz in the context of canonical equational proofs, we give an abstract, strategy-independent presentation of Grobner basis procedures and prove the correctness of two classical criteria for recognising superfluous S-polynomials, Buchberger&#8217;s criteria 1 and 2, w.r.t. arbitrary fair and correct basis construction strategies. To do so, we develop a general method for proving the strategy-independent correctness of superfluous S-polynomial criteria which seems to be quite powerful. We also derive a new superfluous S-polynomial criterion which is a generalization of Buchberger-1 and is proved to be correct strategy-independently.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Using the machinery of proof orders originally introduced by Bachmair and Dershowitz in the context of canonical equational proofs, we give an abstract, strategy-independent presentation of Grobner basis procedures and prove the correctness of two classical criteria for recognising superfluous S-polynomials, Buchberger&#8217;s criteria 1 and 2, w.r.t. arbitrary fair and correct basis construction strategies. To [&hellip;]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":null,"msr_publishername":"Microsoft","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"","msr_number":"MSR-TR-2009-913","msr_organization":"","msr_pages_string":"","msr_page_range_start":"","msr_page_range_end":"","msr_series":"","msr_volume":"","msr_copyright":"","msr_conference_name":"","msr_doi":"","msr_arxiv_id":"","msr_s2_paper_id":"","msr_mag_id":"","msr_pubmed_id":"","msr_other_authors":"Grant Olney 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