{"schema_version":"1.0","canonical_url":"https://patentable.app/patents/US-8532289","patent":{"patent_number":"US-8532289","title":"Fast computation of a single coefficient in an inverse polynomial","assignee":null,"inventors":[],"filing_date":"2011-08-09T00:00:00.000Z","publication_date":"2013-09-10T00:00:00.000Z","cpc_codes":["H04L","H04L","H04L","H04L","H04L"],"num_claims":15,"abstract":"In one exemplary embodiment of the invention, a method for computing a resultant and a free term of a scaled inverse of a first polynomial v(x) modulo a second polynomial fn(x), including: receiving the first polynomial v(x) modulo the second polynomial fn(x), where the second polynomial is of a form fn(x)=xn±1, where n=2k and k is an integer greater than 0; computing lowest two coefficients of a third polynomial g(z) that is a function of the first polynomial and the second polynomial, wherewhere ρ0, ρ1, . . . , ρn−1 are roots of the second polynomial fn(x) over a field; outputting the lowest coefficient of g(z) as the resultant; and outputting the second lowest coefficient of g(z) divided by n as the free term of the scaled inverse of the first polynomial v(x) modulo the second polynomial fn(x)."},"analysis":{"summary":null,"layman_explanation":null,"technical_analysis":null,"business_analysis":null,"faqs":null,"topics":[],"tech_cluster":null},"seo":{"title":"Fast computation of a single coefficient in an inverse polynomial","description":"In one exemplary embodiment of the invention, a method for computing a resultant and a free term of a scaled inverse of a first polynomial v(x) modulo a second polynomial fn(x), including: receiving t","keywords":[]},"attribution":{"source":"Patentable","source_url":"https://patentable.app","canonical_url":"https://patentable.app/patents/US-8532289","license":"CC-BY-4.0-like","license_terms":"AI-generated analysis on this page (summary, layman_explanation, technical_analysis, business_analysis, faqs) may be reused with attribution and a visible link back to the canonical URL above. Patent abstracts, claims, and bibliographic data are USPTO public domain.","required_link":"https://patentable.app/patents/US-8532289","citation_suggestion":"Patentable. \"Fast computation of a single coefficient in an inverse polynomial\" (US-8532289). https://patentable.app/patents/US-8532289","copyright_holder":"Nomic Interactive Technology LLC"},"links":{"html":"https://patentable.app/patents/US-8532289","json":"https://patentable.app/api/llm-context/US-8532289","site":"https://patentable.app","llms_txt":"https://patentable.app/llms.txt"},"generated_at":"2026-05-30T20:58:39.424Z"}