{"schema_version":"1.0","canonical_url":"https://patentable.app/patents/US-8533243","patent":{"patent_number":"US-8533243","title":"Representation converting apparatus, arithmetic apparatus, representation converting method, and computer program product","assignee":null,"inventors":[],"filing_date":"2009-03-04T00:00:00.000Z","publication_date":"2013-09-10T00:00:00.000Z","cpc_codes":["G06F"],"num_claims":25,"abstract":"When converting an affine representation representing a 2r-th degree algebraic torus T2r(Fq) (r is a prime number, and q is an integer) to a projective representation representing a quadratic algebraic torus T2(Fq^r), a representation converting apparatus acquires member (c0, c1, . . . , cr-2), (ci is a member of a finite field Fq, where 0≦i≦r−2) of a 2r-th degree algebraic torus T2r(Fq) represented by the affine representation. The apparatus performs a multiplication operation on the acquired member. The multiplication operation is determined by a condition under which a member of a quadratic algebraic torus T2(Fq^r) is included in the 2r-th degree algebraic torus T2r(Fq), a modulus and a base of a quadratic extension, and a modulus and a base of an r-th degree extension. The representation converting apparatus then performs an addition and subtraction operation determined by the condition, the moduli, and the bases."},"analysis":{"summary":null,"layman_explanation":null,"technical_analysis":null,"business_analysis":null,"faqs":null,"topics":[],"tech_cluster":null},"seo":{"title":"Representation converting apparatus, arithmetic apparatus, representation converting method, and computer program product","description":"When converting an affine representation representing a 2r-th degree algebraic torus T2r(Fq) (r is a prime number, and q is an integer) to a projective representation representing a quadratic algebrai","keywords":[]},"attribution":{"source":"Patentable","source_url":"https://patentable.app","canonical_url":"https://patentable.app/patents/US-8533243","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-8533243","citation_suggestion":"Patentable. \"Representation converting apparatus, arithmetic apparatus, representation converting method, and computer program product\" (US-8533243). https://patentable.app/patents/US-8533243","copyright_holder":"Nomic Interactive Technology LLC"},"links":{"html":"https://patentable.app/patents/US-8533243","json":"https://patentable.app/api/llm-context/US-8533243","site":"https://patentable.app","llms_txt":"https://patentable.app/llms.txt"},"generated_at":"2026-05-30T11:10:44.078Z"}