{"id":"W2100891661","doi":"10.1109/arith.2005.11","title":"Arithmetic Operations in the Polynomial Modular Number System","year":2005,"lang":"en","type":"article","venue":"","topic":"Cryptography and Residue Arithmetic","field":"Computer Science","cited_by":27,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Calgary","funders":"University of Calgary","keywords":"Modular arithmetic; Modular design; Arithmetic; Modulo; Polynomial; Saturation arithmetic; Set (abstract data type); Mathematics; Representation (politics); Computer science; Discrete mathematics; Arbitrary-precision arithmetic; Algebra over a field; Pure mathematics; Programming language","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0003105793,0.0000819307,0.0000845062,0.0000823277,0.0001386475,0.0002204666,0.0007218881,0.00003977251,0.00002297063],"category_scores_gemma":[0.000007113275,0.00005017798,0.00006082291,0.0005391383,0.00003259875,0.0002843695,0.00007121589,0.0001153233,0.0002046111],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002356897,"about_ca_system_score_gemma":0.00002812852,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0002710528,"about_ca_topic_score_gemma":0.0003501624,"domain_scores_codex":[0.9991404,0.000102362,0.0001733198,0.0002028322,0.0001880982,0.0001930336],"domain_scores_gemma":[0.9994228,0.00005331822,0.00001230279,0.0004542119,0.00002208741,0.00003532031],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.000002547243,0.000259644,0.002651904,0.00001558302,0.00001968559,0.00004011294,0.003144498,0.01312103,0.0002859924,0.9587715,0.002598536,0.01908901],"study_design_scores_gemma":[0.0008005516,0.0000417283,0.02917858,0.00003092431,0.00001210727,0.0003212936,0.0007501158,0.9515702,0.0008200553,0.0004750314,0.01565927,0.0003402171],"study_design_candidate":"simulation_or_modeling","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.3643289,0.0001982931,0.5753359,0.01276018,0.0003778486,0.0004634827,0.000001576486,0.0002696667,0.04626419],"genre_scores_gemma":[0.9544713,0.000003828996,0.0446508,0.0005893747,0.0001099199,0.00002453943,5.366073e-7,0.000003176959,0.000146442],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.9582964,"threshold_uncertainty_score":0.262993,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.007164941213894422,"score_gpt":0.225597816348077,"score_spread":0.2184328751341826,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}