{"id":"W185179213","doi":"10.1007/978-3-7643-7984-1_7","title":"New Algorithms for Exact and Approximate Polynomial Decomposition","year":2007,"lang":"en","type":"book-chapter","venue":"Birkhäuser Basel eBooks","topic":"Numerical Methods and Algorithms","field":"Computer Science","cited_by":7,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"","keywords":"Polynomial; Decomposition; Mathematics; Algorithm; Bivariate analysis; Computation; Exponential function; Square-free polynomial; Matrix polynomial; Discrete mathematics; Combinatorics; Applied mathematics; Mathematical analysis","routes":{"ca_aff":true,"ca_fund":false,"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":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0006026769,0.0005914582,0.0006408864,0.0003000616,0.0002170492,0.0003045838,0.0006994812,0.0004409701,0.00003480213],"category_scores_gemma":[0.00001811425,0.0005513681,0.0002796316,0.00003287536,0.0000945374,0.0001724923,0.0003385,0.0003740762,0.00002912385],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00008071526,"about_ca_system_score_gemma":0.000181492,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00005325515,"about_ca_topic_score_gemma":0.000004543094,"domain_scores_codex":[0.9974276,0.00003536737,0.000548802,0.001028666,0.000381664,0.0005778811],"domain_scores_gemma":[0.998013,0.0003736395,0.0003072733,0.0007133561,0.0001070774,0.0004856079],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"design_other","study_design_gemma":"not_applicable","study_design_scores_codex":[0.00003604946,0.00001155788,6.927744e-7,0.00005239097,0.00005775647,0.00003393724,0.00008046015,7.512529e-7,0.0001647723,0.1065621,0.001996382,0.8910031],"study_design_scores_gemma":[0.002291349,0.0007602191,0.00002850492,0.0003402995,0.00016217,0.0002219246,0.000006288662,0.03419896,0.004094643,0.1725965,0.7832997,0.001999413],"study_design_candidate":"design_other","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.000003042515,0.0003195541,0.8631366,0.0001340711,0.0007968767,0.0006994166,0.00004861268,0.0002645222,0.1345972],"genre_scores_gemma":[0.0000227555,0.00002826352,0.8198655,0.0006404467,0.001064523,0.00002808832,0.00001869392,0.00009658971,0.1782351],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.8890038,"threshold_uncertainty_score":0.9996938,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05509629544858043,"score_gpt":0.3217164365635686,"score_spread":0.2666201411149882,"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."}}