{"id":"W1971160839","doi":"10.1145/2465506.2465947","title":"Computing column bases of polynomial matrices","year":2013,"lang":"en","type":"article","venue":"","topic":"Polynomial and algebraic computation","field":"Computer Science","cited_by":16,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"","keywords":"Column (typography); Matrix (chemical analysis); Mathematics; Basis (linear algebra); Matrix multiplication; Polynomial matrix; Degree (music); Univariate; Integer matrix; Polynomial; Combinatorics; Matrix polynomial; Discrete mathematics; Symmetric matrix; Algorithm; Nonnegative matrix; Mathematical analysis; Statistics; Geometry","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":[],"consensus_categories":[],"category_scores_codex":[0.00008658111,0.00007242685,0.0001205074,0.00007748227,0.00005746158,0.0001028931,0.0004316344,0.00002373207,0.000113019],"category_scores_gemma":[0.00001582459,0.00006256918,0.00004710115,0.0002546777,0.0000275117,0.000415762,0.00021466,0.0000386107,0.0001383526],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001112933,"about_ca_system_score_gemma":0.00004311423,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001273894,"about_ca_topic_score_gemma":0.000009587664,"domain_scores_codex":[0.9992829,0.00002661244,0.0002193309,0.0001724816,0.0001365141,0.0001621854],"domain_scores_gemma":[0.9994553,0.0001467505,0.00009724004,0.0001785848,0.00006280401,0.00005930546],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"design_other","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.000005669594,0.0002177141,0.007422487,0.00005537889,0.00003874509,0.000004119172,0.0009245175,0.0008257119,0.009322715,0.05860166,0.07154317,0.8510381],"study_design_scores_gemma":[0.0008989551,0.000269505,0.1115541,0.00005045545,0.000009026086,0.00002401929,0.0001310183,0.8494961,0.02665357,0.005879019,0.004527343,0.000506858],"study_design_candidate":"design_other","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5907681,0.00004573965,0.4016588,0.0007518061,0.000315822,0.0001378492,5.983737e-7,0.0001593447,0.006161908],"genre_scores_gemma":[0.9471847,0.000001113531,0.05219041,0.0002500374,0.00008424698,0.000002029967,6.939816e-7,0.000002867764,0.0002839434],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.8505313,"threshold_uncertainty_score":0.2551497,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.009104269012221718,"score_gpt":0.219333257819703,"score_spread":0.2102289888074813,"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."}}