{"id":"W2115982610","doi":"10.1145/1993886.1993913","title":"Computing hermite forms of polynomial matrices","year":2011,"lang":"en","type":"article","venue":"","topic":"Polynomial and algebraic computation","field":"Computer Science","cited_by":10,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"","keywords":"Hermite polynomials; Invertible matrix; Degree (music); Mathematics; Dimension (graph theory); Matrix (chemical analysis); Polynomial matrix; Polynomial; Field (mathematics); Las vegas; Degree of a polynomial; Combinatorics; Matrix polynomial; Discrete mathematics; Algorithm; Pure mathematics; Mathematical analysis; Physics","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":[0.0001252308,0.000075173,0.0001141515,0.00008540468,0.0000464995,0.00002584061,0.0004867575,0.00002730144,0.00003163458],"category_scores_gemma":[0.0000058921,0.00005869091,0.00005619852,0.0002370634,0.00002464979,0.0003530457,0.0002189156,0.0000419538,0.00003599027],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000009101548,"about_ca_system_score_gemma":0.00003267804,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001661341,"about_ca_topic_score_gemma":0.00000773777,"domain_scores_codex":[0.9993235,0.00001469772,0.0002197701,0.0001657113,0.0001138965,0.0001623521],"domain_scores_gemma":[0.9995798,0.00003881495,0.0001086733,0.0001885941,0.00003264149,0.00005141342],"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":[0.00002281302,0.0001923739,0.006547587,0.00003826235,0.00003775737,0.00001046714,0.004934763,0.00006166982,0.001849323,0.3096728,0.00144413,0.6751881],"study_design_scores_gemma":[0.002759475,0.0009987849,0.3445801,0.0001232469,0.00003304094,0.0001203122,0.0004045096,0.3830101,0.2109091,0.05211331,0.00352082,0.001427156],"study_design_candidate":"design_other","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.4750405,0.00003419152,0.4951269,0.00005485637,0.0002506195,0.00006070131,4.113865e-7,0.0001361041,0.02929569],"genre_scores_gemma":[0.9397688,0.000001244769,0.05995642,0.00009672579,0.0000454861,5.452113e-7,4.047247e-7,0.000003094853,0.0001272736],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.6737609,"threshold_uncertainty_score":0.2393346,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02136985856734581,"score_gpt":0.228951296609139,"score_spread":0.2075814380417932,"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."}}