{"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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0009165665,0.0005778042,0.0007765552,0.0009161583,0.0009969837,0.002090842,0.001013546,0.0008404864,0.005969815],"category_scores_gemma":[0.007503007,0.0005406039,0.0006534564,0.0009258518,0.001399231,0.004389008,0.002331675,0.001622354,0.00166338],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001013563,"about_ca_system_score_gemma":0.001464572,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001253995,"about_ca_topic_score_gemma":0.002955468,"domain_scores_codex":[0.9980785,0.0003217268,0.0001006634,0.0003585592,0.0008358727,0.000304734],"domain_scores_gemma":[0.9972025,0.001063399,0.0002464313,0.0007994049,0.0005273992,0.0001607621],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.001269129,0.0003339337,0.003418586,0.0001686383,0.00007914796,0.0002606186,0.0005283432,0.09568616,0.04227254,0.4812715,0.009101624,0.3656098],"study_design_scores_gemma":[0.0001363743,0.0002134256,0.0006290242,0.00002223692,0.00001761442,0.0002198172,0.0001798591,0.5485534,0.03460168,0.407176,0.008181449,0.00006909978],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.170382,0.0001175751,0.8179501,0.0003032003,0.00009266483,0.00007980791,0.000185659,0.001716972,0.009172065],"genre_scores_gemma":[0.6419569,0.0001231478,0.3463522,0.0001519785,0.0001060663,0.0001104417,0.0005916101,0.0003448627,0.01026275],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.005969815,"threshold_uncertainty_score":0.01997107,"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."}}