{"id":"W2158079656","doi":"10.1016/j.jsc.2007.03.001","title":"Output-sensitive modular algorithms for polynomial matrix normal forms","year":2007,"lang":"en","type":"article","venue":"Journal of Symbolic Computation","topic":"Polynomial and algebraic computation","field":"Computer Science","cited_by":10,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Waterloo; University of Lethbridge","funders":"","keywords":"Mathematics; Unimodular matrix; Polynomial matrix; Algorithm; Matrix multiplication; Polynomial; Normalization (sociology); Modular arithmetic; Matrix (chemical analysis); Homomorphism; Integer matrix; Matrix polynomial; Algebra over a field; Discrete mathematics; Combinatorics; Pure mathematics; Symmetric matrix; Eigenvalues and eigenvectors","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":[0.002705716,0.001396727,0.001296527,0.001395302,0.001271848,0.003685024,0.002582331,0.001235913,0.01304852],"category_scores_gemma":[0.01364321,0.0008307165,0.001445553,0.001602862,0.001768194,0.007752037,0.006422179,0.003295593,0.003226938],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001828279,"about_ca_system_score_gemma":0.001795064,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0006591128,"about_ca_topic_score_gemma":0.001670761,"domain_scores_codex":[0.9961111,0.0009142244,0.0002438305,0.0006635115,0.001367598,0.0006997653],"domain_scores_gemma":[0.9916545,0.003397443,0.0004533907,0.003084637,0.001124674,0.0002853793],"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":[0.001814799,0.0004111614,0.002422619,0.0003203518,0.0001346416,0.0001732497,0.0005761835,0.05077999,0.01678119,0.5218536,0.01299218,0.3917401],"study_design_scores_gemma":[0.0002272597,0.0001886526,0.0003488416,0.00005229436,0.00009369886,0.0001387091,0.0001066395,0.2780045,0.02410652,0.6921076,0.004572996,0.00005233207],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.05968747,0.00025744,0.9250386,0.0006281934,0.0001601046,0.0001375887,0.0002277982,0.00340339,0.01045941],"genre_scores_gemma":[0.6805241,0.0002808397,0.3034808,0.0004392257,0.0002934072,0.0002170881,0.0008266762,0.001257059,0.01268095],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01304852,"threshold_uncertainty_score":0.0436517,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01627198849750778,"score_gpt":0.2861105198451552,"score_spread":0.2698385313476474,"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."}}