{"id":"W2035855915","doi":"10.1016/j.laa.2008.09.003","title":"An application of lattice basis reduction to polynomial identities for algebraic structures","year":2008,"lang":"en","type":"article","venue":"Linear Algebra and its Applications","topic":"Coding theory and cryptography","field":"Computer Science","cited_by":23,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Saskatchewan","funders":"Natural Sciences and Engineering Research Council of Canada; Universidade de São Paulo; University of Saskatchewan","keywords":"Mathematics; Hermite polynomials; Gröbner basis; Lattice reduction; Lattice (music); Algebraic number; Basis (linear algebra); Degree (music); Combinatorics; Reduction (mathematics); Pure mathematics; Commutative property; Matrix (chemical analysis); Degree of a polynomial; Row; Polynomial; Discrete mathematics; Algebra over a field; Mathematical analysis; Geometry; Computer science; Statistics","routes":{"ca_aff":true,"ca_fund":true,"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":[0.0001175458,0.00009523832,0.0001183321,0.0001475801,0.0003141265,0.00003276277,0.000366669,0.00005090921,0.000004731571],"category_scores_gemma":[0.0000131657,0.00009712759,0.00005083694,0.0004254173,0.00005570281,0.0003125087,0.00005127737,0.00004775412,0.000006572627],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000006804618,"about_ca_system_score_gemma":0.00002431263,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000008724453,"about_ca_topic_score_gemma":0.000002093032,"domain_scores_codex":[0.9992315,0.0000236425,0.0001984307,0.000314075,0.0001034226,0.0001289558],"domain_scores_gemma":[0.9992433,0.00006170858,0.00008206953,0.0003948544,0.0001237675,0.00009435853],"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":[0.00002030158,0.00007195152,0.00008914595,0.00002924413,0.00001752166,6.072783e-8,0.0009748531,0.00007608881,0.0263207,0.9425306,0.000289807,0.02957973],"study_design_scores_gemma":[0.001606114,0.0011414,0.0191012,0.00002871392,0.00016731,0.0001741717,0.0006123923,0.06689513,0.2919198,0.5535499,0.06349634,0.001307496],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.3008625,0.0001129883,0.6979373,0.0003058091,0.00004704614,0.0005326612,0.00002132823,0.00008961982,0.00009071843],"genre_scores_gemma":[0.9606952,0.00003356503,0.03849987,0.0001159579,0.0002085592,0.000361934,0.00001964655,0.000008913051,0.0000563618],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.6598327,"threshold_uncertainty_score":0.3960749,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0152494029441316,"score_gpt":0.2670228281900699,"score_spread":0.2517734252459383,"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."}}