{"id":"W3016943584","doi":"10.1016/j.jalgebra.2020.04.014","title":"Algorithms for computing bases for 3-variable homogeneous integer-valued polynomials","year":2020,"lang":"en","type":"article","venue":"Journal of Algebra","topic":"Polynomial and algebraic computation","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"","funders":"Dalhousie University","keywords":"Degree (music); Homogeneous; Integer (computer science); Mathematics; Variable (mathematics); Polynomial; Homogeneous polynomial; Connection (principal bundle); Range (aeronautics); Combinatorics; Discrete mathematics; Mathematical analysis; Computer science; Physics; Geometry; Matrix polynomial","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0006540293,0.0001845366,0.0004527842,0.0001224298,0.0001806471,0.0002343699,0.0008571055,0.00006821128,0.00001027528],"category_scores_gemma":[0.0005438154,0.0001605279,0.0003082544,0.0003080889,0.00002884846,0.0004670098,0.0001496567,0.0001482606,0.000005459301],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00005634427,"about_ca_system_score_gemma":0.0003313113,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000006369231,"about_ca_topic_score_gemma":4.51208e-7,"domain_scores_codex":[0.9983092,0.0000584234,0.0007545775,0.0002747858,0.0002571238,0.0003458968],"domain_scores_gemma":[0.9978938,0.0006573551,0.0006392403,0.0001585417,0.0003889556,0.0002621126],"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":[0.0008138541,0.0004834315,0.0001116889,0.0004185171,0.0007000936,0.00008809431,0.004550275,0.0200591,0.03277223,0.154271,0.1075766,0.6781551],"study_design_scores_gemma":[0.003145289,0.002064213,0.00009698386,0.000121824,0.00008444909,0.0002418193,0.00009937853,0.9084331,0.02245697,0.03097979,0.03183294,0.0004431771],"study_design_candidate":"simulation_or_modeling","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.02083244,0.000345977,0.9714886,0.00572553,0.001145459,0.0003276551,0.00001638511,0.00006058415,0.00005738844],"genre_scores_gemma":[0.3984988,0.000006845177,0.5953559,0.003768851,0.002286023,0.00000551312,0.000004694862,0.00002444207,0.00004898424],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.8883741,"threshold_uncertainty_score":0.6546138,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03669622431571282,"score_gpt":0.2770379393879311,"score_spread":0.2403417150722183,"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."}}