{"id":"W4396218073","doi":"10.1016/j.jalgebra.2024.04.018","title":"Newton iteration for lexicographic Gröbner bases in two variables","year":2024,"lang":"en","type":"article","venue":"Journal of Algebra","topic":"Polynomial and algebraic computation","field":"Computer Science","cited_by":5,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Waterloo","funders":"","keywords":"Mathematics; Lexicographical order; Newton's method; Applied mathematics; Algebra over a field; Calculus (dental); Pure mathematics; Combinatorics; Nonlinear system","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":[0.0005263814,0.00008863107,0.0001451368,0.0004841482,0.00004050517,0.0003733255,0.0002809956,0.00002571913,0.00001023285],"category_scores_gemma":[0.00005475078,0.00007061807,0.0001237813,0.0005311383,0.00001409099,0.00123641,0.00003839173,0.0001284928,0.000005042208],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003677248,"about_ca_system_score_gemma":0.0001444191,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000016542,"about_ca_topic_score_gemma":0.00001802413,"domain_scores_codex":[0.9991147,0.00003669766,0.0003786713,0.0001454655,0.0001755279,0.0001489371],"domain_scores_gemma":[0.9994059,0.0002504314,0.0001142504,0.00009488736,0.00008651605,0.0000480045],"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":[0.00005549515,0.0001396851,0.0006235561,0.0001059011,0.00007154486,0.0001107926,0.0009963657,0.003222919,0.007008041,0.7633635,0.01144364,0.2128586],"study_design_scores_gemma":[0.001253779,0.0003897312,0.003475777,0.0004543153,0.0000310422,0.000257704,0.00002145749,0.4334255,0.003804335,0.5243336,0.03228068,0.0002720564],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1988491,0.001177028,0.7927914,0.005065727,0.001777497,0.0001117048,0.000001572716,0.00004619891,0.0001798172],"genre_scores_gemma":[0.9782598,0.00002392247,0.02056894,0.0004233455,0.0006181,0.000004356304,0.000001691444,0.000007783043,0.00009204824],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.7794107,"threshold_uncertainty_score":0.3599987,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01431333325438504,"score_gpt":0.283058965541225,"score_spread":0.26874563228684,"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."}}