{"id":"W2126797173","doi":"10.1016/j.bulsci.2004.04.001","title":"Polynomial differential systems having a given Darbouxian first integral","year":2004,"lang":"en","type":"article","venue":"Bulletin des Sciences Mathématiques","topic":"Advanced Differential Equations and Dynamical Systems","field":"Mathematics","cited_by":14,"is_retracted":false,"has_abstract":false,"ca_institutions":"Toronto Metropolitan University","funders":"","keywords":"Mathematics; Polynomial; Matrix polynomial; Monic polynomial; Invariant (physics); Symmetric polynomial; Algebraic function; Differential (mechanical device); Homogeneous polynomial; Inverse; Vector-valued function; Algebraic number; Pure mathematics; Mathematical analysis; Physics; Geometry","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":[0.0005674671,0.0006805485,0.001455381,0.002116432,0.002272442,0.003038598,0.0008369252,0.001497216,0.005900923],"category_scores_gemma":[0.002228273,0.0003104767,0.0008824029,0.001218521,0.00204877,0.002658938,0.001749192,0.002404169,0.000680615],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002493698,"about_ca_system_score_gemma":0.001086013,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001163825,"about_ca_topic_score_gemma":0.0007774582,"domain_scores_codex":[0.9996099,0.00005476061,0.00001495451,0.00007995931,0.0001293623,0.0001111103],"domain_scores_gemma":[0.999222,0.000202194,0.0001087101,0.00006082195,0.0001911671,0.000214947],"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":[0.00003126421,0.00001681153,0.00009624875,0.0000268732,0.000008768578,0.00007758338,0.0001125936,0.001806502,0.001360293,0.9935406,0.0004526901,0.002469758],"study_design_scores_gemma":[0.00004015549,0.00005586496,0.0003075968,0.00001583716,0.00001944821,0.0003781674,0.0001106129,0.04148366,0.001909815,0.9508119,0.004833379,0.00003365692],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.4786765,0.001851768,0.3570027,0.00344366,0.0008945058,0.0001375529,0.0005542467,0.0005825442,0.1568565],"genre_scores_gemma":[0.9523915,0.000615186,0.01908148,0.0001975677,0.0003027831,0.00004289547,0.0001443005,0.0001034172,0.02712103],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.005900923,"threshold_uncertainty_score":0.01974052,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05666801024993984,"score_gpt":0.3163539485121709,"score_spread":0.2596859382622311,"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."}}