{"id":"W2342906401","doi":"10.1080/00927872.2015.1057828","title":"On Linear Dependence Over Complete Differential Algebraic Varieties","year":2015,"lang":"en","type":"article","venue":"Communications in Algebra","topic":"Polynomial and algebraic computation","field":"Computer Science","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"McMaster University","funders":"University of Waterloo; American Mathematical Society","keywords":"Mathematics; Variety (cybernetics); Completeness (order theory); Differential (mechanical device); Algebraic number; Projective space; Differential algebraic geometry; Projective variety; Linear differential equation; Differential algebra; Pure mathematics; Algebra over a field; Projective test; Differential equation; Algebraic variety; Differential algebraic equation; Mathematical analysis; Statistics; Physics","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":[0.0003501577,0.0001980215,0.0002235439,0.0002572164,0.0002003028,0.0001700983,0.003393458,0.0000862428,0.00002843508],"category_scores_gemma":[0.0002059205,0.0001956678,0.0000700599,0.0006360406,0.0001806464,0.0004896146,0.001525594,0.0004046134,0.000283721],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000129177,"about_ca_system_score_gemma":0.0001629497,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001245403,"about_ca_topic_score_gemma":0.0001229442,"domain_scores_codex":[0.9982523,0.0002916498,0.0003965196,0.0003728787,0.000377655,0.0003090538],"domain_scores_gemma":[0.9967355,0.0004973742,0.0001275413,0.002377312,0.0001007543,0.0001615603],"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":[0.00001451398,0.0002546217,0.0005505043,0.000004548884,0.00001324105,0.000003898576,0.00108846,0.0003179543,0.0001257609,0.9800357,0.001373308,0.01621755],"study_design_scores_gemma":[0.001584825,0.0002086404,0.02225726,0.00006957993,0.000009612812,0.00001734716,0.0000649135,0.4202672,0.0002755052,0.5468053,0.007896925,0.0005429946],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.3500997,0.0008300265,0.6263189,0.00866494,0.00125893,0.0005904315,0.00001456564,0.0006465333,0.01157602],"genre_scores_gemma":[0.9795533,0.00003756096,0.01942903,0.0006834751,0.00005534251,0.00004586671,0.00003047039,0.00001363274,0.0001512693],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.6294537,"threshold_uncertainty_score":0.7979103,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06526809990563727,"score_gpt":0.3032395176261505,"score_spread":0.2379714177205133,"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."}}