{"id":"W4296297618","doi":"10.1155/2022/7049980","title":"Computing Independent Variable Sets for Polynomial Ideals","year":2022,"lang":"en","type":"article","venue":"Journal of Mathematics","topic":"Polynomial and algebraic computation","field":"Computer Science","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"Science North","funders":"Fundamental Research Funds for the Central Universities","keywords":"Mathematics; Lexicographical order; Polynomial; Ideal (ethics); Gröbner basis; Variable (mathematics); Computation; Field (mathematics); Variables; Algorithm; Discrete mathematics; Combinatorics; Pure mathematics; Mathematical analysis","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":[0.001050645,0.0005642613,0.0008309488,0.001775397,0.001483803,0.002063941,0.001194494,0.0006539536,0.003216015],"category_scores_gemma":[0.004135354,0.0004618915,0.001398783,0.001572315,0.001402615,0.003306335,0.002439884,0.001888652,0.0009993655],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001163825,"about_ca_system_score_gemma":0.00149475,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001104088,"about_ca_topic_score_gemma":0.001523607,"domain_scores_codex":[0.9986532,0.0002852646,0.0000885377,0.0002986134,0.0004617134,0.000212628],"domain_scores_gemma":[0.9984745,0.0008314805,0.0001010547,0.0002712308,0.0002524058,0.00006927306],"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":[0.0002737874,0.000129804,0.002253522,0.0003045019,0.00006427024,0.0002214754,0.0006322687,0.06672337,0.01293316,0.6790221,0.005587715,0.231854],"study_design_scores_gemma":[0.00003177941,0.00005271033,0.0004679722,0.00003401966,0.00003497409,0.000127986,0.0001222905,0.2781113,0.01302675,0.7005598,0.007396062,0.00003429796],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.05854542,0.0002291632,0.9341331,0.000243726,0.00005167502,0.00006968185,0.0001810253,0.0007756996,0.005770448],"genre_scores_gemma":[0.3319082,0.0002724384,0.661417,0.0001128471,0.0000994321,0.0001885379,0.0009913152,0.0002535779,0.004756662],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.003216015,"threshold_uncertainty_score":0.0107587,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02308473907334851,"score_gpt":0.2726818659702463,"score_spread":0.2495971268968978,"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."}}