{"id":"W2807401712","doi":"10.5539/jmr.v10n4p49","title":"Reproduction of Fuchs Relation for the Group $S_4^{SL_2}$ by Using Groebner Bases","year":2018,"lang":"en","type":"article","venue":"Journal of Mathematics Research","topic":"Polynomial and algebraic computation","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Mathematics; Invariant (physics); Gröbner basis; Pure mathematics; Group (periodic table); Galois group; Invariant theory; Polynomial; Algebra over a field; Order (exchange); Relation (database); Combinatorics; Mathematical analysis; Mathematical physics","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"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":[0.004840699,0.00006150686,0.0001455689,0.0001935847,0.0002392232,0.00009346465,0.0005334355,0.00003708287,0.000009613945],"category_scores_gemma":[0.0009665845,0.00003899129,0.00008190121,0.0004115524,0.0001323592,0.0004206692,0.0001180233,0.0001843247,0.000003834441],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00006129246,"about_ca_system_score_gemma":0.00009058995,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001559843,"about_ca_topic_score_gemma":0.000002046952,"domain_scores_codex":[0.9983943,0.0001225643,0.0004828803,0.0001326433,0.0006901152,0.0001774669],"domain_scores_gemma":[0.9972906,0.001017262,0.0004099997,0.0003250537,0.0009107491,0.00004634623],"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":[0.0002685884,0.001618495,0.0002805098,0.0007028138,0.0003405954,0.000007705064,0.01275754,0.001646709,0.3262903,0.1879152,0.05657741,0.4115941],"study_design_scores_gemma":[0.0008057732,0.001169974,0.0004289453,0.0002568738,0.00003472063,0.0001862607,0.0005878002,0.7954867,0.06558806,0.128303,0.007006016,0.0001457959],"study_design_candidate":"simulation_or_modeling","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1505494,0.0002525587,0.8471192,0.001410413,0.000339976,0.0002087006,0.000001257123,0.000006724488,0.0001118307],"genre_scores_gemma":[0.8903206,0.00003120361,0.1087304,0.00002079743,0.0006978071,0.000004095935,5.213102e-7,0.000009754994,0.0001848646],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.7938401,"threshold_uncertainty_score":0.1839935,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1485802392700331,"score_gpt":0.3987465240119296,"score_spread":0.2501662847418964,"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."}}