{"id":"W1991687574","doi":"10.1002/cae.20318","title":"Computer facilitated generalized coordinate transformations of partial differential equations with engineering applications","year":2009,"lang":"en","type":"article","venue":"Computer Applications in Engineering Education","topic":"Modeling and Simulation Systems","field":"Computer Science","cited_by":3,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"","keywords":"Maple; Coordinate system; Elliptic coordinate system; Cartesian coordinate system; Ellipsoidal coordinates; Partial differential equation; Polar coordinate system; Computer science; Partial derivative; Coordinate descent; Spherical coordinate system; Algebraic number; Applied mathematics; Algebra over a field; Mathematics; Algorithm; Mathematical analysis; Pure mathematics; Geometry; Artificial intelligence","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":[0.0001548561,0.0002384561,0.0002864073,0.0005326147,0.000103009,0.0001094358,0.0005425129,0.00009002149,0.000004058719],"category_scores_gemma":[0.000005355771,0.0002411413,0.00007464538,0.001156261,0.00001789474,0.0004097029,0.00003145508,0.0001701754,0.000009918039],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000111326,"about_ca_system_score_gemma":0.0001400391,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001837916,"about_ca_topic_score_gemma":0.000001350667,"domain_scores_codex":[0.9983791,0.00003379351,0.0006657234,0.0004088431,0.0002485535,0.0002640545],"domain_scores_gemma":[0.9986815,0.0001340179,0.0001414333,0.0006811166,0.0002506026,0.0001113406],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"simulation_or_modeling","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.000002363297,0.000275853,0.00009386575,0.00007246144,0.00001738294,9.099467e-8,0.0008167402,0.883156,0.0005761186,0.09461508,0.00004816854,0.02032589],"study_design_scores_gemma":[0.0003934304,0.00004954723,0.002638173,0.000067844,0.00001220786,0.000004397134,0.000009972471,0.9937584,0.0003424478,0.0001933408,0.002278783,0.0002514908],"study_design_candidate":"simulation_or_modeling","study_design_consensus":"simulation_or_modeling","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.01271531,0.00008796158,0.9854065,0.0001941676,0.0001989341,0.00103376,0.00001046935,0.0003056447,0.0000472841],"genre_scores_gemma":[0.8213173,0.000005835924,0.1776641,0.00002748514,0.0001747787,0.0006441618,0.0001319536,0.00001263691,0.00002169065],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.808602,"threshold_uncertainty_score":0.9833456,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01140843661337563,"score_gpt":0.2376179583096039,"score_spread":0.2262095216962282,"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."}}