{"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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0004573739,0.0005821474,0.0004934504,0.0004902782,0.0003459382,0.001154923,0.000444309,0.0003758821,0.005527545],"category_scores_gemma":[0.001846146,0.000179489,0.0006423144,0.0007683816,0.0008040649,0.0008555957,0.001225749,0.0007791254,0.00138968],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0002773162,"about_ca_system_score_gemma":0.0004231314,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0008370577,"about_ca_topic_score_gemma":0.0006664282,"domain_scores_codex":[0.99964,0.0001963283,0.00001818387,0.00003798151,0.00008669249,0.00002085813],"domain_scores_gemma":[0.9996272,0.0001526986,0.00005199229,0.00007253815,0.00007750774,0.000018096],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.00009545375,0.00004882727,0.0006331841,0.0002059209,0.00003069856,0.000640431,0.0004594532,0.1613029,0.01121795,0.7162519,0.006119309,0.1029939],"study_design_scores_gemma":[0.00006799796,0.00009870291,0.0003663291,0.00003803301,0.00002150113,0.0003922966,0.0001070067,0.7234516,0.006585474,0.1897964,0.07904403,0.0000306154],"study_design_candidate":"simulation_or_modeling","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.02270149,0.0004701636,0.9624861,0.0003403144,0.0001930444,0.00004370405,0.00009419831,0.0005059591,0.01316512],"genre_scores_gemma":[0.3596956,0.001308783,0.6253384,0.0001315939,0.0002153348,0.0002428772,0.0002333416,0.0003271246,0.0125069],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.005527545,"threshold_uncertainty_score":0.01849151,"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."}}