{"id":"W3081736912","doi":"10.1016/j.jsc.2022.10.002","title":"Computing critical points for invariant algebraic systems","year":2022,"lang":"en","type":"article","venue":"Journal of Symbolic Computation","topic":"Polynomial and algebraic computation","field":"Computer Science","cited_by":11,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Waterloo","funders":"H2020 Marie Skłodowska-Curie Actions; Agence Nationale de la Recherche; H2020 Fast Track to Innovation; Horizon 2020; Natural Sciences and Engineering Research Council of Canada; European Commission","keywords":"Mathematics; Combinatorics; Invariant (physics); Polynomial; Jacobian matrix and determinant; Discrete mathematics; Algebraic number; Finite field; Invariant polynomial; Exponential function; Matrix polynomial; Mathematical analysis; Mathematical 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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.000718577,0.0008557526,0.0009953585,0.0041558,0.001077634,0.002164252,0.001063728,0.0007021978,0.008152959],"category_scores_gemma":[0.007025435,0.0005687358,0.000616158,0.001329703,0.002126389,0.003112065,0.001827691,0.001450444,0.0008428536],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00123342,"about_ca_system_score_gemma":0.0007747163,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001782726,"about_ca_topic_score_gemma":0.002874159,"domain_scores_codex":[0.9994643,0.00009167855,0.0000340794,0.0001073291,0.0001744653,0.0001281533],"domain_scores_gemma":[0.996462,0.002288726,0.0002834136,0.0002469128,0.0004945666,0.0002244084],"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":[0.001249711,0.0003838716,0.01560294,0.000721573,0.0001747768,0.0008630216,0.001490514,0.1101189,0.02021534,0.6896685,0.008215861,0.151295],"study_design_scores_gemma":[0.00009377921,0.0001344456,0.001193439,0.00006910507,0.00005764691,0.00009051936,0.0003762705,0.2276601,0.01035894,0.7581375,0.001798616,0.00002958259],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7020085,0.0004603543,0.278964,0.0002928697,0.00008693573,0.0001601862,0.0004408402,0.001274156,0.0163122],"genre_scores_gemma":[0.9585674,0.0001308906,0.03873163,0.00003345331,0.00003220304,0.00003864527,0.000464319,0.0001969903,0.001804541],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.008152959,"threshold_uncertainty_score":0.02727437,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02115593940969856,"score_gpt":0.2819425198729099,"score_spread":0.2607865804632113,"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."}}