{"id":"W2754485517","doi":"10.2168/lmcs-8(1:25)2012","title":"Formal Theories for Linear Algebra","year":2012,"lang":"en","type":"article","venue":"Logical Methods in Computer Science","topic":"Polynomial and algebraic computation","field":"Computer Science","cited_by":30,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto; University of New Brunswick","funders":"","keywords":"Algebra over a field; Mathematics; Linear algebra; Universal algebra; Discrete mathematics; Pure mathematics","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":[0.003402053,0.001226515,0.0007670248,0.003264357,0.002063345,0.005162799,0.001817549,0.00141267,0.0109851],"category_scores_gemma":[0.003104842,0.0005692627,0.001691082,0.002870939,0.00709361,0.01013415,0.00258447,0.006239254,0.002824628],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.003872986,"about_ca_system_score_gemma":0.001469346,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001878542,"about_ca_topic_score_gemma":0.00180317,"domain_scores_codex":[0.9982026,0.0006756272,0.000133757,0.0001790406,0.0006167793,0.0001922719],"domain_scores_gemma":[0.9982865,0.0007588759,0.0001376883,0.0003173352,0.0003847997,0.0001147559],"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":[0.000001212757,0.000003686829,0.00001472105,0.00001312768,0.000001516322,0.000007772749,0.00006652441,0.0001037103,0.00005496024,0.9977446,0.0008048288,0.001183422],"study_design_scores_gemma":[0.000007377224,0.000003875974,0.00002606489,0.00001593973,0.000002254819,0.00002298907,0.00004125499,0.0009324615,0.00008550058,0.9814768,0.01738151,0.000004016155],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.011436,0.0118178,0.7854148,0.01354112,0.001555879,0.000192406,0.001363572,0.001390603,0.1732878],"genre_scores_gemma":[0.5267086,0.009367802,0.3898097,0.006128896,0.004161322,0.001141033,0.003093143,0.0005617709,0.0590277],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.0109851,"threshold_uncertainty_score":0.03674883,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06168111032428622,"score_gpt":0.3851971348274723,"score_spread":0.3235160245031861,"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."}}