{"id":"W2146380740","doi":"10.1016/j.jco.2005.04.002","title":"The shifted number system for fast linear algebra on integer matrices","year":2005,"lang":"en","type":"article","venue":"Journal of Complexity","topic":"Polynomial and algebraic computation","field":"Computer Science","cited_by":76,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Waterloo","funders":"","keywords":"Integer (computer science); Mathematics; Integer matrix; Matrix multiplication; Dimension (graph theory); Unimodular matrix; Discrete mathematics; Matrix (chemical analysis); Multiplication (music); Polynomial; Computation; Integer points in convex polyhedra; Algebra over a field; Combinatorics; Integer programming; Algorithm; Pure mathematics; Symmetric matrix; Branch and price; Eigenvalues and eigenvectors; Computer science; Nonnegative matrix","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":[0.000679403,0.0001139189,0.0002020679,0.00006158184,0.0002714001,0.0001984336,0.0008393648,0.00003511366,0.000007489946],"category_scores_gemma":[0.0000567549,0.00006916034,0.0001785376,0.0001908769,0.00005126463,0.0003626799,0.00008809284,0.000188378,0.00006153219],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001050699,"about_ca_system_score_gemma":0.00008206564,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000006049601,"about_ca_topic_score_gemma":0.00001001818,"domain_scores_codex":[0.9987738,0.00008410811,0.0004840432,0.0001251815,0.0003243946,0.0002085186],"domain_scores_gemma":[0.998553,0.0004465822,0.000456913,0.0002105595,0.0002353388,0.00009756946],"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":[0.0002028824,0.0001451562,0.0001246744,0.00003629034,0.0000844903,0.000008735936,0.0005474394,0.0005324288,0.00006941015,0.8236914,0.007628533,0.1669286],"study_design_scores_gemma":[0.002953392,0.0008684896,0.01145696,0.0003458916,0.00005340999,0.0006289849,0.0002488953,0.6435671,0.004161631,0.1395139,0.1956542,0.0005471875],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.287492,0.0001674404,0.6977208,0.01122063,0.00145888,0.0002111615,0.000005529434,0.00007853303,0.001645049],"genre_scores_gemma":[0.9444093,0.000005957521,0.05401525,0.0002944663,0.001146967,0.000002932241,5.876032e-7,0.000007029344,0.0001174999],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.6841775,"threshold_uncertainty_score":0.2820277,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02981440093235344,"score_gpt":0.2839099586143147,"score_spread":0.2540955576819612,"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."}}