MétaCan
Menu
Back to cohort
Record W2592118566 · doi:10.3929/ethz-a-006654232

On lattice reduction for polynomial matrices

2000· article· en· W2592118566 on OpenAlex
Thom Mulders, Arne Storjohann

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.

Bibliographic record

VenueRepository for Publications and Research Data (ETH Zurich) · 2000
Typearticle
Languageen
FieldComputer Science
TopicPolynomial and algebraic computation
Canadian institutionsUniversity of Waterloo
Fundersnot available
KeywordsUnimodular matrixMathematicsLattice reductionDiophantine equationMatrix polynomialSquare-free polynomialMonic polynomialComputationLattice (music)Reduction (mathematics)PolynomialFactorizationDiscrete mathematicsMatrix similarityCombinatoricsOrthogonal transformationAlgorithmMathematical analysis

Abstract

fetched live from OpenAlex

A simple algorithm for transformation to weak Popov form | essentially lattice reduction for polynomial matrices | is described and analyzed. The algorithm is adapted and applied to various tasks involving polynomial matrices: rank prole and determinant computation; unimodular triangular factorization; transformation to Hermite and Popov canonical form; rational and diophantine linear system solving; short vector computation.

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

Full frame distilled prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.

metaresearch head score (Codex)0.001
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Not applicable · Consensus signal: Not applicable
GenreCandidate signal: Empirical · Consensus signal: none
Teacher disagreement score0.557
Threshold uncertainty score0.884

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.001
Science and technology studies0.0010.000
Scholarly communication0.0010.001
Open science0.0010.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0000.000

Machine scores (provisional)

The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.

Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.

Opus teacher head0.091
GPT teacher head0.372
Teacher spread0.281 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it