MétaCan
Menu
Back to cohort
Record W2115982610 · doi:10.1145/1993886.1993913

Computing hermite forms of polynomial matrices

2011· article· en· W2115982610 on OpenAlex
Somit Gupta, 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

Venuenot available
Typearticle
Languageen
FieldComputer Science
TopicPolynomial and algebraic computation
Canadian institutionsUniversity of Waterloo
Fundersnot available
KeywordsHermite polynomialsInvertible matrixDegree (music)MathematicsDimension (graph theory)Matrix (chemical analysis)Polynomial matrixPolynomialField (mathematics)Las vegasDegree of a polynomialCombinatoricsMatrix polynomialDiscrete mathematicsAlgorithmPure mathematicsMathematical analysisPhysics

Abstract

fetched live from OpenAlex

This paper presents a new algorithm for computing the Hermite form of a polynomial matrix. Given a nonsingular n x n matrix A filled with degree d polynomials with coefficients from a field, the algorithm computes the Hermite form of A using an expected number of (n3d)1+o(1) field operations. This is the first algorithm that is both softly linear in the degree d and softly cubic in the dimension n. The algorithm is randomized of the Las Vegas type.

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)0.000
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: Other design · Consensus signal: none
GenreCandidate signal: Empirical · Consensus signal: none
Teacher disagreement score0.674
Threshold uncertainty score0.239

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0000.000
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 head0.021
GPT teacher head0.229
Teacher spread0.208 · 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

Quick stats

Citations10
Published2011
Admission routes1
Has abstractyes

Explore more

Same topicPolynomial and algebraic computationFrench-language works237,207